Methods of titrimetric analysis examples. Analytical chemistry

Introduction

The laboratory workshop is carried out after studying the theoretical course "Analytical Chemistry and FHMA" and serves to consolidate and deepen the acquired knowledge.

The task of quantitative analysis is to determine the amount (content) of elements (ions), radicals, functional groups, compounds or phases in the analyzed object. This course covers the basic methods of titrimetric (volumetric) analysis, titration methods and their practical application.

Before starting the laboratory workshop, students are instructed in safety precautions. Before performing each work, the student must pass a colloquium on the sections indicated by the teacher, as well as on the methodology for conducting the analysis. For this you need:

1) repeat the relevant section of the course;

2) get acquainted in detail with the methodology of the work;

3) compose the equations of chemical reactions underlying the ongoing chemical analysis;

4) to study the features of the analysis in terms of safety.

Based on the results of the work, students draw up a report, which should indicate:

· job title;

· goal of the work;

· theoretical foundations of the method: the essence of the method, the basic equation, calculations and construction of titration curves, the choice of indicator;

reagents and equipment used in the course of the work;

analysis technique:

Preparation of primary standards;

Preparation and standardization of the working solution;

Determination of the content of the test substance in the solution;

experimental data;

· statistical processing of analysis results;

· findings.

TITRIMETRIC METHODS OF ANALYSIS

Titrimetric method of analysis is based on measuring the volume of a reagent of exactly known concentration (titrant) spent on a chemical reaction with the substance being determined.

The determination procedure (titration) consists in the fact that a titrant is added dropwise from a burette to a precisely known volume of a solution of an analyte with an unknown concentration until the equivalence point is reached.

where X– determined substance; R- titrant, P is the reaction product.

Equivalence point (i.e.)- this is the theoretical state of the solution, occurring at the time of adding an equivalent amount of titrant R to the analyte X. In practice, the titrant is added to the substance to be determined until the end point of the titration (k.t.t.) is reached, which is understood as a visual indication of the equivalence point, the moment of color change of the indicator added to the solution. In addition to visual indication, the equivalence point can be registered by instrumental methods. In this case, the titration end point (c.t.t.) is understood as the moment of a sharp change in the physical quantity measured during the titration process (current strength, potential, electrical conductivity, etc.).

The following types of chemical reactions are used in the titrimetric method of analysis: neutralization reactions, redox reactions, precipitation reactions, and complex formation reactions.

Depending on the type of chemical reaction used, the following are distinguished: methods of titrimetric analysis:

– acid-base titration;

– precipitation titration;

– complexometric titration or complexometry;

– redox titration or redox titration.

The reactions used in the titrimetric method of analysis are as follows: requirements:

The reaction must proceed in stoichiometric ratios, without side reactions;

the reaction should proceed almost irreversibly (≥ 99.9%), the equilibrium constant of the reaction K p > 10 6, the precipitates formed should have solubility S < 10 -5 моль/дм 3 , а образующиеся комплексы – К уст > 10 -6 ;

The reaction must proceed at a sufficiently high rate;

The reaction must proceed at room temperature;

The equivalence point must be fixed clearly and reliably in some way.

Titration methods

In any titrimetric analysis method, there are several titration methods. Distinguish forward titration, back titration and substitution titration .

direct titration– the titrant is added dropwise to the analyte solution until the equivalence point is reached.

Titration scheme: X+R=P.

The law of equivalents for direct titration:

C (1/ z) X V X = C (1/ z) R V R . (2)

The amount (mass) of the analyte contained in the test solution is calculated using the law of equivalents (for direct titration)

m X = C (1/z)R V R M (1/z) X٠10 -3 , (3)

where C (1/z) R– molar concentration of titrant equivalent, mol/dm 3 ;

V R is the titrant volume, cm3;

M( 1/ z) X is the molar mass of the equivalent of the analyte;

C (1/z) X– molar concentration of the analyte equivalent, mol/dm 3 ;

V X is the volume of the analyte, cm3.

Back titration- two titrants are used. At first
the exact volume of the first titrant is added to the analyzed solution ( R1) taken in excess. The rest of the unreacted titrant R 1 is titrated with the second titrant ( R2). Amount of titrant R1, spent
on interaction with the analyzed substance ( X) is determined by the difference between the added volume of titrant R1 (V 1) and titrant volume R2 (V 2) of the titrant residue spent on titration R1.

Titration scheme: X + R1 fixed excess = P1 (R1 remainder).

R1 remainder + R2 = P2.

When using back titration, the law of equivalents is written as follows:

The mass of the analyte in the case of back titration is calculated by the formula

The back titration method is used in cases where it is impossible to select a suitable indicator for a direct reaction or it proceeds with kinetic difficulties (low chemical reaction rate).

Substitution titration (indirect titration)- used in cases where direct or back titration of the analyte is impossible or difficult, or there is no suitable indicator.

To the analyte X add any reagent BUT in excess, upon interaction with which an equivalent amount of a substance is released R. Then the reaction product R titrated with a suitable titrant R.

Titration scheme: X + BUT excess = P1.

P1 + R = P2.

The law of equivalents for substitution titration is written as follows:

Since the number of equivalents of the analyte X and reaction product R are the same, the calculation of the mass of the analyte in the case of indirect titration is calculated by the formula

m X = C (1/z) R V R M (1/z) X٠10 -3 . (7)

Reagents

1. Succinic acid H 2 C 4 H 4 O 4 (chemically pure) - primary standard.

2. A solution of sodium hydroxide NaOH with a molar concentration
~2.5 mol / dm 3

3. H 2 O distilled.

Equipment students describe themselves.

Work progress:

1. Preparation of the primary standard of succinic acid HOOCCH 2 CH 2 COOH.

Succinic acid is prepared with a volume of 200.00 cm 3 with a molar equivalent concentration mol / dm 3.

g/mol.

Reaction equation:

Taking a sample (weighing):

Sample weight

Hinge quantitatively transferred to a volumetric flask cm 3), add 50 - 70 cm 3 of distilled water, mix until the succinic acid is completely dissolved, bring to the mark with distilled water
and mix thoroughly.

count
according to the formula

Reagents

1. Sodium carbonate Na 2 CO 3 (chemically pure) - primary standard.

2. H 2 O distilled.

3. Hydrochloric acid HCl concentration 1:1 (r=1.095 g/cm3).

4. Acid-base indicator (selected from the titration curve).

5. Mixed indicator - methyl orange and methylene blue.

Work progress:

1. Preparation of the primary standard of sodium carbonate (Na 2 CO 3).

A solution of sodium carbonate is prepared with a volume of 200.00 cm 3 with a molar equivalent concentration mol / dm 3.

Calculation of the mass of the sample, g: (the mass is taken with an accuracy of the fourth decimal place).

Reaction equations:

1) Na 2 CO 3 + HCl = NaHCO 3 + NaCl

2) NaHCO 3 + HCl \u003d NaCl + H 2 O + CO 2

_____________________________________

Na 2 CO 3 + 2HCl \u003d 2NaCl + H 2 O + CO 2

H 2 CO 3 is a weak acid (K a1= 10 -6.35, K a2 = 10 -10,32).

Taking a sample (weighing):

Weight of watch glass (glass)

Weight of watch glass (glass) with a hinge

Sample weight

Hinge quantitatively transferred to a volumetric flask cm 3), add 50 - 70 cm 3 of distilled water, mix until sodium carbonate is completely dissolved, bring to the mark with distilled water
and mix thoroughly.

The actual concentration of the primary standard count
according to the formula

2. Preparation and standardization of the titrant (HCl solution)

A solution of hydrochloric acid is prepared with a volume of approximately 500 cm 3
with a molar equivalent concentration of approximately 0.05÷0.06 mol / dm 3)

Titrant - a solution of hydrochloric acid with an approximate concentration of 0.05 mol / dm 3 is prepared from hydrochloric acid diluted 1: 1 (r = 1.095 g / cm 3).

Solution standardization HCl is carried out according to the primary standard Na 2 CO 3 by direct titration, pipetting method.

The indicator is chosen according to the titration curve of sodium carbonate with hydrochloric acid (Fig. 4).

Rice. 4. Titration curve of 100.00 cm 3 Na 2 CO 3 solution with With\u003d 0.1000 mol / dm 3 with a solution of HCl with C 1/z\u003d 0.1000 mol / dm 3

When titrating to the second equivalence point, use the methyl orange indicator, 0.1% aqueous solution (pT = 4.0). Color change from yellow to orange (tea rose color). Transition interval
(pH = 3.1 - 4.4).

Scheme 3. Standardization of HCl solution

In a 250 cm3 conical titration flask, place an aliquot of 25.00 cm3 of Na 2 CO 3 standard solution (with a pipette), add 2–3 drops of methyl orange, dilute with water to 50–75 cm3, and titrate with hydrochloric acid until the color changes. from yellow to the color of "tea rose" from one drop of titrant. Titration is carried out in the presence of a "witness" (the original solution of Na 2 CO 3 with an indicator). The results of the titration are entered in table. 4. The concentration of hydrochloric acid is determined by the law of equivalents: .

Table 4

Results of standardization of hydrochloric acid solution

Tasks

1. Formulate the concept of equivalent in acid-base reactions. Calculate the equivalents of soda and phosphoric acid in the following reactions:

Na 2 CO 3 + HCl \u003d NaHCO 3 + NaCl

Na 2 CO 3 + 2HCl \u003d 2NaCl + CO 2 + H 2 O

H 3 PO 4 + NaOH = NaH 2 PO 4 + H 2 O

H 3 PO 4 + 2NaOH \u003d Na 2 HPO 4 + H 2 O

H 3 PO 4 + 3NaOH \u003d Na 3 PO 4 + 3H 2 O

2. Write the reaction equations between hydrochloric acid, sulfuric acid, sodium hydroxide, aluminum hydroxide, sodium carbonate, potassium bicarbonate and calculate the equivalent mass of these substances.

3. Plot a titration curve for 100.00 cm 3 of hydrochloric acid with a molar concentration equivalent of 0.1 mol/dm 3 with sodium hydroxide with a molar concentration equivalent of 0.1 mol/dm 3 . Select Possible Indicators

4. Plot a titration curve for 100.00 cm 3 of acrylic acid (CH 2 =CHCOOH, pK a= 4.26) with a molar equivalent concentration
0.1 mol / dm 3 sodium hydroxide with a molar equivalent concentration
0.1 mol / dm 3. How does the composition of a solution change during titration? Select possible indicators and calculate the indicator titration error.

5. Plot the titration curve for hydrazine (N 2 H 4 +H 2 O, pK b= 6,03)
with a molar concentration of the equivalent of 0.1 mol / dm 3 hydrochloric acid
with a molar concentration of the equivalent of 0.1 mol / dm 3. What is the similarity
and the difference between the pH calculations and the titration curve compared to the titration curve of a weak acid with an alkali? Select Possible Indicators
and calculate the indicator titration error.

6. Calculate activity coefficients and active concentrations of ions
in 0.001 M aluminum sulfate solution, 0.05 M sodium carbonate, 0.1 M potassium chloride.

7. Calculate the pH of a 0.20 M methylamine solution if its ionization in an aqueous solution is described by the equation

B + H 2 O \u003d VN + + OH -, K b\u003d 4.6 × 10 - 3, where B is the base.

8. Calculate the dissociation constant of hypochlorous acid HOCl if a 1.99 × 10 - 2 M solution has pH = 4.5.

9. Calculate the pH of a solution containing 6.1 g / mol of glycolic acid (CH 2 (OH) COOH, K a= 1.5 × 10 - 4).

10. Calculate the pH of a solution obtained by mixing 40 ml of a 0.015 M hydrochloric acid solution with:

a) 40 ml of water;

b) 20 ml of 0.02 M sodium hydroxide solution;

c) 20 ml of 0.02 M barium hydroxide solution;

d) 40 ml of 0.01 M solution of hypochlorous acid, K a=5.0 × 10 - 8 .

11. Calculate the concentration of acetate ion in a solution of acetic acid
with a mass fraction of 0.1%.

12. Calculate the concentration of the ammonium ion in an ammonia solution with a mass fraction of 0.1%.

13. Calculate the mass of sodium carbonate sample required to prepare 250.00 ml of 0.5000 M solution.

14. Calculate the volume of hydrochloric acid solution with a molar equivalent concentration of 11 mol/l and the volume of water that must be taken to prepare 500 ml of 0.5 M hydrochloric acid solution.

15. 0.15 g of metallic magnesium was dissolved in 300 ml of a 0.3% solution of hydrochloric acid. Calculate the molar concentration of hydrogen, magnesium and chlorine ions in the resulting solution.

16. When mixing 25.00 ml of a sulfuric acid solution with a solution of barium chloride, 0.2917 g of barium sulfate was obtained. Determine the titer of the sulfuric acid solution.

17. Calculate the mass of calcium carbonate that has reacted
with 80.5 mmol hydrochloric acid.

18. How many grams of monobasic sodium phosphate should be added
to 25.0 ml of 0.15 M sodium hydroxide solution to obtain a solution with pH = 7? For phosphoric acid pK a1= 2.15; pK a2= 7.21; pK a3 = 12,36.

19. Titration of 1.0000 g of fuming sulfuric acid, carefully diluted with water, consumes 43.70 ml of 0.4982 M sodium hydroxide solution. It is known that fuming sulfuric acid contains sulfuric anhydride dissolved in anhydrous sulfuric acid. Calculate the mass fraction of sulfuric anhydride in fuming sulfuric acid.

20. The absolute error of volume measurement with a burette is 0.05 ml. Calculate the relative error in measuring volumes in 1; 10 and 20 ml.

21. A solution is prepared in a volumetric flask with a capacity of 500.00 ml.
from a sample of 2.5000 g of sodium carbonate. Calculate:

a) the molar concentration of the solution;

b) the molar concentration of the equivalent (½ Na 2 CO 3);

c) solution titer;

d) titer for hydrochloric acid.

22. What is the volume of a 10% sodium carbonate solution with a density
1.105 g / cm 3 you need to take for cooking:

a) 1 liter of solution with a titer of ТNa 2 CO 3 = 0.005000 g/cm 3 ;

b) 1 liter of solution with ТNa 2 CO 3 /HCl = 0.003000 g/cm 3?

23. What volume of hydrochloric acid with a mass fraction of 38.32% and a density of 1.19 g / cm 3 should be taken to prepare 1500 ml of a 0.2 M solution?

24. What volume of water must be added to 1.2 liters of 0.25 M HCl to prepare a 0.2 M solution?

25. From 100 g of technical sodium hydroxide containing 3% sodium carbonate and 7% indifferent impurities, 1 liter of solution was prepared. Calculate the molar concentration and the hydrochloric acid titer of the resulting alkaline solution, assuming that sodium carbonate is titrated to carbonic acid.

26. There is a sample that may contain NaOH, Na 2 CO 3 , NaHCO 3 or a mixture of these compounds weighing 0.2800 g. The sample was dissolved in water.
The titration of the resulting solution in the presence of phenolphthalein consumes 5.15 ml, and in the presence of methyl orange - 21.45 ml of hydrochloric acid with a molar equivalent concentration of 0.1520 mol / l. Determine the composition of the sample and the mass fractions of the components in the sample.

27. Draw a titration curve of 100.00 cm 3 of 0.1000 M ammonia solution with 0.1000 M hydrochloric acid solution, justify the choice of indicator.

28. Calculate the pH of the equivalence point, start and end of the titration of 100.00 cm 3 0.1000 M malonic acid solution (HOOCCH 2 COOH) 0.1000 M sodium hydroxide solution (pK a 1=1.38; RK a 2=5,68).

29. For the titration of 25.00 cm 3 of a solution of sodium carbonate with a molar concentration of the equivalent of 0.05123 mol / dm 3, 32.10 cm 3 of hydrochloric acid went. Calculate the molar concentration of the equivalent of hydrochloric acid.

30. How many ml of 0.1 M ammonium chloride solution must be added
to 50.00 ml of 0.1 M ammonia solution to make a buffer solution
with pH=9.3.

31. The mixture of sulfuric and phosphoric acids was transferred to a volumetric flask with a volume of 250.00 cm 3 . For titration, two samples of 20.00 cm 3 were taken, one was titrated with a solution of sodium hydroxide with a molar concentration of the equivalent
0.09940 mol / dm 3 with methyl orange indicator, and the second with phenolphthalein. The consumption of sodium hydroxide in the first case was 20.50 cm 3 and in the second 36.85 cm 3 . Determine the masses of sulfuric and phosphoric acids in the mixture.

In complexometry

Up to the equivalence point =( C M V M- C EDTA V EDTA)/( V M+ V EDTA). (21)

At the equivalence point = . (22)

After the equivalence point = . (23)

On fig. 9 shows the titration curves of calcium ion in buffer solutions with different pH values. It can be seen that the titration of Ca 2+ is possible only at pH ³ 8.

Reagents

2. H 2 O distilled.

3. Standard solution of Mg (II) with molar concentration
0.0250 mol / dm 3.

4. Ammonia buffer pH = 9.5.

5. A solution of potassium hydroxide KOH with a mass fraction of 5%.

6. Eriochrome black T, indicator mixture.

7. Calcon, indicator mixture.

Theoretical foundations of the method:

The method is based on the interaction of Ca 2+ and Mg 2+ ions with the disodium salt of ethylenediaminetetraacetic acid (Na 2 H 2 Y 2 or Na-EDTA) with the formation of stable complexes in the molar ratio M:L=1:1 in a certain pH range.

To fix the equivalence point in the determination of Ca 2+ and Mg 2+, calcon and eriochrome black T are used.

The determination of Ca 2+ is carried out at pH ≈ 12, while Mg 2+ is
in solution as a precipitate of magnesium hydroxide and is not titrated with EDTA.

Mg 2+ + 2OH - \u003d Mg (OH) 2 ↓

Ca 2+ + Y 4- "CaY 2-

At pH ≈ 10 (ammonia buffer solution), Mg 2+ and Ca 2+ are
in solution in the form of ions and with the addition of EDTA are titrated together.

Ca 2+ + HY 3- « CaY 2- + H +

Mg 2+ + HY 3- « MgY 2- + H +

To determine the volume of EDTA spent on the titration of Mg 2+,
from the total volume used to titrate the mixture at pH ≈ 10, subtract the volume used to titrate Ca 2+ at pH ≈ 12.

To create pH ≈ 12, a 5% KOH solution is used, to create
pH ≈ 10 using ammonia buffer solution (NH 3 ×H 2 O + NH 4 Cl).

Work progress:

1. Standardization of the titrant - EDTA solution (Na 2 H 2 Y)

EDTA solution is prepared with an approximate concentration of 0.025 M
from ≈ 0.05 M solution, diluting it with distilled water 2 times. For standardization of EDTA, a standard solution of MgSO 4 is used.
with a concentration of 0.02500 mol / dm 3.

Scheme 5. Standardization of titrant - EDTA solution

In a conical flask for titration with a capacity of 250 cm 3, 20.00 cm 3 of a standard solution of MgSO 4 with a concentration of 0.02500 mol / dm 3 are placed, ~ 70 cm 3 of distilled water, ~ 10 cm 3 of an ammonia buffer solution with a pH of ~ 9.5 are added - 10 and add the indicator eriochrome black T about 0.05 g
(at the tip of the spatula). In this case, the solution turns wine-red. The solution in the flask is slowly titrated with EDTA solution until the color changes from wine red to green. The results of the titration are entered in table. 6. The concentration of EDTA is determined by the law of equivalents: .

Table 6

Results of standardization of EDTA solution

2. Determination of Ca 2+ content

Titration curves Ca 2+ solution of EDTA at pH=10 and pH=12 build independently.

The solution of the problem in a volumetric flask was brought to the mark with distilled water and mixed thoroughly.

Scheme 6. Determination of Ca 2+ content in solution

An aliquot of the test solution 25.00 cm 3 containing calcium and magnesium is placed into a conical flask for titration with a capacity of 250 cm 3, ~ 60 cm 3 of water, ~ 10 cm 3 of a 5% KOH solution are added. After precipitation of an amorphous precipitate of Mg (OH) 2 ↓, the indicator calcon about 0.05 g (on the tip of a spatula) is added to the solution and slowly titrated with an EDTA solution until the color changes from pink to pale blue. Titration results ( V 1) are entered in table.7.

Table 7

experience number		EDTA volume, cm 3	Ca 2+ content in solution, g
	25,00
	25,00
	25,00
	25,00
	25,00

3. Determination of Mg 2+ content

The titration curve of Mg 2+ solution of EDTA at pH=10 build independently.

Scheme 7. Determination of Mg 2+ content in solution

An aliquot of 25.00 cm 3 of the test solution containing calcium and magnesium is placed into a conical flask for titration with a capacity of 250 cm 3, ~ 60 cm 3 of distilled water, ~ 10 cm 3 of an ammonia buffer solution with a pH of ~ 9.5–10 are added, and an indicator is added eriochrome black T approx. 0.05 g
(at the tip of the spatula). In this case, the solution turns wine-red. The solution in the flask is slowly titrated with EDTA solution until the color changes from wine red to green. Titration results ( V 2) are entered in the table. eight.

Table 8

Titration results of a solution containing calcium and magnesium

experience number	The volume of the investigated solution, cm 3	EDTA volume, V∑ , cm 3	The content of Mg 2+ in solution, g
	25,00
	25,00
	25,00
	25,00
	25,00

Reagents

1. EDTA solution with a molar concentration of ~ 0.05 mol / dm 3.

2. Standard solution of Cu(II) with a titer of 2.00×10 -3 g/dm 3 .

3. H 2 O distilled.

4. Ammonia buffer with pH ~ 8 - 8.5.

5. Murexide, indicator mixture.

Tasks

1. Calculate α 4 for EDTA at pH=5 if the EDTA ionization constants are as follows: K 1 =1.0 10 -2 , K 2 =2.1 10 -3 , K 3 =6.9 10 -7 , K 4 \u003d 5.5 10 -11.

2. Plot a titration curve for 25.00 ml of 0.020 M nickel solution with 0.010 M EDTA solution at pH=10 if the stability constant is
K NiY = 10 18.62 . Calculate p after adding 0.00; 10.00; 25.00; 40.00; 50.00 and 55.00 ml of titrant.

3. For titration 50.00 ml of a solution containing calcium ions
and magnesium, it took 13.70 ml of 0.12 M EDTA solution at pH=12 and 29.60 ml at pH=10. Express the concentrations of calcium and magnesium in the solution in mg/ml.

4. When analyzed, 0.2173 g of calcium oxide and 0.0927 g of magnesium oxide were found in 1 liter of water. Calculate what volume of 0.0500 mol/l EDTA was used for titration.

5. For titration of 25.00 ml of a standard solution containing 0.3840 g of magnesium sulfate, 21.40 ml of Trilon B solution were used. Calculate the titer of this solution by calcium carbonate and its molar concentration.

6. Based on the formation (stability) constants of metal complexonates given below, evaluate the possibility of complexometric titration of metal ions at pH = 2; 5; ten; 12.

7. When titrating a 0.01 M Ca 2+ solution with a 0.01 M EDTA solution at pH=10, the stability constant K CaY = 10 10.6. Calculate what should be the conditional stability constant of the complex of the metal with the indicator at pH=10, if at the end point of the titration =.

8. The acid ionization constant of the indicator used in complexometric titration is 4.8·10 -6 . Calculate the content of the acidic and alkaline forms of the indicator at pH = 4.9, if its total concentration in the solution is 8.0·10 -5 mol/l. Determine the possibility of using this indicator when titrating the solution
with pH=4.9 if the color of its acid form matches the color of the complex.

9. To determine the aluminum content in the sample, a 550 mg portion of the sample was dissolved and 50.00 ml of a 0.05100 M complexone III solution was added. The excess of the latter was titrated with 14.40 ml of 0.04800 M solution of zinc (II). Calculate the mass fraction of aluminum in the sample.

10. When a complex containing bismuth and iodide ions is destroyed, the latter are titrated with Ag(I) solution, and bismuth with complexone III.
Titration of a solution containing 550 mg of a sample requires 14.50 ml of a 0.05000 M complexone III solution, and titration of the iodide ion contained in 440 mg of a sample requires 23.25 ml of a 0.1000 M Ag(I) solution. Calculate the coordination number of bismuth in the complex if iodide ions are the ligand.

11. A sample weighing 0.3280 g containing Pb, Zn, Cu was dissolved
and transferred to a 500.00 cm 3 volumetric flask. The determination was carried out in three stages:
a) titration of the first portion of a solution with a volume of 10.00 cm 3 containing Pb, Zn, Cu, spent 37.50 cm 3 0.0025 M EDTA solution; b) Cu was masked in the second portion of 25.00 cm 3 , and 27.60 cm 3 EDTA was used for titration of Pb and Zn; c) in the third portion of 100.00 cm 3 masked Zn
and Cu, 10.80 cm 3 of EDTA was spent on the titration of Pb. Determine the mass fraction of Pb, Zn, Cu in the sample.

Titration curves

In redoxmetry, titration curves are plotted in coordinates E = f(C R),
they illustrate the graphic change in the potential of the system during the titration. Before the equivalence point, the potential of the system is calculated from the ratio of the concentrations of the oxidized and reduced forms of the analyte (because up to the equivalence point, one of the forms of the titrant is practically absent), after the equivalence point, from the ratio of the concentrations of the oxidized and reduced forms of the titrant (because after the equivalence point, the analyte is titrated almost completely).

The potential at the equivalence point is determined by the formula

, (26)

where is the number of electrons participating in half-reactions;

are standard electrode potentials of half-reactions.

On fig. 10 shows the titration curve of a solution of oxalic acid H 2 C 2 O 4 with a solution of potassium permanganate KMnO 4 in an acidic medium
(= 1 mol / dm 3).

Rice. 10. Titration curve of 100.00 cm 3 oxalic solution

acid H 2 C 2 O 4 s C 1/z\u003d 0.1000 mol / dm 3 with a solution of permanganate

potassium KMnO 4 s C 1/z\u003d 0.1000 mol / dm 3 at \u003d 1 mol / dm 3

Half-reaction potential MnO 4 - + 5 e+ 8H + → Mn 2+ + 4H 2 O depends on the pH of the medium, since hydrogen ions participate in the half-reaction.

permanganatometry

The titrant is a solution of potassium permanganate KMnO 4 , which is a strong oxidizing agent. Basic Equation:

MnO 4 - + 8H + + 5e \u003d Mn 2+ + 4H 2 O, = +1.51 V.

M 1 / z (KMnO 4) \u003d g/mol.

In slightly acidic, neutral and slightly alkaline environments, due to the lower redox potential, the permanganate ion is reduced to Mn +4.

MnO 4 - + 2H 2 O + 3e \u003d MnO 2 ¯ + 4OH -, = +0.60 V.

M 1 / z (KMnO 4) \u003d 158.03 / 3 \u003d 52.68 g / mol.

In an alkaline environment, a solution of potassium permanganate is reduced
up to Mn+6.

MnO 4 - + 1e \u003d MnO 4 2-, = +0.558 V.

M 1 / z (KMnO 4) \u003d 158.03 g / mol.

To avoid side reactions, titration with potassium permanganate is carried out in an acidic medium, which is created with sulfuric acid. It is not recommended to use hydrochloric acid to create a medium, since potassium permanganate is able to oxidize the chloride ion.

2Cl - - 2e \u003d Cl 2, \u003d +1.359 V.

Most often, potassium permanganate is used as a solution
with a molar concentration equivalent of ~ 0.05 - 0.1 mol / dm 3. It is not a primary standard due to the fact that aqueous solutions of potassium permanganate are able to oxidize water and organic impurities in it:

4MnO 4- + 2H 2 O \u003d 4MnO 2 ¯ + 3O 2 + 4OH -

The decomposition of potassium permanganate solutions is accelerated in the presence of manganese dioxide. Since manganese dioxide is a decomposition product of permanganate, this precipitate has autocatalytic effect to the decomposition process.

Solid potassium permanganate used to prepare solutions is contaminated with manganese dioxide, so it is impossible to prepare a solution from an accurate sample. In order to obtain a sufficiently stable solution of potassium permanganate, after dissolving a sample of KMnO 4 in water, it is left in a dark bottle for several days (or boiled), and then MnO 2 ¯ is separated by filtration through glass filter (do not use a paper filter, as it reacts with potassium permanganate, forming manganese dioxide).

The color of the potassium permanganate solution is so intense that
that the indicator in this method is not required. In order to give a noticeable pink color to 100 cm 3 of water, 0.02 - 0.05 cm 3 of a KMnO 4 solution is enough
with a molar concentration equivalent of 0.1 mol / dm 3 (0.02 M). The color of potassium permanganate at the end point of the titration is unstable and gradually discolors as a result of the interaction of excess permanganate
with manganese (II) ions present at the end point in a relatively large amount:

2MnO 4 - + 3Mn 2+ + 2H 2 O "5MnO 2 ¯ + 4H +

Working solution standardization KMnO 4 spend on sodium oxalate or oxalic acid (freshly recrystallized and dried at 105°C).

Use solutions of primary standards with a molar equivalent concentration With(½ Na 2 C 2 O 4) \u003d 0.1000 or 0.05000 mol / l.

C 2 O 4 2- - 2e ® 2CO 2, \u003d -0.49 V

In titrimetric analysis, the quantitative determination of a substance is carried out on the basis of the volume of a solution of a known concentration spent on the reaction with a certain substance.

The process of determining the content of a substance or the exact concentration of a solution by volumetric analysis is called titration. This most important operation of titrimetric analysis consists in the fact that another solution of precisely known concentration is slowly added to the test solution in an amount equivalent to the amount of the compound being determined.

The volumes of solutions that quantitatively react with each other are inversely proportional to the normal concentrations of these solutions:

V 1 = N 2 or V 1 x N 1 = N 2 x V 2 V 1 x N 1 = V 2 x N 2

Where V is the volume of the reacting solution, l; N – concentration, n.

This provision underlies titrimetric analysis. In order to determine the concentration of one of the solutions, one must know exactly the volumes of the reacting solutions, the exact concentration of the other solution, and the moment when the two substances react in equivalent quantities. The conditions for titrimetric determination are:

a) accurate measurement of volumes of reactants;

b) preparation of solutions of precisely known concentration, with the help of which titration is carried out, the so-called working solutions (titranes)(often such solutions of known concentration are called standard (titrated);

c) determination of the end of the reaction.

Titrimetric determination takes much less time than gravimetric determination. Instead of many lengthy operations of gravimetric analysis (precipitation, filtration, weighing, etc.), only one operation is carried out in titrimetric determination - titration.

The accuracy of titrimetric determinations is somewhat less than the accuracy of gravimetric analysis, but the difference is small, therefore, where possible, they try to carry out the determination by a faster method.

In order for a particular reaction to serve as a basis for titration, it must satisfy a number of requirements.

1. The reaction must pass quantitatively according to a certain equation without side reactions. You need to be sure. That the added reagent is consumed exclusively for the reaction with the substance being determined.

2. The end of the reaction should be accurately recorded so that the amount of reagent is

equivalent to the amount of the analyte. The equivalence of the reactants is the basis for the calculation of the results of the analysis.

3. The reaction must proceed at a sufficient rate and be practically irreversible. It is almost impossible to accurately fix the equivalence point for slow reactions.

TITRATION METHODS

According to the method of performing titration, direct, reverse or indirect titration (substitution method) is distinguished.

In direct titration, the titrant is added directly to the analyte solution. For analysis by this method, one working solution is sufficient. For example, to determine an acid, a working solution of an alkali is needed, to determine an oxidizing agent, a solution of a reducing agent is required.

In a back titration, a known volume of the working solution, taken in excess, is added to the solution of the analyte. After that, the residue of the first working solution is titrated with another working solution and the amount of the reagent that has reacted with the analyte is calculated. For example, to determine chloride ions, a known volume of AqNO 3 solution, taken in excess, is added to the analyzed chloride solution. There is a reaction

Aq + +Cl = AqCl↓.

The excess of AqNO 3 solution is determined using another working solution - ammonium thiocyanate NH 4 SCN:

Aq + + SCN - = AqSCN↓.

In indirect titration, an excess of a reagent is added to the analyzed solution, which reacts with the substance to be determined. Then one of the reaction products is determined by titration. For example, to determine hydrocyanic acid, a solution of AqNO 3 is added in excess. There is a reaction

HCN + AqNO 3 = AqCN↓ + HNO 3

Then nitric acid is easily determined using a working alkali solution of NaOH:

HNO 3 + NaOH = NaNO 3 + H 2 O

In this case, the weak hydrocyanic acid is replaced in equivalent quantities by the strong one.

3. CLASSIFICATION OF TITRIMETRIC METHODS

ANALYSIS

Titrimetric analysis uses reactions of various types (acid-base interaction, complex formation, etc.) that meet the requirements that apply to titrimetric reactions. Individual titrimetric methods are named after the type of the main reaction that occurs during titration or by the name of the titrant (for example, in argentometric methods, the titrant is an AqNO 3 solution, in permanganometric methods, a KMnO 4 solution, etc.). According to the method of fixing the equivalence point, titration methods with color indicators, methods of potentiometric titration, conductometric, photometric, etc. When classifying according to the type of the main reaction occurring during titration, the following methods of titrimetric analysis are usually distinguished:

1. acid-base titration methods based on the reactions associated with the proton transfer process:

H + + OH - \u003d H 2 O, CH 3 COOH + OH - \u003d CH 3 COO - + H 2 O,

CO 3 2- + H + \u003d HCO - 3;

2. methods of complexation using the reactions of formation of coordination compounds (for example, complexometry):

Mg 2+ + H 2 V 2- \u003d MgV 2_ + 2H +

Where V 2 \u003d CH 2 - N /

׀ / CH 2 – COO-

3. Precipitation methods based on the formation of sparingly soluble

connections:

Aq + + Cl - + AqCl↓ (argentometry),

Hg 2 2+ + 2Cl - \u003d Hg 2 Cl 2 ↓ (mercury);

4.methods of redox titration. based

on redox reactions (oxydimetry):

MnO 4 - + 5Fe 2+ + 8H + = Mn 2+ + 5Fe 3+ + 4H 2 O (permanganatometry);

2S 2 O 3 2- + l 2 \u003d S 4 O 6 2- + 2l - (iodine);

5NO - 2 + 2MnO 4 - + 6H + + 5NO - 3 + 2Mn 2+ + 3H 2 O (nitritometry);

3SbCl 4 - + Br - 3 + 6H + + 6Cl - = 3SbCl 6 - + Br _ + 3H 2 O (bromatometry).

In titrimetry, a wide variety of reactions are used. Depending on which reaction underlies the titration, the following methods of titrimetric analysis are distinguished.

Acid-base methods, based on the neutralization reaction:

H + + OH - → H 2 O

This method determines the amount of acids, bases, and some salts.

Oxidation - reduction methods(oxydimetry). These methods are based on oxidation-reduction reactions. Using a solution of an oxidizing agent, the amount of a substance that is a reducing agent is determined and vice versa.

Precipitation and complex formation methods are based on the precipitation of ions in the form of sparingly soluble compounds and on the binding of ions into a poorly dissociated complex.

There are the following titration methods:

straight, when during titration a reaction occurs between the analyte and the titrant;

the opposite, to when a deliberately excessive, but accurately measured volume of a solution of a known concentration is added to the solution to be determined, and the excess of the reagent is titrated with a titrant;

substituent titration when the product of the reaction of the analyte with any reagent is titrated with a titrant.

TITRANTS

titrant a solution is called, with the help of which a titrimetric determination is made, i.e. solution to be titrated. To carry out the determination using a titrant, you need to know its exact concentration. There are two methods for preparing titrated solutions, i.e. solutions of known concentration.

1. An accurate sample taken on an analytical balance is dissolved in a volumetric flask, i.e. a solution is prepared in which the amount of the solute and the volume of the solution are known. In this case, the solutions are called solutions with prepared titers.

2. The solution is prepared to approximately the desired concentration, and the exact concentration is determined by titration, having another solution with a prepared titer. Titrated solutions, the exact concentration of which is found as a result of titration, are called fixed titer solutions.

Titrants are usually prepared at approximately the desired concentration, and their exact concentration is determined. It must be remembered that the titer of solutions changes over time and must be checked at regular intervals (from 1 to 3 weeks, depending on the substance from which the solution is prepared). Therefore, if the titrant is prepared according to a precisely taken sample, then its titer corresponds to that prepared only for a limited time.

One of the rules of titrimetric analysis is the following: the titres of the titrants should be set under the same conditions under which the analysis will be performed.

To determine the exact concentration of the titrant (“titer setting” or standardization) use the so-called starting or setting substance.

The accuracy of determining the titer titer, and, consequently, the accuracy of all subsequent analyzes, depends on the properties of the adjusting substance. The installation substance must meet the following requirements.

Correspondence of the composition of a substance with its chemical formula.

Chemical purity - the total amount of impurities should not exceed 0.1% - Stability in air, i.e. carbon dioxide.

Stable in solution (does not oxidize or decompose).

Perhaps a large equivalent mass - this reduces the relative error in the determination.

Good solubility in water.

The ability to react with a solution whose titer is set according to a strictly defined equation and at high speed.

To set the titer of the titrant from the adjusting agent prepare an exact solution according to a precisely taken sample. The solution is prepared in a volumetric flask. The volumetric flask should be washed with chromium mixture until it "runs down", rinsed many times with tap water and then 3-4 times with distilled water. The funnel must be clean, dry and free to enter the neck of the flask.

A portion of the adjusting substance is weighed on an analytical balance in a bottle. You can weigh out exactly the calculated amount, or you can take the amount close to the calculated, but accurately weighed. In the first case, the solution will be exactly the specified concentration, and in the second, the exact concentration is calculated.

The sample taken is carefully transferred through the funnel into a volumetric flask. The remains of the weighing bottle are thoroughly washed into the funnel with distilled water from the wash bottle. Then they wash the inner walls of the funnel and, slightly raising it, the outer part of the tube. It is necessary to ensure that the total amount of water used to wash the weighing bottle and funnel does not take more than half of the flask. Stir the contents of the flask with a gentle twisting motion until the sample is completely dissolved. Then, the contents of the flask are brought to the mark with distilled water from the wash bottle. To do this, pour water about 1 cm below the mark. Place the flask so that the mark is at eye level and carefully, drop by drop, add water until the lower part of the meniscus touches the mark on the neck of the flask (Fig. 1). Close the flask carefully with a stopper and, inverting the flask, mix the solution 12-15 times. Solutions for setting the titer should be freshly prepared.

Often used to prepare titrated solutions. fixed channels, which are sealed glass ampoules with accurate weighed reagents. Each ampoule has an inscription showing what substance and in what quantity is in the ampoule.

A funnel is inserted into the volumetric flask, also thoroughly washed and rinsed with distilled water. If the ampoule contains not a solution, but a dry substance, then the funnel must be dry. Then a special glass head is inserted into the funnel (usually attached to the box with fixes), also rinsed with distilled water. The ampoule is wiped with ethyl alcohol to remove the inscription and washed with distilled water. Then it is inserted into the funnel so that it touches the striker with its thin, inwardly curved bottom, lifts it up and lightly hits the end of the striker. In this case, the contents of the ampoule enter the flask through the funnel (Fig. 2). On the side or top of the ampoule there is a recess in which a hole is punched with a glass rod with a pointed end. Through this hole, the inner walls of the ampoule are washed with distilled water from the washer. You need to rinse many times in small portions. After that, the outer walls of the ampoule are rinsed and the ampoule is discarded. Rinse the funnel and the head, then raise the funnel and wash the outer

Part of the funnel tube. Wash the top of the neck of the volumetric flask. When performing all these washing operations, make sure that the amount of water in the volumetric flask by the end of all operations does not exceed 2∕3 of the volume of the flask. Gently swirl the contents of the flask. If fixanal contained a dry substance, stir it until complete dissolution. Then dilute the contents of the flask to the mark with distilled water. Close the flask carefully and stir the solution 12-15 times.

To set the titer of the titrant, separate portions of the solution are taken with a pipette and titrated. You can also take separate weighed portions of the starting material and, dissolving each of them in an arbitrary amount of water, titrate the entire resulting solution. This method gives more accurate results than the first, but is too laborious. Therefore, in the laboratory, practically when performing analyzes, they use the first method.

5. DETERMINATION OF THE EQUIVALENCE POINT AND END

REACTIONS

During titration, not an excess of the reagent is used, but an amount equivalent to the amount of the analyte. A necessary condition for determining the content of a substance titrimetrically is the exact establishment of the moment when the reaction between the titratable substance and the titrant ends, that is, fixing the point equivalence. The more precisely the end of the reaction is determined, the more accurate the result of the analysis will be.

To determine the end of the reaction, special reagents, the so-called indicators, are used. The action of indicators is usually reduced to the fact that after the completion of the reaction between the titrated substance and the titrant, in the presence of a small excess of the latter, they undergo changes and change the color of the solution or precipitate. When so much titrant is added from the burette that a noticeable change in the color of the titrated solution is observed, it is said that end point of the titration.

In most cases, indicators are added to a solution of the analyte and the titration takes place in the presence of the indicator. These are the so-called internal indicators. In some cases, they act differently: as the titration proceeds, a drop of the solution is taken from the titrated solution with a capillary, to which a drop of indicator is added over a porcelain plate. Thus, the reaction with the indicator takes place outside the titrated solution. The indicators used in this case are called external.

There are separate indicators for each titrimetric method. In acid-base titrations, indicators change color when the pH of the solution changes. In precipitation methods, the equivalence point is found by the cessation of precipitation. The indicators used in these methods form a brightly colored precipitate or solution with an excess of titrant. Sometimes, if one titrates with a brightly colored solution, for example, with a KMnO 4 solution, the end of the titration can be seen without an indicator, since the first drop of the titrant, which does not react with a certain substance, changes the color of the titrated solution.

Titrimetric or volumetric analysis- a method of quantitative analysis based on measuring the volume (or mass) of the reagent T spent on the reaction with the analyte X. In other words, titrimetric analysis is an analysis based on titration.

The purpose of laboratory classes on titrimetric methods of analysis is to develop practical skills in the technique of performing titrimetric analysis and master the methods of statistical processing of analysis results using the example of specific quantitative determinations, as well as to consolidate theoretical knowledge by solving typical calculation problems for each topic.

Knowledge of the theory and practice of titrimetric analysis methods is necessary for the subsequent study of instrumental methods of analysis, other chemical and special pharmaceutical disciplines (pharmaceutical, toxicological chemistry, pharmacognosy, pharmaceutical technology). The studied methods of titrimetric analysis are pharmacopoeial and are widely used in the practice of a pharmacist to control the quality of drugs.

Conventions

A, X, T - any substance, analyte and titrant, respectively;

m(A), m(X), t(T)- mass of any substance, analyte and titrant, respectively, g;

M(A), M(X), M(T)- molar mass of any substance, analyte and titrant, respectively, g/mol;

n(A), n(X), n(T) - the amount of any substance, analyte and titrant, respectively, mol;

The amount of the substance of the equivalent of any substance, the substance to be determined and the titrant, respectively, mol;

- the volume of a solution of any substance, analyte and titrant, respectively, l;

- the volume of an aliquot of the analyte, equal to the capacity of the pipette, l;

- the volume of the analyzed solution of the analyte, equal to the capacity of the flask, l.

1. Basic concepts of titrimetric

analysis

1.1. Titration- the process of determining substance X by the gradual addition of small amounts of substance T, in which, in some way, the detection of the point (moment) when all substance X has reacted is provided. Titration allows you to find the amount of substance X from a known amount of substance T added up to this point (moment), taking into account the fact that the ratio in which X and T react is known from stoichiometry or otherwise.

1.2. titrant- a solution containing active reagent T, with which the titration is carried out. Titration is usually carried out by adding titrant from a calibrated burette to the titration flask containing the solution to be analyzed. Into this flask before titration add aliquot analyzed solution.

1.3. Aliquot share (aliquot)- precisely known part of the analyzed solution, taken for analysis. It is often taken with a calibrated pipette and its volume is usually indicated by the symbol V ss .

1.4. Equivalence point (TE)- such a point (moment) of titration at which the amount of added titrant T is equivalent to the amount of titrated substance X. Synonyms for TE: stoichiometric point, theoretical end point.

1.5. End point titration (KTT) - the point (moment) of the titration, at which some property of the solution (for example, its color) shows a noticeable (sharp) change. LTT corresponds more or less to TE, but most often does not coincide with it.

1.6. Indicator- a substance that exhibits a visible change in the TE or near it. Ideally, the indicator is present at a concentration low enough to transition interval not cost-

a significant amount of titrant T was used. A sharp visible change in the indicator (for example, its color) corresponds to CTT.

1.7. Indicator transition interval- the area of ​​concentration of hydrogen, metal or other ions within which the eye is able to detect a change in hue, color intensity, fluorescence or other property of a visual indicator caused by a change in the ratio of two corresponding forms of the indicator. This area is usually expressed as the negative logarithm of the concentration, for example: For a redox indicator, the transition interval is the corresponding region of the redox potential.

1.8. Degree of titration - volume ratio V (T) of the added titrant to the volume V (TE) of the titrant corresponding to the TE. In other words, the degree of titration of a solution is the ratio of the amount of the titrated substance to its initial amount in the analyzed solution:

1.9. Titration level- order the concentration of the titrant solution used, for example, 10 -1 , 10 -2 , 10 -3 , etc.

1.10. Titration curve - graphic representation of the dependence of the change in concentration c (X) of the analyte X or some related property of the system (solution) on the volume V (T) added titrant T. The value of c (X) during the titration changes by several orders of magnitude, so the titration curve is often plotted in the coordinates: The abscissa shows the volume of added titrant V (T) or degree of titration / . If the equilibrium concentration c (X) or the intensity of a property proportional to it is plotted along the y-axis, then we get linear titration curve. If on the y-axis we set aside or the logarithm of the intensity of a property proportional to c(X), then one gets logarithmic (or monologarithmic) titration curve. To more clearly identify the features of the titration process and for applied purposes, sometimes they build differential titration curves, plotting along the abscissa axis the volume of the added titrant V (T), and along the y-axis - the first derivative of the logarithm of the concentration (or the intensity of a property proportional to it) with respect to the volume of the added titrant: Such titration curves are usually used in physicochemical methods of analysis, for example, in potentiometric titrations.

1.11. Standard solution- a solution having a known concentration of the active substance.

1.12. Standardization- the process of finding the concentration of an active reagent in a solution (most often by titrating it with a standard solution of the corresponding substance).

1.13. Titration jump- the interval of a sharp change in any physical or physico-chemical property of the solution near the equivalence point, usually observed when 99.9-100.1% of the titrant is added compared to its stoichiometric amount.

1.14. Blank titration- titration of a solution that is identical to the analyzed solution in terms of volume, acidity, amount of indicator, etc., but does not contain the analyte.

2. Basic operations of titrimetric analysis

2.1. Cleaning, washing, storage of measuring utensils.

2.2. Checking the capacity of measuring utensils.

2.3. Taking a sample with a precisely known mass by the difference between the results of two weighings (usually on an analytical balance).

2.4. Quantitative transfer of a sample of a substance into a volumetric flask and dissolution of the substance.

2.5. Filling volumetric utensils (flasks, burettes, pipettes) with a solution.

2.6. Emptying pipettes, burettes.

2.7. Selection of an aliquot of the analyzed solution.

2.8. Titration and calculations based on titration results.

3. Calibration of measuring instruments

In titrimetric analysis, the exact volumes of the solution are measured using measuring utensils, which are volumetric flasks with a capacity of 1000, 500, 250, 100, 50 and 25 ml, pipettes and graduated pipettes with a capacity of 10, 5, 3, 2 and 1 ml. The capacity of the flask and pipette at 20 °C is engraved on the neck of the flask or on the side of the pipette (nominal volume). In the mass production of volumetric utensils, the actual (true) capacity of volumetric flasks, burettes, pipettes may differ from the nominal values ​​indicated on the utensil. To achieve the required accuracy of the obtained results of titrimetric analysis

Calibration of volumetric glassware is based on determining the exact mass of distilled water poured in or poured out, which is determined by the results of weighing the glassware before and after pouring in or pouring out water. The volume of water in the calibrated vessel (its capacity) and the mass of water are related by the ratio:

where - density of water at the temperature of the experiment, g/ml.

The density of water depends on temperature, so when making calculations, you should use the data in Table. 2-1.

Table 2-1. Density values ​​of water at the corresponding temperature

Volumetric flasks are calibrated for infusion, and burettes and pipettes are calibrated for pouring, since small amounts of liquid always remain on the walls of the dish during pouring.

3.1. Volumetric flask capacity check

The flask is thoroughly washed, dried and weighed on an analytical balance with an accuracy of ± 0.002 g. Then it is filled with water (hereinafter - distilled) along the lower meniscus, the drops of water in the upper part of the neck of the flask are removed with filter paper and weighed again. Each weighing of an empty flask and a flask with water is carried out at least twice, while the difference between two weighings should not exceed ± 0.005 g. The difference between the mass of the flask with water and the mass of the empty flask is equal to the mass of water contained by the flask at a given temperature. The true capacity of the flask is calculated by dividing the average mass of water by its density at the test temperature (see Table 2-1).

For example, if a volumetric flask with a nominal volume of 100 ml is calibrated, the average mass of water at 18 °C is 99.0350 g. Then the true capacity of the volumetric flask is:

3.2. Burette capacity check

The burette is a glass cylinder, the inner diameter of which can vary slightly along the length of the burette. Equal divisions on the burette in its various parts correspond to unequal volumes of the solution. That is why burette calibration calculates the true volumes for each selected buret site.

A clean and dried burette is filled with water to the zero mark along the lower meniscus and water drops are removed from the inner surface of the upper part of the burette with filter paper. Then, under the burette substitute a bottle, previously weighed with a lid on an analytical balance. A certain volume of water (for example, 5 ml) is slowly poured into the bottle from the burette. After that, the bottle is closed with a lid and weighed again. The difference between the mass of the weighing bottle with water and the empty weighing bottle is equal to the mass of water contained in the burette between divisions of 0 and 5 ml at the temperature of the experiment. Then the burette is again filled with water to the zero mark along the lower meniscus, 10 ml of water is slowly poured into an empty bottle and the mass of water contained in the burette between divisions 0 and 10 ml is determined in a similar way. When calibrating the burette, for example, for 25 ml, this operation is carried out 5 times and the mass of water corresponding to the nominal volumes indicated on the burette of 5, 10, 15, 20 and 25 ml is calculated. Each weighing of an empty bottle and a bottle of water is repeated at least twice, while the difference between two weighings should not exceed ± 0.005 g.

Then according to the table. 2-1 determine the density of water at the temperature of the experiment and calculate the true capacity of the burette for each value of the nominal volume indicated on it.

Based on the data obtained, the correction value is calculated equal to the difference between the calculated value of the true capacity and the corresponding value of the nominal volume of the burette:

and then draw a curve of burette capacity errors in coordinates (Figure 2-1).

For example, let the following experimental data be obtained when calibrating a burette with a capacity of 25 ml at a temperature of 20 °C, which, together with the results of the corresponding calculations, are presented in Table. 2-2.

Based on the obtained tabular data, a capacity correction curve for a given buret is plotted, using which it is possible to refine the results of reading by buret.

Table 2-2. Calibration results for a 25 ml burette

Rice. 2-1. Burette capacity correction curve

For example, let 7.50 ml of titrant be used for titration of an aliquot of the analyte according to the results of counting on a burette. According to the graph (see Fig. 2-1), the correction value corresponding to this nominal volume is 0.025 ml, the true volume of titrant used is: 7.50 - 0.025 = 7.475 ml.

3.3. Checking pipette capacity

A pipette, clean and weighed on an analytical balance, is filled with water to the zero mark along the lower meniscus and then the water is slowly filled.

poured along the wall into a pre-weighed bottle. The bottle is covered with a lid and weighed with water. Each weighing of an empty bottle and a bottle with water is repeated at least two times, while the difference between two weighings should not exceed ± 0.005 g. The difference between the mass of a bottle with water and an empty bottle is equal to the mass of water contained by a pipette. The true capacity of the pipette is calculated by dividing the average mass of water by the density of the water at the test temperature (see Table 2-1).

4. Typical calculations in titrimetric analysis

4.1. Ways of expressing concentrations used for calculations in titrimetric analysis

4.1.1. Molar concentration of substance c (A), mol / l - the amount of substance A in mol contained in 1 liter of solution:

(2.1)

where - the amount of substance A in mol, dissolved in V (A) l

solution.

4.1.2. Molar concentration equivalent of a substance , mol / l - the amount of substance A equivalent in mol contained in 1 liter of solution (the former name is the “normality” of the solution):

(2.2)

where
- the amount of substance equivalent to A in mol,

dissolved in V (A) l of solution; - molar mass of the equivalent of ve-

substances A, g / mol; - the equivalence factor of the substance.

4.1.3. Substance titer T(A), g / ml - the mass of solute A in grams, contained in 1 ml of solution:

4.1.4. Titrimetric conversion factor I, g / ml - mass of the analyte in grams, interacting with 1 ml of titrant:

(2.4)

4.1.5. Correction factor F- a value showing how many times the practical concentrations of the titrant differ from the corresponding theoretical values ​​specified in the method:

(2.5)

4.2. Calculation of the molar mass equivalent of substances in reactions used in titrimetric analysis

An equivalent is a real or conditional particle that can add or donate one hydrogen ion H + (or be otherwise equivalent to it in acid-base reactions) or add or donate one electron in redox reactions.

Equivalence factor - a number indicating which

the equivalent fraction is from a real particle of substance A. The equivalence factor is calculated based on the stoichiometry of this reaction:

where Z- the number of protons donated or added by one reacting particle (molecule or ion) in an acid-base reaction, or the number of electrons donated or accepted by one reacting particle (molecule or ion) in an oxidation or reduction half-reaction.

The molar mass of the equivalent of a substance is the mass of one mole of the equivalent of a substance, equal to the product of the equivalence factor by the molar mass of the substance, g / mol. It can be calculated using the formula:

(2.6)

4.3. Preparation of a solution by diluting a more concentrated solution with a known concentration

When carrying out titrimetric analysis, in some cases it is required to prepare a solution of substance A with a volume approximately known concentration by diluting a more concentrated solution.

When the solution is diluted with water, the amount of substance A or the amount of substance A does not change, therefore, in accordance with expressions (2.1) and (2.2), we can write:

(2.7)
(2.8)

where indices 1 and 2 refer to solutions before and after dilution, respectively.

From the ratios obtained, the volume of a more concentrated solution is calculated , which must be measured to prepare a given solution.

4.4. Preparation of a predetermined volume of solution by weighing a precisely known mass

4.4.1. Sample Weight Calculation

The theoretical mass of a sample of a standard substance A, necessary to prepare a given volume of a solution with a known concentration, is calculated from expressions (2.1) and (2.2). It is equal to:

(2.9)

if the molar concentration of a substance in solution is used, and:

(2.10)

if the molar concentration of the equivalent of the substance in solution is used.

4.4.2. Calculation of the exact concentration of the prepared solution

The concentration of a solution of substance A, prepared by an accurate sample of mass m (A), is calculated from the relationships (2.1-2.3), where t(A)- the practical mass of substance A, taken from the difference between two weighings on an analytical balance.

4.5. Calculation of titrant concentration during its standardization

Known volume of standard solution with concentration titrated with a titrant solution of volume V (T)(or vice versa). In this case, for the reaction taking place in the solution during the titration process , the law of equivalents has the form:

and

From here, an expression is obtained for calculating the molar concentration of the titrant equivalent from the results of titration:

(2.12)

4.6. Calculation of the mass of the analyte in the analyzed solution4.6.1. direct titration

The substance to be determined in the analyzed solution is titrated directly with a titrant.

4.6.1.1. Calculation using titrant equivalent molar concentration

An aliquot of the analyte solution titrated

titrant solution with volume V(T). In this case, for the reaction occurring in the solution during the titration process:

the law of equivalents has the form: and

(2.13)

Hence, the molar concentration of the equivalent of the analyte, calculated from the results of titration, is equal to:

(2.14)

The resulting expression is substituted into equation (2.2) and a formula is obtained for calculating the mass of the analyte in a flask with a volume according to the results of direct titration:

(2.15)

If, during titration, part of the titrant is consumed by the reaction with the indicator, a "blank experiment" is carried out and the volume of titrant V "(T) is determined,

used for indicator titration. In calculations, this volume is subtracted from the volume of the titrant, which was used to titrate the solution of the analyte. Such an amendment is made during the "blank experiment" in all calculation formulas used in titrimetric analysis. For example, formula (2.15) for calculating the mass of the analyte, taking into account the “blank experiment”, will look like:

(2.16)

4.6.1.2. Calculation using titrimetric conversion factor

We have an analyzed solution with a volume For titration of alik-

mil's share solution of analyte used volume of titrant V (T) with theoretical titrimetric conversion factor and correction factor F. Then the mass of the analyte in an aliquot is equal to:

(2.17)

and throughout the analyzed volume

(2.18)

4.6.2. substitution titration

a known excess of reagent A is added and substituent B is isolated in an amount equivalent to the analyte:

Substituent B is titrated with a suitable titrant:

The law of equivalents for substitution titration:

using relation (2.8) can be written in the form:

From here, a formula is obtained for calculating the molar concentration of the equivalent of the analyte in solution according to the results of substitution titration:

which has the same form as in direct titration (2.14). That is why all calculations of the mass of the analyte in the analyzed problem during substitution titration are carried out according to formulas (2.15-2.18) for direct titration. 4.6.3. Back titration

To an aliquot of the analyte add famous excess of the first titrant :

Then the excess of the unreacted first titrant is titrated with the second titrant, which consumes the volume :

The law of equivalents in this case can be written as:

From here, the molar concentration of the equivalent of substance X in solution is calculated:

(2.19)

Substitute the resulting expression into equation (2.2) and obtain a formula for calculating the mass of the analyte in the analyzed solution, equal to the volume of the flask, based on the results of back titration:

5. Implementation and provision of practical work on titrimetric analysis

5.1. General provisions

When studying the section "Titrimetric analysis", it is planned to carry out work on the following topics.

Theme I Methods of acid-base titration.

Theme II. Methods of redox titration.

Topic III. Methods of precipitation titration.

Topic IV. Methods of complexometric titration.

Lesson 1. Preparation of hydrochloric acid solution and its standardization.

Lesson 2. Determination of the mass of alkali in solution. Determination of the mass of carbonates in solution. Determination of the mass of alkali and carbonate in solution in the joint presence.

Lesson 3. Determination of the mass of ammonia in solutions of ammonium salts.

a) Test control 1.

b) Determination of the mass of ammonia in solutions of ammonium salts. Lesson 4. Permanganometric titration.

a) Written test 1.

b) Determination of the mass of hydrogen peroxide in solution.

c) Determination of the mass of iron(II) in a salt solution. Determination of the mass fraction of iron(II) in a salt sample.

Lesson 5. Iodometric titration.

a) Determination of the mass of hydrogen peroxide in solution.

b) Determination of the mass of copper(II) in solution. Lesson 6. iodimetric titration.

Lesson 7. Bromatometric titration. Determination of the mass of arsenic (III) in solution.

Lesson 8. bromometric titration. Determination of the mass fraction of sodium salicylate in the preparation.

Lesson 9. Nitritometric titration.

a) Test control 2.

b) Determination of the mass fraction of novocaine in the preparation. Lesson 10. Argentometric titration and hexacyanoferratom-

tric titration.

a) Written test 2.

b) Determination of the mass of potassium bromide and potassium iodide in solution by argentometric titration.

c) Determination of the mass of zinc in solution by hexacyanoferratometric titration.

Lesson 11. Complexometric determination of the mass of zinc and lead in solution.

a) Test control 3.

b) Determination of the mass of zinc and lead in solution.

Lesson 12. Complexometric determination of iron(III) and calcium in solution.

a) Written test 3.

b) Determination of the mass of iron(III) and calcium in solution.

Depending on the specific situation, it is allowed to carry out some work during not one, but two lessons. It is also possible to shift the timing of test controls and written tests.

At the end of each topic, examples of test items for intermediate control of students' knowledge, the content of the final written test, an example of a ticket for a written test are given.

At the end of each lesson, the student draws up a protocol that includes the date and name of the work performed, the essence of the methodology, the order of work, the experimental data obtained, calculations, tables, conclusions. All calculations of the results of the analysis (concentration of the solution, mass of the analyte) are performed by students with an accuracy of the fourth significant figure, except for cases specifically specified in the text.

Intermediate control of practical skills and theoretical knowledge is carried out with the help of test control and written tests.

5.2. Material support for classes in titrimetric analysis

Glassware: burettes with a capacity of 5 ml, volumetric pipettes with a capacity of 2 and 5 ml, volumetric flasks with a capacity of 25, 50, 100 and 250 ml, conical flasks with a capacity of 10-25 ml, glass bottles, glass funnels with a diameter of 20-30 mm, plain or dark glass flasks with a capacity of 100, 200 and 500 ml, measuring cylinders with a capacity of 10, 100 ml.

Reagents: Reagents of "chemically pure" qualification are used in the work and "ch.d.a.", indicator paper.

Devices: analytical balances with weights, technical balances with weights, oven, laboratory thermometer with a scale of 20-100 °C, tripods with legs for fixing burettes and rings for asbestos nets, gas burners, water baths.

Auxiliary materials and accessories: detergents (soda, washing powders, chromium mixture), dishwashing brushes, rubber bulbs, asbestos nets, stationery glue, glass pencils, filter paper.

Bibliography

1. Lectures for students on the section "Titrimetric analysis".

2.Kharitonov Yu.Ya. Analytical chemistry (analytics): In 2 volumes - ed. 5th - M .: Higher School, 2010 (hereinafter referred to as the "Textbook").

3.Lurie Yu.Yu. Handbook of Analytical Chemistry.- M.: Chemistry, 1989 (hereinafter referred to as the "Handbook").

4.Dzhabarov D.N. Collection of exercises and tasks in analytical chemistry.- M.: Russian doctor, 2007.

Classification of titrimetric analysis methods

Analytical chemistry

Methods of titrimetric analysis can be classified according to the nature of the chemical reaction underlying the determination of substances, and according to the method of titration.

By their nature, the reactions used in titrimetric analysis are of various types - ion combination reactions and oxidation-reduction reactions. In accordance with this, titrimetric determinations can be divided into the following main methods: acid-base titration (neutralization), precipitation and complexation methods, oxidation-reduction method.

Method of acid-base titration (neutralization). This includes definitions based on the interaction of acids and bases, i.e. on the neutralization reaction:

The method of acid-base titration (neutralization) determines the amount of acids (alkalimetry) or bases (acidimetry) in a given solution, the amount of salts of weak acids and weak bases, as well as substances that react with these salts. The use of non-aqueous solvents (alcohols, acetone, etc.) made it possible to expand the range of substances that can be determined by this method.

Methods of precipitation and complexation. This includes titrimetric determinations based on the precipitation of an ion in the form of a poorly soluble compound or its binding into a poorly dissociated complex.

Methods of oxidation - recovery (redoximetry). These methods are based on oxidation and reduction reactions. They are usually named according to the titrated reagent solution used, for example:

permanganatometry, which uses oxidation reactions with potassium permanganate KMnO4;

iodometry, which uses oxidation reactions with iodine or reduction with I-ions;

bichromatometry, which uses oxidation reactions with potassium dichromate K2Cr2O7;

bromatometry, which uses the oxidation reactions with potassium bromate KBrO3.

The methods of oxidation-reduction also include cerimetry (oxidation with Ce4+ ions), vanadatometry (oxidation with VO3 ions), titanometry (reduction with T13+ ions). According to the method of titration, the following methods are distinguished.

Direct titration method. In this case, the ion to be determined is titrated with a reagent solution (or vice versa).

replacement method. This method is used when, for one reason or another, it is difficult to determine the equivalence point, for example, when working with unstable substances, etc.

Back titration method (titration by residue). This method is used when no suitable indicator is available or when the main reaction is not proceeding very rapidly. For example, to determine CaCO3, a sample of a substance is treated with an excess of titrated hydrochloric acid solution:

Whichever method is used to determine, it is always assumed:

1) accurate measurement of the volumes of one or both reacting solutions;

2) the presence of a titrated solution, with which titration is carried out;

3) calculation of the results of the analysis.

In accordance with this, before proceeding to the consideration of individual methods of titrimetric analysis, let us dwell on the measurement of volumes, calculation of concentrations and preparation of titrated solutions, as well as on calculations for titrimetric determinations.

Equivalence point

Equivalence point (in titrimetric analysis) - the moment of titration when the number of equivalents of the added titrant is equivalent or equal to the number of equivalents of the analyte in the sample. In some cases, several equivalence points are observed following one after another, for example, when titrating polybasic acids or when titrating a solution in which there are several ions to be determined.

The titration curve plot has one or more inflection points corresponding to equivalence points.

The end point of a titration (similar to the equivalence point, but not the same) is the point at which the indicator changes color in a colorimetric titration.

Methods for determining the equivalence point

Using indicators

These are substances that change their color due to chemical processes. Acid-base indicators, such as phenolphthalein, change color depending on the pH of the solution they are in. Redox indicators change their color following a change in the potential of the system, and are thus used in redox titrations. Before the start of titration, a few drops of the indicator are added to the test solution and the titrant is added dropwise. As soon as the solution after the indicator changes its color, the titration is stopped, this moment is approximately the equivalence point.

Indicator selection rule - when titrating, an indicator is used that changes its color near the equivalence point, i.e. the transition interval of the color of the indicator should, if possible, coincide with the jump in the titration.

Potentiometry

In this case, a device is used to measure the electrode potential of the solution. When the equivalence point is reached, the potential of the working electrode changes dramatically.

With pH meters

A pH meter is essentially also a potentiometer, which uses an electrode whose potential depends on the content of H+ ions in the solution, this is an example of using an ion selective electrode. In this way, the change in pH can be monitored during the entire titration process. When the equivalence point is reached, the pH changes dramatically. This method is more accurate than titration using acid-base indicators, and can be easily automated.

Conductivity

The conductivity of an electrolyte solution depends on the ions present in it. During a titration, the conductivity often changes significantly (For example, in an acid-base titration, the H+ and OH− ions interact to form a neutral H2O molecule, which causes a change in the conductivity of the solution). The overall conductivity of the solution also depends on other ions present (for example, counterins), which make different contributions to it. It, in turn, depends on the mobility of each ion and on the total concentration of ions (ionic strength). In this regard, it is much more difficult to predict the change in conductivity than to measure it.

Color change

During some reactions, a color change occurs even without the addition of an indicator. This is most often observed in redox titrations, when the starting materials and reaction products have different colors in different oxidation states.

precipitation

If an insoluble solid is formed during the reaction, a precipitate is formed at the end of the titration. A classic example of such a reaction is the formation of highly insoluble silver chloride AgCl from Ag+ and Cl− ions. Surprisingly, this does not accurately determine the end of the titration, so the precipitation titration is most often used as a back titration.

Isothermal calorimetric titration

An isothermal titration calorimeter is used, which determines the equivalence point by the amount of heat released or absorbed by the reacting system. This method is important in biochemical titrations, for example, to determine how an enzyme substrate binds to an enzyme.

Thermometric titrimetry

Thermometric titrimetry is an extremely flexible technique. It differs from calorimetric titrimetry in that the heat of reaction, indicated by a fall or rise in temperature, is not used to determine the amount of a substance contained in the test sample. On the contrary, the equivalence point is determined based on the area in which the temperature change occurs. Depending on whether the reaction between the titrant and the analyte is exothermic or endothermic, the temperature during the titration process will rise or fall accordingly. When all of the test substance has reacted with the titrant, changing the area in which the temperature rises or falls makes it possible to determine the equivalence point and the bend in the temperature curve. The exact equivalence point can be determined by taking the second derivative of the temperature curve: a clear peak will indicate the equivalence point.

Spectroscopy

The equivalence point can be determined by measuring the light absorption of the solution during the titration if the spectrum of the product, titrant, or analyte is known. The relative content of the reaction product and the test substance allows you to determine the equivalence point. However, the presence of free titrant (indicating the completion of the reaction) can be detected at very low values.

Amperometry

A method that allows you to determine the equivalence point by the magnitude of the current at a given potential. The magnitude of the current due to the oxidation/reduction reaction of the test substance or product at the working electrode depends on their concentration in the solution. The equivalence point corresponds to a change in the magnitude of the current. This method is most useful when it is necessary to reduce the consumption of titrant, for example, when titrating halides with Ag+ ion.

Direct and back titration.

In the simplest variant of titration, the analyte interacts directly with the titrant. The amount of analyte is calculated from the molar concentration of the titrant, its volume required to reach the equivalence point, and the stoichiometry of the reaction between the analyte and the titrant.

In a back titration, the analyte does not interact with the titrant, but with another reagent present in excess. The excess is then determined by titration. If the initial amount of the reagent is known and its excess is determined, then the difference between them is the amount of the reagent that went into the reaction with the analyte.

Back titration is used, for example, when the equilibrium constant of the direct titration reaction is too small. Other reasons for using back titrations include the lack of a suitable indication method or the insufficient reaction rate in direct titration.

substitution titration.

Magnesium complex MgY2- is added to the analyzed solution containing metal ions to be determined. Because it is less stable than the complex of the metal ion to be determined with the complexone, then a substitution reaction takes place and the Mg2+ ion is released.

Then the Mg2+ ion is titrated with complexone III in the presence of eriochrome black T.

Based on the volume of EDTA used for titration, the mass of the metal ion to be determined is calculated. This method of titration is possible only if the complex compounds of the metals being determined are more stable than the magnesium complex.

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Titrimetric analysis is a method for determining the amount of a substance by accurately measuring the volume of solutions of substances that react with each other.

Titer- the amount of the substance contained in 1 ml. solution or equivalent to the analyte. For example, if the titer of H 2 SO 4 is 0.0049 g / ml, this means that each ml of the solution contains 0.0049 g of sulfuric acid.

A solution whose titer is known is called titrated. Titration- the process of adding to the test solution or an aliquot of an equivalent amount of a titrated solution. In this case, standard solutions are used - fixed channels- solutions with the exact concentration of the substance (Na 2 CO 3, HCl).

The titration reaction must meet the following requirements:

high reaction rate;

the reaction must proceed to completion;

the reaction must be highly stoichiometric;

have a convenient method of fixing the end of the reaction.

HCl + NaOH → NaCl + H 2 O

The main task of titrimetric analysis is not only to use a solution of exactly known concentration (fixanal), but also to correctly determine the equivalence point.

There are several ways to fix an equivalence point:

According to the intrinsic color of the ions of the element being determined, for example, manganese in the form of an anionMNO 4 -

By witness substance

Example: Ag + + Cl - "AgCl $

Ag + + CrO 4 "Ag 2 CrO $ 4 (bright orange color)

In the flask where it is required to determine the chlorine ion, a small amount of salt K 2 CrO 4 is added (witness). Then, the test substance is gradually added from the burette, while chloride ions are the first to react and a white precipitate (AgCl) is formed, i.e. PR AgCl<< ПР Ag2Cr O4.

Thus, an extra drop of silver nitrate will give a bright orange color, since all the chlorine has already reacted.

III. Using indicators: for example, acid-base indicators are used in the neutralization reaction: litmus, phenolphthalein, methyl orange - organic compounds that change color when moving from an acidic to an alkaline medium.

Indicators- organic dyes that change their color when the acidity of the medium changes.

Schematically (omitting intermediate forms), the indicator equilibrium can be represented as an acid-base reaction

HIn + H 2 O In - + H 3 O +

H2O
H++OH-

H + + H 2 O
H3O+

The area of ​​color transition of the indicator (position and interval) is influenced by all factors that determine the equilibrium constant (ionic strength, temperature, foreign substances, solvent), as well as the indicator.

Classification of methods of titrimetric analysis.

acid-base titration (neutralization): this method determines the amount of acid or alkali in the analyzed solution;

precipitation and complexation (argentometry)

Ag + + Cl - "AgCl $

redox titration (redoximetry):

a) permanganatometry (KMnO 4);

b) iodometry (Y 2);

c) bromatometry (KBrO 3);

d) dichromatometry (K 2 Cr 2 O 7);

e) cerimetry (Ce(SO 4) 2);

f) vanadometry (NH 4 VO 3);

g) titanometry (TiCl 3), etc.