Chapter 17, Problem 33PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# You titrate 25.0 mL of 0.10 M NH3 with 0.10 M HCl. (a) What is the pH of the NH3 solution before the titration begins? (b) What is the pH at the equivalence point? (c) What is the pH at the halfway point of the titration? (d) What indicator in Figure 17.11 could be used to detect the equivalence point? (e) Calculate the pH of the solution after adding 5.00, 15.0, 20.0, 22.0, and 30.0 mL of the acid. Combine this information with that in parts (a)–(c) and plot the titration curve.

(a)

Interpretation Introduction

Interpretation:

The value of pH has to be calculated at the various points during the titration between HCl and NH3. The value of pH for the original solution of NH3 has to be calculated.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution. This method is used to determine the concentration an acid in the solution by titrating it against a base.

For strong acid-weak base titration, the pH value can be calculated at various points before and after the equivalence point. The equilibrium established during the titration of HCl with NH3 is represented as,

NH3(aq)+ HCl(aq)NH4+(aq)+Cl(aq)

Calculation of pH at various points is done as follows,

(1) The pH value before the titration can be calculated by using Kb and its relation with OH ion concentration.

Kb=[OH](eq)[BH+](eq)[B](eq) (1)

(2) The pH calculation just before the equivalence point,

As the addition of HCl is done, there will be the formation of buffer solution NH4+/NH3. The pH calculation for buffer solution is done by using the Henderson-Hasselbalch equation.

pH=pKa+log[Base][conjugateacid] (2)

At the midpoint of the titration, the concentration of acid and its conjugate base is equal. Therefore pH value at midpoint will be given as

pH=pKa+log[conjugatebase][acid]

Substitute, [conjugatebase]for[acid].

pH=pKa+log[conjugatebase][conjugatebase]=pKa+log(1)=pKa+0=pKa

Therefore, pH the value at the midpoint is equal to pKa.

(3) The pH calculation the equivalence point.

At equivalence point, all the base will be neutralized, and there will be only NH4+. The H3O+ will be produced due to the hydrolysis of Ammonium ion at the equivalence point. The hydrolysis equilibrium is represented as,

NH4+(aq)+H2O(l)H3O+(aq)+NH3(aq)

By using the value of Ka for the ammonium ion, the concentration of H3O+ can be calculated. Thus the value of pH is less than 7 at equivalence point for the strong acid-weak base titrations.

The relation between Ka and Kb for a weak acid and its conjugate base is given as,

Kw=(Ka)(Kb) (3)

Explanation

The pH value before the titration can be calculated by using Kb and its relation with OHâˆ’ ion concentration.

Kb=[OHâˆ’](eq)[BH+](eq)[B](eq)

Given:

Refer to the Appendix I in the textbook for the value of Kb.

The value of Kb for ammonia is 1.8Ã—10âˆ’5.

The initial concentration of NH3 is 0.10â€‰â€‹M.

The initial concentration of HCl is 0.10Â M.

The volume of the solvent is 25Â mL.

Therefore the volume of the solvent is 0.025Â L.

ICE table (1) gives the ionization reaction of NH3.

EquationNH3(aq)+H2O(l)â‡ŒOHâˆ’(aq)+NH4+(aq)Initial(molâ‹…L)0.10000Change(molâ‹…Lâˆ’1)âˆ’x+x+xAfterâ€‰reaction(molâ‹…Lâˆ’1)0.100âˆ’x+x+x

From the ICE table (1),

The concentration of NH3 left after the reaction is (0.100âˆ’x)â€‰molâ‹…Lâˆ’1.

The concentration of ammonium ion produced after the reaction is xâ€‰molâ‹…Lâˆ’1.

The concentration of OHâˆ’ produced after the reaction is xâ€‰molâ‹…Lâˆ’1

(b)

Interpretation Introduction

Interpretation:

The value of pH has to be calculated at the various points during the titration between HCl and NH3.  The value of pH at equivalence point has to be calculated.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution. This method is used to determine the concentration an acid in the solution by titrating it against a base.

For strong acid-weak base titration, the pH value can be calculated at various points before and after the equivalence point. The equilibrium established during the titration of HCl with NH3 is represented as,

NH3(aq)+ HCl(aq)NH4+(aq)+Cl(aq)

Calculation of pH at various points is done as follows,

(1) The pH value before the titration can be calculated by using Kb and its relation with OH ion concentration.

Kb=[OH](eq)[BH+](eq)[B](eq) (1)

(2) The pH calculation just before the equivalence point,

As the addition of HCl is done, there will be the formation of buffer solution NH4+/NH3. The pH calculation for buffer solution is done by using the Henderson-Hasselbalch equation.

pH=pKa+log[Base][conjugateacid] (2)

At the midpoint of the titration, the concentration of acid and its conjugate base is equal. Therefore pH value at midpoint will be given as

pH=pKa+log[conjugatebase][acid]

Substitute, [conjugatebase]for[acid].

pH=pKa+log[conjugatebase][conjugatebase]=pKa+log(1)=pKa+0=pKa

Therefore, pH the value at the midpoint is equal to pKa.

(3) The pH calculation the equivalence point.

At equivalence point, all the base will be neutralized, and there will be only NH4+. The H3O+ will be produced due to the hydrolysis of Ammonium ion at the equivalence point. The hydrolysis equilibrium is represented as,

NH4+(aq)+H2O(l)H3O+(aq)+NH3(aq)

By using the value of Ka for the ammonium ion, the concentration of H3O+ can be calculated. Thus the value of pH is less than 7 at equivalence point for the strong acid-weak base titrations.

The relation between Ka and Kb for a weak acid and its conjugate base is given as,

Kw=(Ka)(Kb) (3)

(c)

Interpretation Introduction

Interpretation:

The value of pH is to be calculated at the various points during the titration between HCl and NH3. The value of pH at halfway point of the titration has to be calculated.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution. This method is used to determine the concentration an acid in the solution by titrating it against a base.

For strong acid-weak base titration, the pH value can be calculated at various points before and after the equivalence point. The equilibrium established during the titration of HCl with NH3 is represented as,

NH3(aq)+ HCl(aq)NH4+(aq)+Cl(aq)

Calculation of pH at various points is done as follows,

(1) The pH value before the titration can be calculated by using Kb and its relation with OH ion concentration.

Kb=[OH](eq)[BH+](eq)[B](eq) (1)

(2) The pH calculation just before the equivalence point,

As the addition of HCl is done, there will be the formation of buffer solution NH4+/NH3. The pH calculation for buffer solution is done by using the Henderson-Hasselbalch equation.

pH=pKa+log[Base][conjugateacid] (2)

At the midpoint of the titration, the concentration of acid and its conjugate base is equal. Therefore pH value at midpoint will be given as

pH=pKa+log[conjugatebase][acid]

Substitute, [conjugatebase]for[acid].

pH=pKa+log[conjugatebase][conjugatebase]=pKa+log(1)=pKa+0=pKa

Therefore, pH the value at the midpoint is equal to pKa.

(3) The pH calculation the equivalence point.

At equivalence point, all the base will be neutralized, and there will be only NH4+. The H3O+ will be produced due to the hydrolysis of Ammonium ion at the equivalence point. The hydrolysis equilibrium is represented as,

NH4+(aq)+H2O(l)H3O+(aq)+NH3(aq)

By using the value of Ka for the ammonium ion, the concentration of H3O+ can be calculated. Thus the value of pH is less than 7 at equivalence point for the strong acid-weak base titrations.

The relation between Ka and Kb for a weak acid and its conjugate base is given as,

Kw=(Ka)(Kb) (3)

(d)

Interpretation Introduction

Interpretation:

The value of pH has to be calculated at the various points during the titration between HCl and NH3. The best indicator that can be used to detect the equivalence point is to be chosen for the titration has to be determined.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution. This method is used to determine the concentration an acid in the solution by titrating it against a base.

For strong acid-weak base titration, the pH value can be calculated at various points before and after the equivalence point. The equilibrium established during the titration of HCl with NH3 is represented as,

NH3(aq)+ HCl(aq)NH4+(aq)+Cl(aq)

Calculation of pH at various points is done as follows,

(1) The pH value before the titration can be calculated by using Kb and its relation with OH ion concentration.

Kb=[OH](eq)[BH+](eq)[B](eq) (1)

(2) The pH calculation just before the equivalence point,

As the addition of HCl is done, there will be the formation of buffer solution NH4+/NH3. The pH calculation for buffer solution is done by using the Henderson-Hasselbalch equation.

pH=pKa+log[Base][conjugateacid] (2)

At the midpoint of the titration, the concentration of acid and its conjugate base is equal. Therefore pH value at midpoint will be given as

pH=pKa+log[conjugatebase][acid]

Substitute, [conjugatebase]for[acid].

pH=pKa+log[conjugatebase][conjugatebase]=pKa+log(1)=pKa+0=pKa

Therefore, pH the value at the midpoint is equal to pKa.

(3) The pH calculation the equivalence point.

At equivalence point, all the base will be neutralized, and there will be only NH4+. The H3O+ will be produced due to the hydrolysis of Ammonium ion at the equivalence point. The hydrolysis equilibrium is represented as,

NH4+(aq)+H2O(l)H3O+(aq)+NH3(aq)

By using the value of Ka for the ammonium ion, the concentration of H3O+ can be calculated. Thus the value of pH is less than 7 at equivalence point for the strong acid-weak base titrations.

The relation between Ka and Kb for a weak acid and its conjugate base is given as,

Kw=(Ka)(Kb) (3)

(e)

Interpretation Introduction

Interpretation:

The value of pH is to be calculated at the various points during the titration between HCl and NH3. The value of pH when 5mL,15 mL, 20 mL,22mL and 30 mL HCl is added to the NH3 solution. A titration curve is to be plotted by using pH values calculated in part (a), (b), (c) and (d) has to be calculated and plotted.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution. This method is used to determine the concentration an acid in the solution by titrating it against a base.

For strong acid-weak base titration, the pH value can be calculated at various points before and after the equivalence point. The equilibrium established during the titration of HCl with NH3 is represented as,

NH3(aq)+ HCl(aq)NH4+(aq)+Cl(aq)

Calculation of pH at various points is done as follows,

(1) The pH value before the titration can be calculated by using Kb and its relation with OH ion concentration.

Kb=[OH](eq)[BH+](eq)[B](eq) (1)

(2) The pH calculation just before the equivalence point,

As the addition of HCl is done, there will be the formation of buffer solution NH4+/NH3. The pH calculation for buffer solution is done by using the Henderson-Hasselbalch equation.

pH=pKa+log[Base][conjugateacid] (2)

At the midpoint of the titration, the concentration of acid and its conjugate base is equal. Therefore pH value at midpoint will be given as

pH=pKa+log[conjugatebase][acid]

Substitute, [conjugatebase]for[acid].

pH=pKa+log[conjugatebase][conjugatebase]=pKa+log(1)=pKa+0=pKa

Therefore, pH the value at the midpoint is equal to pKa.

(3) The pH calculation the equivalence point.

At equivalence point, all the base will be neutralized, and there will be only NH4+. The H3O+ will be produced due to the hydrolysis of Ammonium ion at the equivalence point. The hydrolysis equilibrium is represented as,

NH4+(aq)+H2O(l)H3O+(aq)+NH3(aq)

By using the value of Ka for the ammonium ion, the concentration of H3O+ can be calculated. Thus the value of pH is less than 7 at equivalence point for the strong acid-weak base titrations.

The relation between Ka and Kb for a weak acid and its conjugate base is given as,

Kw=(Ka)(Kb) (3)

The value of pH at different volume addition of HCl and the corresponding point on the curve is given as,

Points volume of HCl       (mL)pHa011.13b59.85c159.07d208.65e228.38f302.04

Graph between pH and volume of HCl added is plotted as,

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