Chemistry & Chemical Reactivity, Hybrid Edition (with OWLv2 24-Months Printed Access Card)
Chemistry & Chemical Reactivity, Hybrid Edition (with OWLv2 24-Months Printed Access Card)
9th Edition
ISBN: 9781285462530
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
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Chapter 17, Problem 28PS

Assume you dissolve 0.235 g of the weak acid benzoic acid, C6H5CO2H, in enough water to make 1.00 × 102 mL of solution and then titrate the solution with 0.108 M NaOH.

C6H5CO2H(aq) + OH(aq) ⇄ C6H5CO2(aq) + H2O()

  1. (a) What was the pH of the original benzoic add solution?
  2. (b) What are the concentrations of all of the following ions at the equivalence point: Na+, H3O+, OH, and C6H5CO2?
  3. (c) What is the pH of the solution at the equivalence point?

a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The value of pH has to be calculated at the various points during the titration between C6H5COOH and NaOH. The value of pH, of the original solution of C6H5COOH.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution.

For weak acid-strong base titration the pH value can be calculated at various points before and after equivalence point. The equilibrium established during the titration of C6H5COOH with NaOH is represented as,

C6H5COOH(aq)+ OH(aq)H2O(l)+C6H5COONa(aq)

Ka and its relation with H3O+ ion concentration.

Ka=[H3O+](eq)[A](eq)[HA](eq) (1)

Explanation of Solution

The pH value before the titration can be calculated by using Ka and its relation with H3O+ ion concentration.

Ka=[H3O+](eq)[A](eq)[HA](eq)

Given:

Refer to the Apendix H in the textbook for the value of Ka.

The value of Ka for benzoic acid is 6.3×105.

The value of Kw for water is 1.0×1014.

The amount of C6H5COOH dissolved is 0.235 g.

Molar mass of C6H5COOH l is 122 gmol1.

Number of moles of C6H5COOH are calculated by using following expression,

Number of moles = weight of solute molar mass of solute(mol)

Substitute 0.235 g for weight of solute , 122 gmol1 for molar mass of solute.

Number of moles = 0.235 g122 gmol1=0.0019 mol

Therefore Number of moles of C6H5COOH are 0.0019 mol.

The  volume of the solvent is 0.100 L.

The initial concentration of C6H5COOH is calculated by using the expression,

Molarity=Number of molesvolume of the solvent(molL1)

Substitute 0.0019 mol for Number of moles, 0.100 L for volume of the solvent.Molarity=0.0019 mol0.100 L=0.019 molL1

Therefore initial concentration of C6H5COOH is 0.019 molL1.

ICE table (1) gives the dissociation of C6H5COOH.

EquationC6H5COOH(aq)+H2O(l)H3O+(aq)+C6H5COO(aq)Initial(molL1)0.01900Change(molL1)x+x+xAfterreaction(molL1)0.019x+x+x

There is an approximation, that the value of x is very small as comparison to 0.019 thus it can be neglected with respect to it.

Therefore, Concentration of benzoic acid left after reaction is 0.019 molL1.

The hydronium ion concentration is calculated by expression,

Ka=[H3O+](eq)[A](eq)[HA](eq)

Substitute x for [H3O+](eq), x for [A](eq), 0.019 for [HA](eq) and 6.3×105 for Ka.

6.3×105=(x)(x)(0.019)6.3×105=(x2)(0.019)

Rearrange for x,

x=(6.3×105)(0.019)x=1.09×103

Therefore, concentration of hydronium ion is 1.09×103.

Calculate the pH value by using following expression,

pH = log[H3O+]

Substitute 1.09×103 for [H3O+].

pH = log(1.09×103)=2.96

The value of pH for the original solution of benzoic acid is 2.96.

 (b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The value of pH is to be calculated at the various points during the titration between C6H5COOH and NaOH. The concentration of OH,H3O+,C6H5COO and Na+ has to be calculated at equivalence point.

Concept introduction:

Titration is a quantitative method to determine the quantity of an acid or base in a solution.

For weak acid-strong base titration the pH value can be calculated at various points before and after equivalence point. The equilibrium established during the titration of C6H5COOH with NaOH is represented as,

C6H5COOH(aq)+ OH(aq)H2O(l)+C6H5COONa(aq)

Ka and its relation with H3O+ ion concentration.

Ka=[H3O+](eq)[A](eq)[HA](eq) (1)

Explanation of Solution

The concentration value of OH, benzoate ion, H3O+ and Na+ is calculated below.

Given:

The concentration of NaOH is 0.108 molL1.

The volume of NaOH used to neutralize all the phenol is calculated.

Expression used for the neutralization is as follows,

C1V1=C2V2

Here,

  • C1 is the concentration of benzoic acid
  • V1 is the volume of benzoic acid.
  • C2 is the concentration of NaOH used.
  • V2 is the volume of NaOH used for the neutralization.

Substitute 0.019 molL1 for C1, 0.100 L for V1,0.108 molL1 for C2.

(0.019 molL1)(0.100 L)=(0.108 molL1)(V2)

Rearrange for V2,

V2=(0.019 molL1)(0.100L)(0.108 molL1)=0.0175 L

Therefore, volume of the NaOH used is 0.0175 L or 17.5 mL.

The calculation of moles is done by using the expression,

Numberof moles=concentration(molL1)volume(L)

The ICE table (2) for the reaction between NaOH and C6H5OH is given below,

EquationC6H5COOH(aq)+   OH(aq)H2O(l)+C6H5COONa(aq)Initial(mol)0.00190.00190Change(mol)0.00190.0019+0.0019Afterreaction(mol)000.0019

From ICE table (2),

Number of moles of benzoate ion produced after the reaction are 0.0019 mol.

The total volume after the reaction is calculated as,

totalvolume = 0.100(L)+0.0175 L=0.1175 L

Therefore, total volume after reaction is 0.1175 L.

Concentration calculations is done by using the expression,

concentration = Numberof molestotal volume(molL1)

Calculate the concentration of benzoate ion after reaction.

Substitute, 0.0019 mol for Numberof moles and 0.1175 L for volume.

concentration = 0.00190.1175 (molL1)=0.0161molL1

The concentration of benzoate ion after reaction is 0.0161molL1.

The C6H5COO ion produced will undergo hydrolysis in presence of water and the reaction equilibrium is written in ICE table (3).

EquationC6H5COO(aq)+H2O(l)OH(aq)+C6H5COOH(aq)Initial(molL1)0.016100Change(molL1)x+x+xAfterreaction(molL1)0.0161x+x+x

From ICE table (3),

Concentration of benzoate ion left after reaction is (0.0161x) molL1.

Concentration of benzoic acid produced after the reaction is xmolL1.

Concentration of OH produced after the reaction is xmolL1.

The value of x is very small as comparison to 0.0161 and thus it can be neglected.

Calculate the concentration of OH by using the equation (3).

The expression of Kb for benzoate ion from the ICE table (3) will be written as,

Kb=[C6H5COOH](eq)[OH](eq)[C6H5COO](eq)

Substitute, 0.158×109 for Kb, x for [OH](eq), x for [C6H5COOH](eq), (0.0161) for [C6H5COO](eq).

0.158×109=(x)(x)(0.0161)

Rearrange for x,

x=(0.158×109)(0.0161)=0.0025×109=0.158×105

Therefore value of OH concentration is 1.58×106molL1.

The value of C6H5COOH concentration is 1.58×106molL1.

The concentration of C6H5O at equivalence point is 0.0161 molL1.

The concentration of Na+ at equivalence point is equal to the initial concentration of benzoate ion before undergo hydrolysis i.e. 0.0161 molL1 .

Calculate the value of pOH by using the expression,

pOH = log[OH]

Substitute, 1.58×106 for [OH].

pOH = log(1.58×106)=(5.80)=5.80

Therefore, the value of pOH is 5.80.

Thus, the value of pH is calculated by using expression,

pH + pOH =14

Rearrange for pH,

pH  =14 pOH

Substitute, 5.80 for pOH.

pH  =145.808.20

Therefore, the value of pH at equivalence point is 8.20.

The pH value is used to calculate the concentration of hydronium ion at equivalence point.

Calculate the hydronium ion concentration by using expression,

pH = log[H3O+]

Rearrange for [H3O+],

[H3O+]=10(pH)

Substitute 8.60 for pH.

[H3O+]=10(8.20)=6.30×109

Therefore, hydronium ion concentration at equivalence point is 6.30×109molL1.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The value of pH has to be calculated at the various points during the titration between C6H5COOH and NaOH. 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.

For weak acid-strong base titration the pH value can be calculated at various points before and after equivalence point. The equilibrium established during the titration of C6H5COOH with NaOH is represented as,

C6H5COOH(aq)+ OH(aq)H2O(l)+C6H5COONa(aq)

Ka and its relation with H3O+ ion concentration.

Ka=[H3O+](eq)[A](eq)[HA](eq) (1)

Explanation of Solution

The addition of 17.5 mL NaOH will required to reach the equivalence point of titration. At equivalence point all the benzoic acid and hydroxide ions will be used only benzoate will be present. The hydrolysis of benzoate ion will produce a very small amount of OH ions. The pH calculation at equivalence point is given below.

Given:

The value of pH is calculated by using expression,

pH + pOH =14

Rearrange for pH,

pH  =14 pOH

Substitute, 5.80 for pOH.

pH  =145.808.20

Therefore, the value of pH at equivalence point is 8.20.

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Chapter 17 Solutions

Chemistry & Chemical Reactivity, Hybrid Edition (with OWLv2 24-Months Printed Access Card)

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