# The following data were obtained for the reaction 2ClO 2 ( a q ) + 2 OH − ( a q ) → ClO 3 − ( a q ) + ClO 2 − ( a q ) + H 2 O ( l ) where Rate = − Δ [ ClO 2 ] Δ t [ClO 2 ] 0 (mol/L) [OH − ] 0 (mol/L) Initial Rate (mol/L · s) 0.0500 0.100 5.75 × 10 −2 0.100 0.100 2.30 × 10 −1 0.100 0.0500 1.15 × 10 −1 a. Determine the rate law and the value of the rate constant. b. What would be the initial rate for an experiment with [ClO 2 ] 0 = 0.175 mol/L and [OH − ] 0 = 0.0844 mol/L?

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 36E
Textbook Problem
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## The following data were obtained for the reaction 2ClO 2 ( a q )   +   2 OH − ( a q ) → ClO 3 − ( a q ) + ClO 2 − ( a q ) + H 2 O ( l ) where     Rate   =   − Δ [ ClO 2 ] Δ t [ClO2]0(mol/L) [OH−]0(mol/L) Initial Rate (mol/L · s) 0.0500 0.100 5.75 × 10−2 0.100 0.100 2.30 × 10−1 0.100 0.0500 1.15 × 10−1 a. Determine the rate law and the value of the rate constant.b. What would be the initial rate for an experiment with [ClO2]0 = 0.175 mol/L and [OH−]0 = 0.0844 mol/L?

(a)

Interpretation Introduction

Interpretation: The data related to the rate of reaction at different initial concentrations of [ClO2] and [OH] is given for the reaction between ClO2 and OH . The rate law, the value of the rate constant and the initial rate of the reaction for the given values of concentration of [ClO2] and [OH] are to be calculated.

Concept introduction: The relation between the reaction rate and the concentration of the reactants is stated by the rate law.

### Explanation of Solution

Given

The stated reaction is,

2ClO2(aq)+2OH(aq)ClO3(aq)+ClO2(aq)+H2O(l)

The rate law for the given reaction is calculated by the expression,

Rate=k[ClO2]m[OH]n

Where,

• [ClO2] and [OH] are the concentrations of ClO2 and OH .
• k is the rate constant.

The values of m and n are calculated by the comparison of the different rate values from the given table.

The value of m is calculated using the first and second result. Substitute the values of the concentration of [ClO2] and [OH] for the first two experiments in the above expression.

Rate1=k[0.0500]m[0.100]n

Rate2=k[0.100]m[0.100]n

According to the given rate values in the table,

Rate2Rate1=2.30×101mol/Ls5.75×102mol/Ls

Therefore,

k[0.100]m[0.100]nk[0.0500]m[0.100]n=2.30×101mol/Ls5.75×102mol/Ls(0.1000.0500)m=44=(2)m

Simplify the above expression.

4=(2)mm=2

The value of n is calculated using the second and third result. Substitute the values of the concentration of [ClO2] and [OH] for the second and the third experiment in the above expression.

Rate2=k[0.100]m[0.100]n

Rate3=k[0.100]m[0.0500]n

According to the given rate values in the table,

Rate3Rate2=1

(b)

Interpretation Introduction

Interpretation: The data related to the rate of reaction at different initial concentrations of [ClO2] and [OH] is given for the reaction between ClO2 and OH . The rate law, the value of the rate constant and the initial rate of the reaction for the given values of concentration of [ClO2] and [OH] are to be calculated.

Concept introduction: The relation between the reaction rate and the concentration of the reactants is stated by the rate law.

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