Chemistry: An Atoms First Approach
Chemistry: An Atoms First Approach
2nd Edition
ISBN: 9781305079243
Author: Steven S. Zumdahl, Susan A. Zumdahl
Publisher: Cengage Learning
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Textbook Question
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Chapter 11, Problem 33E

The reaction

I ( a q ) + OCl ( a q ) IO ( a q ) + Cl ( a q )

was studied, and the following data were obtained:

[I]0(mol/L) [OCl]0(mol/L) Initial Rate (mol/L · s)
0.12 0.18 7.91 × 10−2
0.060 0.18 3.95 × 10−2
0.030 0.090 9.88 × 10−3
0.24 0.090 7.91 × 10−2

a. What is the rate law?

b. Calculate the value of the rate constant.

c. Calculate the initial rate for an experiment where both I·and OCl are initially present at 0.15 mol/L.

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: A reaction between I and OCl certain data related to this reaction is given. The rate law, initial rate and the value of the rate constant 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,

I(aq)+OCl(aq)IO(aq)+Cl(aq)

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

Rate=k[I]m[OCl]n

Where,

  • [I] and [OCl] are the concentrations of I and OCl .
  • 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 [I] and [OCl] for the first two experiments in the above expression.

Rate1=k[0.12]m[0.18]n

Rate2=k[0.060]m[0.18]n

According to the given rate values in the table,

Rate2Rate1=3.95×102mol/Ls7.91×102mol/Ls

Therefore,

k[0.060]m[0.18]nk[0.12]m[0.18]n=3.95×102mol/Ls7.91×102mol/Ls(0.01080.0216)m=0.50.5=(0.5)m

Simplify the above expression.

0.5=(0.5)mm=1

The value of n is calculated using the second and third result. Substitute the values of the concentration of [I] and [OCl] for the second and third experiments in the above expression.

Rate2=k[0.060]m[0.18]n

Rate3=k[0.030]m[0.090]n

According to the given rate values in the table,

Rate3Rate2=9.88×103mol/Ls3.95×102mol/Ls

Therefore,

k[0.030]m[0.090]nk[0.060]m[0.18]n=9.88×103mol/Ls3.95×102mol/Ls(0.00270.0108)n=0.250.25=(0.25)n

Simplify the above expression.

0.25=(0.25)nn=1

Substitute the values of m and n in the rate law expression.

Rate=k[I]1[OCl]1

Conclusion

The relation between the reaction rate and the concentration of the reactants is stated by the rate law. The rate law for the given reaction is, Rate=k[I]1[OCl]1 .

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: A reaction between I and OCl certain data related to this reaction is given. The rate law, initial rate and the value of the rate constant 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,

I(aq)+OCl(aq)IO(aq)+Cl(aq)

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

Rate=k[I]1[OCl]1

The given values for experiment 1 ,

[I]ο=0.12mol/L[OCl]ο=0.18mol/LRate=7.91×102mol/Ls

Substitute the value of rate, the concentration of I and the concentration of OCl in the rate expression.

Rate=k[I]1[OCl]17.91×102mol/Ls=k[0.12mol/L]1[0.18mol/L]1k=7.91×102mol/Ls[0.12mol/L]1[0.18mol/L]1

Simplify the above expression.

k=7.91×102mol/Ls[0.12mol/L]1[0.18mol/L]1=7.91×102mol/Ls0.0216mol2/L23.7L/mols_

Conclusion

The value of k for the given reaction is 3.7L/mols_ .

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation: A reaction between I and OCl certain data related to this reaction is given. The rate law, initial rate and the value of the rate constant 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,

I(aq)+OCl(aq)IO(aq)+Cl(aq)

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

Rate=k[I]1[OCl]1

The given concentration values are,

[I]ο=0.15mol/L[OCl]ο=0.15mol/L

The calculated rate constant value is 3.7L/mols .

Substitute the value of the rate constant, the concentration of I and the concentration of OCl in the rate expression.

Rate=k[I]1[OCl]1=(3.7L/mols)[0.15mol/L]1[0.15mol/L]1=0.083mol/Ls_

Conclusion

The initial rate for the given concentration values of I and OCl is 0.083mol/Ls_ .

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Chapter 11 Solutions

Chemistry: An Atoms First Approach

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