   Chapter 12, Problem 95CWP

Chapter
Section
Textbook Problem

# The reaction A ( a q )  + B ( a q ) → products ( a q ) was studied, and the following data were obtained: [Al]0 (mol/L) [B]0 (mol/L) Initial Rate (mol/L·s) 0.12 0.18 3.46 × 10−2 0.060 0.12 1.15 × 10−2 0.030 0.090 4.32 × 10−3 0.24 0.090 3.46 × 10−2 What is the order of the reaction with respect to A? What is the order of the reaction with respect to B? What is the value of the rate constant for the reaction?

Interpretation Introduction

Interpretation: The data analysis table for the initial concentrations of two reactants and initial rate is given. By using these values, the order of recation with respect to each reactant and the value of rate constant is to be calculated.

Concept introduction: All chemical reactions follow rate law. This law shows that how the rate of a chemical reaction depends on the concentration of reactants.

Example: Suppose a chemical reaction is as follows:

A+BC+D

According to the rate law, rate of a chemical reaction is expressed by following expression.

Rate=k[A]m[B]n

To determine: The order of the chemical reaction with respect to A and B as well as rate constant of the reaction.

Explanation

Given

Data analysis table along with the chemical reaction is as follows:

A(aq)+B(aq)products(aq)

 [A]0(mol/L) [B]0(mol/L) Initial  rate(mol/L⋅s) 0.12 0.18 3.46×10−2 0.060 0.12 1.15×10−2 0.030 0.090 4.32×10−3 0.24 0.090 3.46×10−2

Rate law for the reaction is calculated by using the formula,

Rate=k[A]m[B]n

Where,

• k is rate constantof reaction.
• [A] is the concentration of reactant A.
• [B] is the concentration of reactant B.
• m is the order of reaction with respect to reactant A.
• n is the order of reaction with respect to reactant B.

For the first row of table:

Substitute the value of rate and concentrations [A]and[B] in the above formula.

3.46×102=k(0.12)m(0.18)n (1)

For the second  row of table:

Substitute the value of rate and concentrations [A]and[B] in the above formula.

1.15×102=k(0.060)m(0.12)n (2)

For the third row of table:

Substitute the value of rate and concentrations [A]and[B] in the above formula.

4.32×103=k(0.030)m(0

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