   # A certain reaction has the following general form: aA → bB At a particular temperature and [A] 0 = 2.00 × 10 −2 M , concentration versus time data were collected for this reaction, and a plot of ln[A] versus time resulted in a straight line with a slope value of −2.97 × 10 −2 min −1 . a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to 2.50 × 10 −3 M ? ### Chemistry: An Atoms First Approach

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

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 38E
Textbook Problem
36 views

## A certain reaction has the following general form: aA → bB At a particular temperature and [A]0 = 2.00 × 10−2 M, concentration versus time data were collected for this reaction, and a plot of ln[A] versus time resulted in a straight line with a slope value of −2.97 × 10−2 min−1.a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction.b. Calculate the half-life for this reaction.c. How much time is required for the concentration of A to decrease to 2.50 × 10−3 M?

(a)

Interpretation Introduction

Interpretation: The general reaction, initial concentration of reactant and slope of straight line graph of ln[A] versus time is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

### Explanation of Solution

The given reaction is,

aAbB

The rate law gives the relation between reaction rate and concentration of reactants. The rate law is represented as,

Rate=k[A]a

Where,

• k isthe rate constant.
• [A] isthe concentration of reactant.
• a is the reaction order of reactant.

The integral rate law equation of first order reaction is,

ln[A]=kt+ln[A]0

The order of the given reaction can be determined by using following parameters,

• For first order reaction, ln[A]vstime graph is straight line
• For second order reaction, 1[A]vstime graph is straight line.
• For zero order reaction, [A]vstime graph is straight line.

It is given that, theplot of ln[A]vstime graphis a straight line. It means that the given reaction is the first order (a=1) reaction.

The integral rate law equation of first order reaction is,

ln[A]=kt+ln[A]0 (1)

Where,

• k isthe rate constant

(b)

Interpretation Introduction

Interpretation: The general reaction, initial concentration of reactant and slope of straight line graph of ln[A] versus time is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

(c)

Interpretation Introduction

Interpretation: The general reaction, initial concentration of reactant and slope of straight line graph of ln[A] versus time is given. The answers are to be given for each option.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

The half-life of the first order reaction is calculated using the formula,

t12=0.693k

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