   Chapter 12, Problem 40E

Chapter
Section
Textbook Problem

# A certain reaction has the following general form: aA   →   bB At a particular temperature and [A]0 = 2.80 × 10−3 M, concentration versus time data were co11ected for this reaction, and a plot of 1/[A] versus time resulted in a straight line with a slope value of + 3.60 × 10−2 L/mol · s.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 7.00 × 10−4 M?

(a)

Interpretation Introduction

Interpretation: The general reaction is given. The initial concentration and slope value of 1/[A] versus time graph is given. Based on these data answers are to be given.

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.

To determine: The rate law, the integrated rate law and the value of rate constant for the given reaction.

Explanation

To determine: The rate law for the given reaction.

Given

The initial concentration is 2.80×103M .

The value of slope is 3.60×102 .

The given general equation 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 is rate constant.
• [A] is concentration of reactant.
• a is reaction order.

To determine: The integrated rate law for the given reaction.

Given

The initial concentration of A is 2.80×103M .

The given general equation is,

aAbB

The rate law in integral form is known as integrated rate law. It gives the relation between concentration of reactant or product with time

(b)

Interpretation Introduction

Interpretation: The general reaction is given. The initial concentration and slope value of 1/[A] versus time graph is given. Based on these data answers are to be given.

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.

c

Interpretation Introduction

Interpretation: The general reaction is given. The initial concentration and slope value of 1/[A] versus time graph is given. Based on these data answers are to be given.

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.

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