   Chapter 12, Problem 93AE

Chapter
Section
Textbook Problem

# Consider the reaction 3A+B+C → D+E where the rate law is defined as − Δ [ A ] Δ t = k [ A ] 2 [ B ] [ C ] An experiment is carried out where [B]0 = [C]0 = 1.00 M and [A]0 = 1.00 × 10−4M.a. If after 3.00 min, [A] = 3.26 × 10−5M, calculate the value of k.b. Calculate the half-life for this experiment.c. Calculate the concentration of B and the concentration of A after 10.0 min.

(a)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 3.00min are 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

Explanation

Given

The initial concentration of [A]0 is 1.0×104M .

The initial concentration of [B]0 is 1.0M .

The initial concentration of [C]0 is 1.0M .

The initial concentration of A after 3.00min is 3.26×105M .

The stated reaction is,

3A+B+CD+E

The rate law is represented as,

Rate=Δ[A]Δt=k[A]2[B][C]

The graph of 1A versus time (min) is plotted for the given concentration of A

Since, the obtained graph is a straight line, hence, the order of the reaction is second. The slope of graph is 6891.6

(b)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 3.00min are 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

To determine: The half life of the given reaction.

(c)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 3.00min are 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

To determine: The concentration of A 10min .

(d)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 3.00min are 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

To determine: The concentration of B after 10min .

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