   # Consider the hypothetical reaction A + B + 2C → 2D + 3E where the rate law is Rate = − Δ [ A ] Δ t = k [ A ] [ B ] 2 An experiment is carried out where [A] 0 = 1.0 × 10 −2 M , [B] 0 = 3.0 M, and [C] 0 = 2.0 M. The reaction is started, and after 8.0 seconds, the concentration of A is 3.8 × 10 −3 M . a. Calculate the value of k for this reaction. b. Calculate the half-life for this experiment. c. Calculate the concentration of A after 13.0 seconds. d. Calculate the concentration of C after 13.0 seconds. ### 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 58E
Textbook Problem
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## Consider the hypothetical reaction A   +   B   +   2C  → 2D   +   3E where the rate law is Rate   =   − Δ [ A ] Δ t   =   k [ A ] [ B ] 2 An experiment is carried out where [A]0 = 1.0 × 10−2 M, [B]0 = 3.0 M, and [C]0 = 2.0 M. The reaction is started, and after 8.0 seconds, the concentration of A is 3.8 × 10−3 M.a. Calculate the value of k for this reaction.b. Calculate the half-life for this experiment.c. Calculate the concentration of A after 13.0 seconds.d. Calculate the concentration of C after 13.0 seconds.

(a)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 8.0s 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 value of the rate constant (k) for the given reaction.

### Explanation of Solution

Explanation

Given

The initial concentration of [A]0 is 1.0×102M .

The initial concentration of [B]0 is 3.0M .

The initial concentration of [C]0 is 2.0M .

The initial concentration of A after 8.0s is 3.8×103M .

The stated reaction is,

A+B+2C2D+3E

The rate law is represented as,

Rate=Δ[A]Δt=k[A][B]2

The above reaction is assumed to be pseudo first order. Since, the initial concentration of B is very less as compared to A , therefore, change in its concentration is negligible, that is,

[B]0[B]

The simplified rate law is,

d[A]dt=k'[A]

Where, k' is rate constant, and it is equal to,

k'=k[B]02 (1)

The integral rate law equation of the first order reaction is,

ln[A]=k't+ln[A]0k'=ln[A]0ln[A]t

Where,

• [A]0 is the initial concentration of reactant A

(b)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 8.0s 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 8.0s 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 after 13.0s .

(d)

Interpretation Introduction

Interpretation: A hypothetical reaction and its rate law, initial concentration of reactants and the concentration A after 8.0s 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 C after 13.0s .

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