   # Two isomers (A and B) of a given compound dimerize as follows: 2A → k 1 A 2 2B → k 2 B 2 Both processes are known to be second order in reactant, and k 1 is known to be 0.250 L/mol · s at 25°C. In a particular experiment A and B were placed in separate containers at 25°C, where [A] 0 = 1.00 × 10 −2 M and [B] 0 = 2.50 × 10 −2 M . It was found that after each reaction had progressed for 3.00 min, [A] = 3.00[B]. In this case the rate laws are defined as Rate = − Δ [ A ] Δ t = k 1 [ A ] 2 R a t e = − Δ [ B ] Δ t = k 2 [ B ] 2 a. Calculate the concentration of A 2 after 3.00 min. b. Calculate the value of k 2 . c. Calculate the half-life for the experiment involving A. ### 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 104CP
Textbook Problem
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## Two isomers (A and B) of a given compound dimerize as follows: 2A → k 1 A 2 2B → k 2 B 2 Both processes are known to be second order in reactant, and k1is known to be 0.250 L/mol · s at 25°C. In a particular experiment A and B were placed in separate containers at 25°C, where [A]0 = 1.00 × 10−2M and [B]0 = 2.50 × 10−2 M. It was found that after each reaction had progressed for 3.00 min, [A] = 3.00[B]. In this case the rate laws are defined as Rate = − Δ [ A ] Δ t = k 1 [ A ] 2 R a t e = − Δ [ B ] Δ t = k 2 [ B ] 2 a. Calculate the concentration of A2 after 3.00 min.b. Calculate the value of k2 .c. Calculate the half-life for the experiment involving A.

(a)

Interpretation Introduction

Interpretation: The concentration of the product is to be calculated corresponding to the given reactions and data. The value of rate constant k2 is to be calculated. The half-life for the experiment involving A is to be stated.

Concept introduction: Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

Half-life is the time in which any species decreased by half of its original amount.

To determine: The concentration of the product A2 after 3 min

### Explanation of Solution

Explanation

Given

The given reaction is stated as,

2Ak1A22Bk2B2

Both are the second order reaction processes.

The rate constant k1=0.250L/mols

The initial concentration of [A]0=1.00×102M

The initial concentration of [B]0=2.50×102M

t=3min

After the three minute of the concentration of the reaction relates as [A]=3[B]

The rate constant for second order reaction is given by the equation.

k1=1t[1[A]11[A]0]

• [A]° is the initial concentration of the reactant.
• [A]1 is the final concentration of the reactant.
• t is the time.
• k1 is the rate constant.

Substitute the value of [A]0,t and k1 in the above equation.

k1=1t[1[A]11[A]0]0.250L/mols=13s[1[A]111×102M]0

(b)

Interpretation Introduction

Interpretation: The concentration of the product is to be calculated corresponding to the given reactions and data. The value of rate constant k2 is to be calculated. The half-life for the experiment involving A is to be stated.

Concept introduction: Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

Half-life is the time in which any species decreased by half of its original amount.

To determine: The value of the rate constant k2 for the given reaction.

(c)

Interpretation Introduction

Interpretation: The concentration of the product is to be calculated corresponding to the given reactions and data. The value of rate constant k2 is to be calculated. The half-life for the experiment involving A is to be stated.

Concept introduction: Rate constant is a proportionality coefficient that relates the rate of chemical reaction at a specific temperature to the concentration of the reactant or the product.

Half-life is the time in which any species decreased by half of its original amount.

To determine: The half-life of the reactant A .

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