   # Consider the following hypothetical data collected in two studies of the reaction 2 A + 2 B → C + 2 D Time(s) Experiment 1 [A] (mol/L) Experiment 2 [A] (mol/L) 0 1.0 × 10 −2 1.0 × 10 −2 10. 8.4 × 10 −3 5.0× 10 −3 20. 7.1 × 10 −3 2.5 × 10 −3 30. ? 1.3 × 10 −3 40. 5.0 × 10 −3 6.3 × 10 −4 In Experiment 1, [B] 0 = 10.0 M. In Experiment 2, [B] 0 = 20.0 M. Rate = − Δ [ A ] Δ t a. Use the concentration versus time data to determine the rate law for the reaction. b. Solve for the value of the rate constant (k) for the reaction. Include units. c. Calculate the concentration of A in Experiment 1 at t =30.s ### 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 110CP
Textbook Problem
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## Consider the following hypothetical data collected in two studies of the reaction 2 A + 2 B → C + 2 D Time(s) Experiment 1 [A] (mol/L) Experiment 2 [A] (mol/L) 0 1.0 × 10−2 1.0 × 10−2 10. 8.4 × 10−3 5.0× 10−3 20. 7.1 × 10−3 2.5 × 10−3 30. ? 1.3 × 10−3 40. 5.0 × 10−3 6.3 × 10−4 In Experiment 1, [B]0 = 10.0 M.In Experiment 2, [B]0 = 20.0 M. Rate = − Δ [ A ] Δ t a. Use the concentration versus time data to determine the rate law for the reaction.b. Solve for the value of the rate constant (k) for the reaction. Include units.c. Calculate the concentration of A in Experiment 1 at t =30.s

(a)

Interpretation Introduction

Interpretation: The rate law for the given reaction is to be determined by the use of the concentration verses time data. The value of rate constant is to be solved. The concentration of A is to be calculated in experiment 1 at t=30s.

Concept introduction: The rate law or rate equation is the mathematical relation between the rate of the reaction and the concentration of the reactant.

The straight line plot between ln[A] verses time always represents the first order reaction.

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

The concentration of reactant at any time is determined with the help of concentration verses time plot.

To determine: The rate law for the given reaction.

### Explanation of Solution

Explanation

Given

The stated reaction is,

2A+2BC+2D

A very high initial concentration values for the reactant B in both the experiments.

The common expression for the rate law is given by the equation,

Rate=k[A]X[B]Y

Where,

• X and Y are the experimentally determined values.

The rate equation according to the given chemical reaction is given as,

Rate=k[A]2[B]2

In the experiment 1 and 2, concentration of [B] is quite higher than that of the [A]

(b)

Interpretation Introduction

Interpretation: The rate law for the given reaction is to be determined by the use of the concentration verses time data. The value of rate constant is to be solved. The concentration of A is to be calculated in experiment 1 at t=30s.

Concept introduction: The rate law or rate equation is the mathematical relation between the rate of the reaction and the concentration of the reactant.

The straight line plot between ln[A] verses time always represents the first order reaction.

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

The concentration of reactant at any time is determined with the help of concentration verses time plot.

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

(c)

Interpretation Introduction

Interpretation: The rate law for the given reaction is to be determined by the use of the concentration verses time data. The value of rate constant is to be solved. The concentration of A is to be calculated in experiment 1 at t=30s.

Concept introduction: The rate law or rate equation is the mathematical relation between the rate of the reaction and the concentration of the reactant.

The straight line plot between ln[A] verses time always represents the first order reaction.

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

The concentration of reactant at any time is determined with the help of concentration verses time plot.

To determine: The concentration of [A] in experiment 1 at t=30s.

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