   # Consider the hypothetical reaction A + B +2C → 2 D + 3E In a study of this reaction three experiments were run at the same temperature. The rate is defined as −∆[B]/∆ t . Experiment 1: [A] 0 = 2.0 M [B] 0 = 1.0 × 10 −3 M [C] 0 = 1.0 M [B] (mol/L) Time(s) 2.7 × 10 −4 1.0 × 10 5 1.6 × 10 −4 2.0 × 10 5 1.1 × 10 −4 3.0 × 10 5 8.5 × 10 −5 4.0 × 10 5 6.9 × 10 −5 5.0 × 10 5 5.8 × 10 −5 6.0 × 10 5 Experiment 2: [A] 0 = 1.0 × 10 −2 M [B] 0 = 3.0 M [C] 0 = 1.0 M [A] (mol/L) Time(s) 8.9 × 10 −3 1.0 7.1 × 10 −3 3.0 5.5 × 10 −3 5.0 3.8 × 10 −3 8.0 2.9 × 10 −3 10.0 2.0 × 10 −3 13.0 Experiment 3: [A] 0 = 10.0 M [B] 0 = 5.0 M [C] 0 = 5.0 × 10 −1 M [C] (mol/L) Time(s) 0.43 1.0 × 10 −2 0.36 2.0 × 10 −2 0.29 3.0 × 10 −2 0.22 4.0 × 10 −2 0.15 5.0 × 10 −2 0.08 6.0 × 10 −2 Write the rate law for this reaction, and calculate the value of the rate constant. ### 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 111CP
Textbook Problem
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## Consider the hypothetical reaction A   +   B   +2C   →   2 D   +   3E In a study of this reaction three experiments were run at the same temperature. The rate is defined as −∆[B]/∆t.Experiment 1:[A]0 = 2.0 M      [B]0 = 1.0 × 10−3 M     [C]0 = 1.0 M [B] (mol/L) Time(s) 2.7 × 10−4 1.0 × 105 1.6 × 10−4 2.0 × 105 1.1 × 10−4 3.0 × 105 8.5 × 10−5 4.0 × 105 6.9 × 10−5 5.0 × 105 5.8 × 10−5 6.0 × 105 Experiment 2:[A]0 = 1.0 × 10−2M     [B]0 = 3.0 M     [C]0 = 1.0 M [A] (mol/L) Time(s) 8.9 × 10−3 1.0 7.1 × 10−3 3.0 5.5 × 10−3 5.0 3.8 × 10−3 8.0 2.9 × 10−3 10.0 2.0 × 10−3 13.0 Experiment 3:[A]0 = 10.0 M     [B]0 = 5.0 M     [C]0 = 5.0 × 10−1M [C] (mol/L) Time(s) 0.43 1.0 × 10−2 0.36 2.0 × 10−2 0.29 3.0 × 10−2 0.22 4.0 × 10−2 0.15 5.0 × 10−2 0.08 6.0 × 10−2 Write the rate law for this reaction, and calculate the value of the rate constant.

(a)

Interpretation Introduction

Interpretation: The rate law for the given reaction is to be written. The value of rate constant is to be calculated.

Concept introduction: The rate law or rate equation is a mathematical representation that relates the rate of the reaction with the concentration or pressure.

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.

The order of a reaction is the number or the index raise to the concentration term with respect to each component.

The order of reaction may or may not be equal to the stoichiometric coefficient.

Stoichiometric coefficient is the number which tells the number of the reactant or products in a chemical reaction.

The zero order reaction always gives the straight line plot of [reactant] Vs time.

The first order reaction always gives the straight line plot of ln[reactant] Vs time.

The second order reaction always gives the straight line plot of 1/[reactant] Vs time.

To determine: The rate law for the given reaction.

### Explanation of Solution

Explanation

Given

The given reaction is stated as,

A+B+2C2D+3E

There are three reactants are present in the given reaction. Therefore to calculate the rate law the following steps are observed.

Firstly the order of the reaction with respect to each reactant is to be calculate.

With the help of the given data the value of 1/[B] is determined and are given by the following expression,

 [B] (mol/L) 1[B] (mol/L) Time (s) 2.7×10−4 0.37×104 1.0×105 1.6×10−4 0.62×104 2.0×105 1.1×10−4 0.909×104 3.0×105 8.5×10−5 0.117×105 4.0×105 6.9×10−5 0.144×105 5.0×105 5.8×10−5 0.172×105 6.0×105

Table 1

With the help of the above determined values the plot of 1/[B] Vs time is drawn as,

Figure 1

The above figure clearly indicates that in the 1/[B] Vs time plot the straight line is observed therefore, the given reaction is second order with respect to reactant B .

With the help of the given data the value of ln[A] is determined and are given by the following expression,

 [A](mol/L) ln[A] Time(s) 8.9×10−3 −4.721 1

(b)

Interpretation Introduction

Interpretation: The rate law for the given reaction is to be written. The value of rate constant is to be calculated.

Concept introduction: The rate law or rate equation is a mathematical representation that relates the rate of the reaction with the concentration or pressure.

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.

The order of a reaction is the number or the index raise to the concentration term with respect to each component.

The order of reaction may or may not be equal to the stoichiometric coefficient.

Stoichiometric coefficient is the number which tells the number of the reactant or products in a chemical reaction.

The zero order reaction always gives the straight line plot of [reactant] Vs time.

The first order reaction always gives the straight line plot of ln[reactant] Vs time.

The second order reaction always gives the straight line plot of 1/[reactant] Vs time.

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

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