   # The decomposition of hydrogen peroxide was studied, and the following data were obtained at a particular temperature: Time(s) [H 2 O 2 ](mol/L) 0 1.00 120 ± 1 0.91 300 ± 1 0.78 600 ± 1 0.59 1200 ± 1 0.37 1800 ± 1 0.22 2400 ± 1 0.13 3000 ± 1 0.082 3600 ± 1 0.050 Assuming that Rate = − Δ [ H 2 O 2 ] Δ t determine the rate law, the integrated rate law, and the value of the rate constant. Calculate [H 2 O 2 ] at 4000. s after the start of the reaction. ### 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 37E
Textbook Problem
125 views

## The decomposition of hydrogen peroxide was studied, and the following data were obtained at a particular temperature: Time(s) [H2O2](mol/L) 0 1.00 120 ± 1 0.91 300 ± 1 0.78 600 ± 1 0.59 1200 ± 1 0.37 1800 ± 1 0.22 2400 ± 1 0.13 3000 ± 1 0.082 3600 ± 1 0.050 Assuming that Rate   =   − Δ [ H 2 O 2 ] Δ t determine the rate law, the integrated rate law, and the value of the rate constant. Calculate [H2O2] at 4000. s after the start of the reaction.

Interpretation Introduction

Interpretation: The table based on the decomposition of Hydrogen peroxide and equation for rate of reaction is given. The rate law, integrated rate law, the value of rate constant and the concentration of [H2O2] at 4000s after the start of reaction is to be calculated.

Concept introduction: Chemical kinetics determines the rate of a reaction. It is basically used to study the chemical processes.

To determine: The table based on the decomposition of Hydrogen peroxide and equation for rate of reaction is given. The rate law, integrated rate law, the value of rate constant and the concentration of [H2O2] at 4000s after the start of reaction.

### Explanation of Solution

Explanation

The rate law expression is given as,

Rate=k[H2O2]n

As the rate of reaction depends on the concentration of concentration of the reactants that are involved in the reaction. The rate law determines the relationship between the rate of the reaction and the concentration of the reactants that are involved in the reaction. As in the given data only one reactant is present that is Hydrogen peroxide, therefore the rate of reaction depends on the concentration of Hydrogen peroxide. Therefore, the rate law expression is given as,

Rate=k[H2O2]n

Where,

• k is the rate constant of the reaction.
• n is the order of the reaction.

The integrated rate law for the first order reaction for the given reaction is shown as,

ln[H2O2]t=kt+ln[H2O2]0

 Time (s) [H2O2] mole/L 1[H2O2] ln[H2O2] 0 1.00 1.00 0.00 120 0.91 1.098901 −0.09431 300 0.78 1.282051 −0.24846 600 0.59 1.694915 −0.52763 1200 0.37 2.702703 −0.99425 1800 0.22 4.545455 −1.51413 2400 0.13 7.692308 −2.04022 3000 0.082 12.19512 −2.50104 3600 0.050 20 −2.99573

Figure 1

The graph between [H2O2]mole/L and Time (s) is plotted as,

Figure 2

The graph between 1[H2O2] and Time (s) is plotted as,

Figure 3

The graph between ln[H2O2] and Time (s) is plotted as,

Figure 4

In the above graph, a straight line is obtained. Therefore, the given reaction is of first order. The integrated rate law for the first order reaction for the given reaction is shown as,

ln[H2O2]t=kt+ln[H2O2]0

Where,

• [H2O2]t is the concentration of Hydrogen peroxide at any time

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