   # Hydrogen peroxide, H 2 O 2 (aq), decomposes to H 2 O( ℓ ) and O 2 (g) in a reaction that is first-order in H 2 O 2 and has a rate constant k = 1.06 × 10 −3 min −1 at a given temperature. (a) How long will it take for 15% of a sample of H 2 O 2 to decompose? (b) How long will it take for 85% of the sample to decompose? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 19PS
Textbook Problem
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## Hydrogen peroxide, H2O2(aq), decomposes to H2O(ℓ) and O2(g) in a reaction that is first-order in H2O2 and has a rate constant k = 1.06 × 10−3 min−1 at a given temperature. (a) How long will it take for 15% of a sample of H2O2 to decompose? (b) How long will it take for 85% of the sample to decompose?

(a)

Interpretation Introduction

Interpretation:

The time taken for 15% of sample to decompose has to be given.

Concept introduction:

Rate law or rate equation: The relationship between the reactant concentrations and reaction rate is expressed by an equation.

aA + bBxXRate of reaction = k [A]m[B]n

Rate constant, k: It is a proportionality constant that relates rate and concentration at a given temperature.

### Explanation of Solution

The time required for the reaction is calculated as,

Reactionrate = k [H2O2].Given:The reaction is first order reaction,rate law is , ln[H2O2]t=-kt+ln[H2O2]0time = ?Therefore,ln[H2O2]t=- kt+ ln[H2O2]0ln (85 mol/L)     = (1

(b)

Interpretation Introduction

Interpretation:

The time taken for 85% of sample to decompose has to be given.

Concept introduction:

Rate law or rate equation: The relationship between the reactant concentrations and reaction rate is expressed by an equation.

aA + bBxXRate of reaction = k [A]m[B]n

Rate constant, k: It is a proportionality constant that relates rate and concentration at a given temperature.

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