   Chapter 14.4, Problem 14.8CYU

Chapter
Section
Textbook Problem

The catalyzed decomposition of hydrogen peroxide is first-order in [H2O2]. It was found that the concentration of H2O2 decreased from 0.24 M to 0.060 M over a period of 282 minutes. What is the half-life of H2O2? What is the rate constant for this reaction? What is the initial rate of decomposition at the beginning of this experiment (when [H2O2] = 0.24 M)?

Interpretation Introduction

Interpretation:

The rate constant, half-life and the initial rate of decomposition of hydrogen peroxide has to be given.

Concept Introduction:

Integrated rate law for first order reaction:

Consider A as substance, that gives the product based on the equation,

aAproducts

Where a= stoichiometric co-efficient of reactant A.

Consider the reaction has first-order rate law,

Rate=-Δ[A]Δt=k[A]

The integrated rate law equation can be given as,

ln[A]t[A]o=-kt

The above expression is called integrated rate law for first order reaction.

Half-life for first order reactions:

The half-life for the first order reaction is constant and it is independent of the reactant concentration.

Half-life period of first order reaction can be calculated using the equation,

t1/2=0.693k

Explanation

The rate constant, half-life and the initial rate of decomposition of hydrogen peroxide is calculated as,

Given:Rate = k [H2O2]t = 282 min [H2O2]t=0.060M;[H2O2]0=0.24M;t1/2 = ?;  k = ?Calculate the rate constant:_lan[H2O2]t[H2O2]0=-ktlan0.060M0.24M=-k(282min)k = 1.386282 = 4.9×10-3min-1Calculatethehalf-life:_t1/2=0

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