   Chapter 12, Problem 81AE

Chapter
Section
Textbook Problem

# A popular chemical demonstration is the “magic genie” procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is 70.0 kJ/mol. When the catalyst is added, the activation energy (at 20.°C) is 42.0 kJ/mol. Theoretically, to what temperature (°C) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at 20.°C? Assume the frequency factor A is constant, and assume the initial concentrations are the same.

Interpretation Introduction

Interpretation: The activation energy of decomposition reaction of hydrogen peroxideat 20°C with catalyst and at unknown temperature without catalyst is given. Based on these data,the temperature of uncatalyzed reaction for the decomposition of hydrogen peroxideis to be calculated.

Concept introduction: The substance that speeds up the rate of reaction without getting consumed itself in a chemical reaction is known as catalyst.

The relationship between the rate constant and temperature is given by the Arrhenius equation,

k=AeEaRT

To determine: The temperature of uncatalyzed reaction for the decomposition of hydrogen peroxide.

Explanation

Given

The activation energy of uncatalyzed reaction at 20°C is 70kJ/mol .

The activation energy of catalyzed reaction is 42kJ/mol .

The conversion of kilojoules (kJ) into joule (J) is done as,

1kJ=103J

Hence, the conversion of 70kJ/mol into joule is,

70kJ=(70×103)J=70×103J

The conversion of 42kJ into joule is,

42kJ=(42×103)J=42×103J

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273

Hence, the conversion of 20°C into Kelvin is,

T(K)=T(°C)+273T(K)=(20+273)K=293K

Formula

The rate constant for uncatalyzed reaction is calculated using the formula,

k1=AeEa1RT

Where,

• k1 is the rate constant for uncatalyzed reaction.
• A is the frequency factor.
• Ea1 is the activation energy for uncatalyzed reaction.
• R is the universal gas constant (8.314J/Kmol) .
• T1 is the temperature for uncatalyzed reaction.

Substitute the values of Ea1,R and T1 for uncatalyzed reaction.

k1=AeEa1RT=Ae70×103J/mol8

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