   # The activation energy for a reaction is changed from 184 kJ/ mol to 59.0 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2400 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant, and assume the initial concentrations are the same. ### 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 82E
Textbook Problem
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## The activation energy for a reaction is changed from 184 kJ/ mol to 59.0 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2400 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant, and assume the initial concentrations are the same.

Interpretation Introduction

Interpretation: The change in activation energy of a reaction without catalyst at 600K and with catalyst is given. Also, the time of uncatalyzed reaction to occur is given. Based on these data, the time ofcatalyzed reaction is 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=AeEaRTlnk=EaRT+lnA

To determine: The total time of catalyzed reaction.

### Explanation of Solution

Given

The activation energy of uncatalyzed reaction is 184kJ/mol .

The activation energy of catalyzed reaction is 59kJ/mol .

The time taken for the occurrence of uncatalyzed reaction is 2400years .

Temperature is 600K .

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

1kJ=103J

Hence, the conversion of 184kJ/mol into joule is,

184kJ=(184×103)J=184×103J

The conversion of 59kJ into joule is,

59kJ=(59×103)J=59×103J

Formula

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

lnk1=Ea1RT+lnA (1)

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) .
• T is the absolute temperature.

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

lnk2=Ea2RT+lnA (2)

Where,

• k2 is the rate constant for catalyzed reaction.
• Ea2 is the activation energy for catalyzed reaction.
• T is the absolute temperature.

It is assumed that frequency factor (A) and initial condition are same for each reaction

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