   # A first-order reaction has rate constants of 4.6 × 10 −2 s −1 and 8.1 × 10 −2 s −1 at 0°C and 20.°C, respectively. What is the value of the activation energy? ### 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 70E
Textbook Problem
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## A first-order reaction has rate constants of 4.6 × 10−2 s−1 and 8.1 × 10−2 s−1 at 0°C and 20.°C, respectively. What is the value of the activation energy?

Interpretation Introduction

Interpretation: The rate constants of first order reaction at 0°C and 20°C are given. By using these values, the value of activation energy is to be calculated.

Concept introduction: The energy difference between activated complex and reactants is known as activation energy. The relationship between the rate constant and temperature is given by the Arrhenius equation,

k=AeEaRT .

To determine: The value of activation energy for the first order reaction.

### Explanation of Solution

Given

The value of rate constantat 0°C is 4.6×102s1 .

The value of rate constantat 20°C is 8.1×102s1 .

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

The conversion of 0°C into Kelvin is,

T(K)=T(°C)+273T(K)=(0+273)K=273K

Formula

The activation energy is calculated by using the formula,

ln(k2k1)=EaR(1T11T2)

Where,

• k1 is the rate constant at temperature T1 .
• k2 is the rate constant at temperature T2 .
• Ea is the activation energy.
• R is the universal gas constant (8.314J/Kmol) .

Substitute the values of R,k1,k2,T1 and T2 in the above expression

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