   # A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from 22°C to a higher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature. ### 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 71E
Textbook Problem
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## A certain reaction has an activation energy of 54.0 kJ/mol. As the temperature is increased from 22°C to a higher temperature, the rate constant increases by a factor of 7.00. Calculate the higher temperature.

Interpretation Introduction

Interpretation: The activation energy of certain reaction is given. When the temperature is increased from a given temperature to higher temperature, the rate constant is also increased by certain factor. The higher temperature 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 higher temperature.

### Explanation of Solution

Given

The value of activation energy is 54kJ/mol.

The given initial temperature is 22°C.

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

T(K)=T(°C)+273

Hence, the conversion of 22°C into Kelvin is,

T(K)=T(°C)+273T(K)=(22+273)K=293K

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

1kJ=103J

Hence, the conversion of 54kJ/mol into joule is,

54kJ=(54×103)J=54×103J

Hence, the value of activation energy is 54×103J/mol.

It is assumed that the rate constant at 295K is k1=k. Since, as the temperature is increased to higher temperature, the rate constant is also increased by a factor of 7.00. Therefore, the rate constant at higher temperature is,

k2=7k

Formula

The activation energy is calculated by using the formula,

ln(k2k1)=EaR(1T11T2)

Where,

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

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

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