   # The activation energy for the decomposition of HI( g ) to H 2 ( g ) and I 2 ( g ) is 186 kJ/mol. The rate constant at 555 K is 3.52 × 10 −7 L/mol · s. What is the rate constant at 645 K? ### 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 69E
Textbook Problem
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## The activation energy for the decomposition of HI(g) to H2(g) and I2(g) is 186 kJ/mol. The rate constant at 555 K is 3.52 × 10−7 L/mol · s. What is the rate constant at 645 K?

Interpretation Introduction

Interpretation: The activation energy and rate constant at 555K for the decomposition of HI is given. By using these values, the rate constant at 645K 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 rate constant at 645K for the decomposition of HI .

### Explanation of Solution

Given

The value of activation energy is 186kJ/mol .

The value of rate constantat 555K is 3.52×107L/mols .

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

1kJ=103J

Hence, the conversion of 186kJ into joule is,

186kJ=(186×103)J=186×103J

Hence, the value of activation energy is 186×103J/mol .

Formula

The rate constant 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,Ea,T1,k1 and T2 in the above expression

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