Chemistry: The Molecular Science
Chemistry: The Molecular Science
5th Edition
ISBN: 9781285199047
Author: John W. Moore, Conrad L. Stanitski
Publisher: Cengage Learning
Question
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Chapter 11, Problem 52QRT

(a)

Interpretation Introduction

Interpretation:

Activation energy and frequency factor for the given reaction has to be calculated.

Concept Introduction:

The temperature dependence of rate constant can be explained through Arrhenius equation.

  k=AeEaRT

Where k the rate is constant, A is the frequency factor, Ea is the activation energy, R is the universal gas constant and T is the temperature.

The logarithmic form of Arrhenius is given below.

  lnk2k1=EaR(1T11T2)

Where, k1 and k2 are the rate constants at temperature T1 and T2 respectively.

(a)

Expert Solution
Check Mark

Answer to Problem 52QRT

The activation energy is calculated as 29.3kJ/mol and the value of frequency factor is 7.55×103Lmol-1s-1.

Explanation of Solution

The activation energy can be calculated using following formula,

  lnk2k1=EaR(1T11T2)

Given,

    k1=2.34×102Lmol1s1k2=1.52×101Lmol1s1T1=10oC=283.15KT2=60oC=333.15K

On substituting these values in the above equation gives the activation energy as shown below.

    lnk2k1=EaR(1T11T2)ln(1.52×101Lmol1s1)(2.34×102Lmol1s1)=Ea0.008314kJ/K/mol(1283.15K1333.15K)ln(6.49)=Ea×(0.0637kJ1mol)Ea=29.3kJ/mol

The activation energy is calculated as 29.3kJ/mol.

Frequency factor can be calculated using the two given temperature.

Frequency factor calculated using T1 temperature is given below.

  k1=AeEaRT12.34×102Lmol1s1=Ae29.3kJ/mol(0.008134kJ/K/mol)×283.15KA=(2.34×102Lmol1s1)e29.3kJ/mol(0.008134kJ/K/mol)×283.15KA=(2.34×102Lmol1s1)×e12.7=7.66×103Lmol-1s-1

Frequency factor calculated using T2 temperature is given below.

  k2=AeEaRT21.52×101Lmol1s1=Ae29.3kJ/mol(0.008134kJ/K/mol)×333.15KA=(1.52×101Lmol1s1)e29.3kJ/mol(0.008134kJ/K/mol)×333.15KA=(1.52×101Lmol1s1)×e10.8=7.45×103Lmol-1s-1

Therefore the average value of frequency factor is 7.55×103Lmol-1s-1.

(b)

Interpretation Introduction

Interpretation:

Rate constant of the reaction at a temperature of 100oC has to be estimated.

Concept Introduction:

Refer to part (a).

(b)

Expert Solution
Check Mark

Answer to Problem 52QRT

The value of the rate constant is calculated as 0.597Lmol-1s-1.

Explanation of Solution

Rate constant can be calculated using Arrhenius equation.

Given,

    A=7.55×103Lmol-1s-1Ea=29.3kJ/molR=0.008314kJ/K/molT=100oC=373.15K

Substituting these values gives the value of rate constant as follows,

    k=AeEaRT=(7.55×103Lmol-1s-1)e(29.3kJ/mol)(0.008314kJ/K/mol)×(373.15K)=0.597Lmol-1s-1.

The value of the rate constant is calculated as 0.597Lmol-1s-1.

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Chapter 11 Solutions

Chemistry: The Molecular Science

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