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The reaction ( CH 3 ) 3 CBr + OH − → ( CH 3 ) 3 COH + Br − in a certain solvent is first order with respect to (CH 3 ) 3 CBr and zero order with respect to OH − .In several experiments. The rate constant k was determined at different temperatures. A plot of ln( k ) versus 1/ T was constructed resulting in a straight line with a slope value of −1.10 × 10 4 K and y -intercept of 33.5. Assume k has units of s −1 a. Determine the activation energy for this reaction. b. Determine the value of the frequency factor A. c. Calculate the value of k at 25°C.

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Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

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Section
BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 68E
Textbook Problem
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The reaction

( CH 3 ) 3 CBr + OH ( CH 3 ) 3 COH + Br

in a certain solvent is first order with respect to (CH3)3CBr and zero order with respect to OH .In several experiments. The rate constant k was determined at different temperatures. A plot of ln(k) versus 1/T was constructed resulting in a straight line with a slope value of −1.10 × 104 K and y-intercept of 33.5. Assume k has units of s−1

a. Determine the activation energy for this reaction.

b. Determine the value of the frequency factor A.

c. Calculate the value of k at 25°C.

(a)

Interpretation Introduction

Interpretation: The reaction between (CH3)3CBr and OH is given. The reaction is first order with respect to (CH3)3CBr and zero order with respect to OH . The values of slope and y intercept is given from the plot of lnk versus 1/T(K) . The value of activation energy and frequency factor A is to be calculated for the given reaction. Also the value of k for the given temperature is to be calculated.

Concept introduction: A certain threshold energy which is necessary for the reaction to occur is called activation energy.

The relationship between the rate constant and activation energy is given by the Arrhenius equation,

k=AeEaRT

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

Explanation of Solution

Given

The value of slope is 1.10×104K .

The relationship between the rate constant and temperature is given by the Arrhenius equation.

k=AeEaRT

Where,

  • k is the rate constant.
  • A is the frequency factor.
  • Ea is the activation energy.
  • R is the universal gas constant (8.314J/Kmol) .
  • T is the absolute temperature.

Take natural log on both the sides in the above expression.

lnk=ln(AeEaRT)lnk=EaR(1T)+lnA (1)

Equation (1) represents an equation of straight line.

Compare this equation with the general equation of straight line,

y=mx+c

Where,

  • m is the slope

(b)

Interpretation Introduction

Interpretation: The reaction between (CH3)3CBr and OH is given. The reaction is first order with respect to (CH3)3CBr and zero order with respect to OH . The values of slope and y intercept is given from the plot of lnk versus 1/T(K) . The value of activation energy and frequency factor A is to be calculated for the given reaction. Also the value of k for the given temperature is to be calculated.

Concept introduction: A certain threshold energy which is necessary for the reaction to occur is called activation energy.

The relationship between the rate constant and activation energy is given by the Arrhenius equation,

k=AeEaRT

To determine: The value of frequency factor A .

(c)

Interpretation Introduction

Interpretation: The reaction between (CH3)3CBr and OH is given. The reaction is first order with respect to (CH3)3CBr and zero order with respect to OH . The values of slope and y intercept is given from the plot of lnk versus 1/T(K) . The value of activation energy and frequency factor A is to be calculated for the given reaction. Also the value of k for the given temperature is to be calculated.

Concept introduction: A certain threshold energy which is necessary for the reaction to occur is called activation energy.

The relationship between the rate constant and activation energy is given by the Arrhenius equation,

k=AeEaRT

To determine: The value of k at 25°C .

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Chemistry: An Atoms First Approach
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