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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

Give the Arrhenius equation. Take the natural log of both sides and place this equation in the form of a straight-line equation (y = mx + b). What data would you need and how would you graph those data to get a linear relationship using the Arrhenius equation? What does the slope of the straight line equal? What does the y-intercept equal? What are the units of R in the Arrhenius equation? Explain how if you know the rate constant value at two different temperatures, you can determine the activation energy for the reaction.

Interpretation Introduction

Interpretation: The Arrhenius equation is to be stated. The data required when the natural log is taken on both sides and the equation is placed in the form of a straight-line equation is to be stated. The slope and the y-intercept of this straight line is to be given. The units of R in the Arrhenius equation are to be given. The reason is to be explained for the fact that if the rate constant value at two different temperatures is known, the activation energy for the reaction can be determined.

Concept introduction: The energy difference between the activated complex and reactants is known as activation energy. The relationship between the rate of reaction and activation energy is given by the Arrhenius equation, k=AeEaRT .

To determine: The mathematical expression of the Arrhenius equation; the data required when the natural log is taken on both sides and the equation is placed in the form of a straight-line equation; the slope and the y -intercept of this straight line; the units of R in the Arrhenius equation; the reason for the fact that if the rate constant value at two different temperatures is known, the activation energy for the reaction can be determined.

Explanation

Explanation

The Arrhenius equation is,

k=AeEaRT

The relationship between the rate of reaction andactivation energy is given by the Arrhenius equation. The Arrhenius equation is,

k=AeEaRT

Where,

  • k is the rate constant.
  • A is the Arrhenius parameter.
  • Ea is the activation energy.
  • R is the universal gas constant.
  • T is the absolute temperature.

The slope of given equation is EaR and y-intercept is lnA .

The Arrhenius equation is,

k=AeEaRT

Take natural log on both sides in the above expression,

k=AeERTlnk=EaR(1T)+lnA (1)

This is similar to the equation of a straight line, that is,

y=mx+c .

Where,

  • y is the y-intercept.
  • x is the x-intercept.
  • m is the slope.
  • c is a constant.

Hence, the slope of equation (1) is EaR and y-intercept is lnA .

The unit of universal gas constant is J/Kmol .

The equation ln(k1k2)=EaR(1T11T2) suggests that, if the rate constant value at two different temperatures is known, the activation energy for the reaction can be determined

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