   Chapter 12, Problem 67AE

Chapter
Section
Textbook Problem

# The rate constant for the gas-phase decomposition of N2O5, N 2 O 5   →   2 NO 2   +   1 2 O 2 has the following temperature dependence: T(K) k(s−1) 338 4.9 × 10−3 318 5.0 × 10−4 298 3.5 × 10−5 Make the appropriate graph using these data, and determine the activation energy for this reaction.

Interpretation Introduction

Interpretation: The table for the temperature dependence rate constant for the decomposition of N2O5 is given. By using this data, the graph is to be drawn and the activation energy for the reaction 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 activation energy for the decomposition of N2O5 .

Explanation

The relationship between the rate constant and activation energy 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

Thus,

Slope, m=EaR (2)

A plot of lnk versus 1/T(K) is obtained using the given values of rate constant (k) and temperature (T).

The values obtained are,

 Temperature (K) 1/T(K) k(s−1) ln k 338 0

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