Practice Problem 11

Use the following data to determine the activation energy for the decomposition of HI:

Temperature (K)           Rate Constant (M/s)

573                                  2.91 x 10-6

673                                  8.38 x 10-4

773                                  7.65 x 10-2

Solution

We can determine the activation energy for a reaction from a plot of the natural log of the rate constants versus the reciprocal of the absolute temperature.  We therefore start by calculating 1/T and the natural logarithm of the rate constants:

 ln k 1/T (K-1) -12.75 0.00175 -7.08 0.00149 -2.57 0.00129

When we construct a graph of these data, we get a straight line with a slope of -22,200 K, as seen in Figure 1.

 Figure 1.  A plot of the natural log of the rate constant for the reaction at different temperatures versus the inverse of the temperature in kelvin is a straight line with a slope equal to -Ea/R.

According to the Arrhenius equation, the slope of this line is equal to -Ea/R:

When this equation is solved, we get the follwoing value for the activation energy for this reaction:

Ea = 183 kJ/mol