Hydrogen iodide, HI, decomposes in the gas phase to produce hydrogen, H₂, and iodine, I₂. The value of the rate constant, k, for the reaction was measured at several different temperatures, and the data are shown here:

Temperature(K)	k(M-1s-1)
555	6.23*10-7
575	2.42*10-6
645	1.44*10-4
700	2.01*10-3

What is the value of the activation energy (in kJ/mol) for this reaction?

The plot of ln k vs 1/T gives a straight line.

The activated energy of a reaction is the minimum energy that a reactant must possess to convert into products.

The Arrhenius equation is given as

\(\begin{align}k &= A{e^{\frac{{ - {E_a}}}{{RT}}}}\\\ln k &= \ln A + (\frac{{ - {E_a}}}{{RT}})\end{align}\)

Here k is the rate constant; A is the pre-exponential factor, E_ais the activation energy, R is the universal gas constant, and T is the temperature.

The value of\({{\bf{E}}_{\bf{a}}}\)can be calculated from the slope of the plot.

\({\bf{Slope = }}\frac{{{\bf{ - }}{{\bf{E}}_{\bf{a}}}}}{{\bf{R}}}\)

Considering the second and third data points on the plot, the slope is

\(\begin{align}Slope &= \frac{{\Delta y}}{{\Delta x}}\\\frac{{ - {E_a}}}{R} &= \frac{{ - 12.9317 - \left( { - 8.8457} \right)}}{{0.00174 - 0.00155}}\\ - {E_a} &= - 21505.26 \times 8.314\\{E_a} &= 178794.7J/mol\\{E_a} &= 178.79kJ/mol\end{align}\)