Question

The rate of a certain reaction was studied at various temperatures. The table shows temperature (T) and rate constant (k) data collected during the experiments. Plot the data to answer the questions.

What is the value of the activation energy, Ea , for this reaction?

T (K)	k (s−1)
400	0.000108
420	0.000626
440	0.00310
460	0.0134
480	0.0511
500	0.175
520	0.547
540	1.57
560	4.18
580	10.4

Answer 1

The temperature dependence of rate constant of a reaction is given by the Arrhenius equation.

Taking the natural logarithm on both sides, we get

Where

E_a = activation energy

R = gas constant

T = temperature in Kelvin

A = frequency factor

Hence, plotting ln k in y axis vs 1/T in x axis, we should get a straight line with slope -E_a/R and intercept ln A.

Hence, for the given data, we can tabulate the data points needed to plot the above graph.

Now, we can plot ln k in y axis vs 1/T in x axis as follows:

Hence, the equation of the line is

Where

y = ln k

x = 1/T.

Now, we know that the slope of the equation is equal to -E_a/R.

Note that the slope will have a unit of K since y axis is unitless and x axis has a unit of K^-1

We know

Hence we can write

Hence, the activation energy of the reaction is approximately 123 kJ/mol.