The activation energy Ea for a particular reaction is 42.2 kJ/mol. How much faster is the reaction at 343 K than at 323 K? (R = 8.314 J/mol • K)

Answer 1

Look at the Arrhenius equation:

ln(k1/k2) = -Ea/R (1/T1 -1/T2) [there are other forms of the equation and any of them will work]

NOTE: R = 8.314 J/K-mol so since it has units of joules (J) we will change Ea to joules also (42,200 J/mol)

We don't know k1 or k2, but all we need to do is find the ratio and that should tell us the ratio of the speed of the reaction at the two temperatures. We will set T2 = 343K and T1 = 323K and we can arbitrarily set k1 = 1 and solve for k2

ln(1/k2) = -42,200/8.314 (1/323 - 1/343)

ln 1 - ln k2 = -5076 (0.003096 - 0.002915)

-ln k2 = -5076 (0.0001810) = -0.9188

k2 = 2.5

So, the rate of reaction would be approximately 2.5 times faster at 343K than at 323K (please do check the math)