A certain reaction has an activation energy of 42.16 kJ/mol. At what Kelvin temperature will the reaction proceed 5.50 times faster than it did at 291 K?

Question

A certain reaction has an activation energy of 42.16 kJ/mol.  At what Kelvin temperature will the reaction proceed 5.50 times faster than it did at 291 K?

anonymous · Answer

If you assume the Arrhenius model of chemical kinetics, and further assume the so-called prefactor doesn't change, both of which are at least somewhat plausible, then the question comes down to the exponential part of the Arrhenius equation:
$$k(T) = k(T_0) e^{- (E_a/R) \left(1/T - 1/T_0\right)}$$
I get 323 K.