A reaction has an uncatalysed path ( $E_{a} = 100.0 kJ mo l^{- 1}$ ). Adding a catalyst opens a second, parallel path with $E_{a} = 90.0 kJ mo l^{- 1}$ , and the uncatalysed path remains open. Both paths have the same pre-exponential factor. At $300 K$ ( $R = 8.314 J mo l^{- 1} K^{- 1}$ ), the ratio of the overall rate constant (both paths) to the uncatalysed rate constant, rounded to the nearest integer, is

Answer: D

Parallel paths add:

k_{total} = k_{u} + k_{c}

, with

k_{c} / k_{u} = exp (10000/ (8.314 \times 300)) = e^{4.009} = 55.1

. So

k_{total} / k_{u} = 1 + 55.1 = 56.1 \approx 56

. The value 55 results from wrongly assuming the catalysed path replaces the uncatalysed one.