# Question #fec06

Apr 9, 2015

Rate enhancement would be about ${10}^{5}$ fold

The rate enhancement can be calculated if you know the temperature and the activation energy for both the catalyzed and uncatalyzed reactions.

$\text{rate enhancement} = {e}^{\frac{\left(\Delta {G}_{1} - \Delta {G}_{2}\right)}{R T}}$

$\text{rate enhancement} = {e}^{\frac{\left(30000 - 15000\right)}{R \left(273 + 25\right)}}$

$\text{rate enhancement} = {e}^{\frac{\left(285000\right)}{8.3145 \left(298\right)}}$

$\text{rate enhancement"=98963 " or about } {10}^{5}$

Notes
- The universal gas constant R is written with Joules - to obtain the correct answer, the activation energies given need to be converted from kJ

• I could have used 273.15 for my Celsius to Kelvin conversion (I simplified) but you must convert temperatures to Kelvin