Question

How much does an enzyme need to reduce the activation energy of a reaction at 25 ºC in order to increase the rate 100-fold over the uncatalyzed reaction? R = 8.3145 J/K mol. When answering, convert your response to kJ/mol and input ONLY a number, rounded to one decimal place.

Hint: the rate constant for an enzymatic reaction divided by the uncatalyzed reaction = 10

Answer 1

Since the rate is to be increased 100 times,

k_enzyme/ k_uncatalyzed = 100 ( Unlike the 100 given in the hint)

k_enzyme = k_o exp(-E_enzyme / RT)

k_uncatalyzed = k_oexp(-E_uncat/RT)

Divide the two,

k_enzyme / k_uncat = exp((E_uncat - E_cat)/RT) = 100

Substituting values for R = 8.314 and T = 298

We get

100 = exp(E_red / 8.314 / 298)

Take log on both sides to get

log (100) = 4.6052 = E_red / (2477.57)

E_red = 11,409.7 J/mol = 11.41 kJ/mol

Required ans - 11.4

( Since its not clear if its 10 fold or 100 fold, for 10 fold, the log value will be half of this, and for 10 fold the answer will be 5.7 accordingly)