Suppose a certain biologically important reaction is quite slow at physiological temperature (37 °C) in the absence of a catalyst. Assuming that the frequency factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a million- fold (1.0 x 106) increase in the reaction rate constant?

The answer to the question is

The enzyme must lower the activation energy by 35624.5 KJ/mol

Explanation:

The relation is

k =

Where k = rate of chemical reaction

A = Arrhenius constant

Ea = Activation energy

T = Temperature

R = Gas constant

at 37 °C we have T = (37 +273.15)  K = 310.15 K

k =

when a catalyst is introduced we have Ea(catalyst)

kc =

Finding the ratio of the two reaction rate and noting that Kc/K = 1.0 x 10⁶

Thus we have

Kc/k =  = 1.0 x 10⁶ by taking natural logarithm of both sides, we have

6 × ln (10) = Ln (Kc/k ) =  

so that Ea - Eacatalyst = 8.314 × 310.15 × 13.816 = 35624.5 KJ/mol

Therefore the enzyme must lower the activation energy by 35624.5 KJ/molto achieve a million fold increse in the reaction rate constant

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