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

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.