Question

An uncatalyzed reaction is estimated to take 1.22 x 109 minutes for a given amount of substrate to be converted to a given amount of product (assuming sterile conditions). If the addition of an aliquot of purified enzyme catalyzes the same amount of product to be produced from the same amount of substrate in 26 minutes, then what is the value of the rate enhancement (which we typically call x) to the nearest ones? (Please note that the answer will be expressed to far more precision than is warranted, but that is a limitation of the Canvas software.)

Answer 1

Outline to solve the problem:

The rate of formation of a product = rate of a reaction, r = d[product]/dt

i.e. r₁t₁ = r₂t₂, where, r₁ = rate of uncatalyzed reaction, r₂ = rate of enzyme-catalyzed reaction, t₁ = time taken by the uncatalyzed reaction to form the given amount product and t₂ = time taken by enzyme-catalyzed reaction to form the given amount product.

Here, t₁ = 1.22 x 10⁹ min., t₂ = 26 min.

Now, r₁*​1.22 x 10⁹ = r₂*26

i.e. r₂ = r₁*​1.22 x 10⁹/26

i.e. r₂ = r₁*4.69*10⁷

Therefore, the rate of enhancement by using the enzyme is 4.69*10⁷ times of the rate of uncatalyzed reaction.