Question

An enzyme enhances the rate of a reaction at pH 8, 20 °C, by a factor of 1.8E10. If a given quantity of enzyme catalyzes the conversion of a given quantity of substrate in 11 minutes at 20 °C and pH 8, how long (in years) would it take for the same amount of substrate to be converted to product under the same conditions but in the absence of the enzyme? Assume sterile conditions such that bacteria cannot affect the time, and enter your answer to the nearest ones.

Answer 1

For uncatalyzed reaction, the time required is

$t = 11 \: min \times 1.8 \times 10^{10} = 1.98 \times 10^{11} \min \\ 1 year = 365 \times 24 \times 60 \: min = 525600 \: min \\ t = 1.98 \times 10^{11} \min = \dfrac {1.98 \times 10^{11} \min}{525600 \: min/yr} = 3.77 \times 10^5 \: years$