If E_a for a certain biological reaction is 50.kJ/mol, by what factor (how many times)will the rate of this reaction increase when body temperature increases from 37°C (normal)to 40°C (fever)?

Question

Quizplus · Accepted Answer

The rate of a biological reaction is given by the Arrhenius equation:

k = Ae^(-Es/RT)

where k is the rate constant, A is the pre-exponential factor, Es is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

Taking the ratio of the rate constants at two temperatures, we can find the factor by which the rate changes with temperature:

k2/k1 = (Ae^(-Es/R(1/T2 - 1/T1))) / (Ae^(-Es/R(1/T1 - 1/T1)))

Canceling out the pre-exponential factors and simplifying, we get:

k2/k1 = e^(Es/R((1/T1 - 1/T2)))

Substituting the given values:

k2/k1 = e^(50,000 J/mol / (8.314 J/mol•K) ((1/310 K) - (1/313 K)))

k2/k1 = 1.20

Therefore, the rate of the reaction will increase by a factor of 1.20 when body temperature increases from 37°C to 40°C.

If Ea for a Certain Biological Reaction Is 50

If E_a for a Certain Biological Reaction Is 50