Ea=59kJ/mol, how many times will the rate of the reaction increase when body temp goes from 37C-40C?

Question

Ea=59kJ/mol, how many times will the rate of the reaction increase when body temp goes from 37C-40C?

Answer 1

The dependency of rate of reaction is determined by the dependency of the rate constant on temperature. (for small temperature changes)

Arrhenius equation relates rate constant to temperature as:

k = A · exp( - Ea / (R · T) )

So the ratio of rate constants (and the reaction rates) at two different temperatures is:

k₂/k₁ = [ A · exp( - Ea / (R · T₂) ) ] / [ A · exp( - Ea / (R · T₁) ) ]

= exp( - Ea / (R · T₂) ) / exp( - Ea / (R · T₁) ) ]

= exp(  (Ea/R) · (1/T₁ - 1/T₂) )

For

Ea = 59kJ/mol

T₁ = 37°C = 310K

T₂ = 40°C = 313K

k₂/k₁ = exp(  (59000J/mol / 8.314472J/molK) · (1/310K - 1/313K) )

= 1.245

So rate of reaction increases by about 25%

Answer 2

ask this under chemistry, not physics!