The rate constant k for a chemical reaction is related to the temperature T by the Arrhenius equation.
k = Ae– (Ea/RT)
Where A and Ea are constants for a given chemical reaction; R is the gas constant R = 8.314 J K-1 mol-1; and T is the absolute temperature in K. For a particular biochemical reaction k= 20 L mol-1 s-1 when T = 300 K. If Ea = 50 kJ mol-1 for this reaction, by differentiating the Arrhenius equation with respect to T, find the change in the value of k when T increases by 1 K to 301 K. Remember to use the base unit of Ea = 50000 J mol-1 in the calculation and not its multiple of KJ mol-1.
k = Ae– (Ea/RT) ;
(20 L mol-1 s-1) = Ae– [(50000 J mol-1/(8.314 JK mol-1)(300K)]
A = 1.017 x 1010 L mol-1 s-1
Let x = 1/T, then dx/dT = – T-2 and so,
Treating the differential as separable terms and substituting the values for the variables with dT = 1 K gives