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 E_{a} 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 E_{a} = 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 E_{a} = 50000 J mol^{-1} in the calculation and not its multiple of KJ mol^{-1}.

Here,

**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 10 ^{10} 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