Write the Arrhenius equation for the rate constant (k) of a reaction.

Explanation

Arrhenius equation explains the temperature dependence of the rate of a chemical reac-tion. Arrhenius equation is
`k = Ae^(-E_(a)"/" RT)`
Where A is the Arrhenius factor, or the frequency factor. R is gas constant and `E_(a)` is activation energy in `J mol^(-1)`.
Taking natural logarithms of both sides
ln `k = - (E_a)/(RT^2)+ln A"..............."(1)`
At temperature `T_(1)`, the equation (1) is
ln `k_(1)= - (E_a)/(RT)+lnA"................."(2)`
At temperature `T_2`, the equation (1) is
ln `k_(2)= -(E_a)/(RT)+lnA"................"(3)`
Subtracting equation (2) from (3) we get
`ln k_(2)= ln"" k_(1)= (E_a)/(RT_1)-(E_a)/(RT_2)`
`ln ""(k_2)/(k_1)= (E_a)/(R )[(1)/(T_1)-(1)/(T_2)]`
`log"" (k_2)/(k_1)= (E_a)/(2.303R)[(1)/(T_1)-(1)/(T_2)]`
`log ""(k_2)/(k_1)= (E_a)/(2.303R)[(T_(2)-T_(1))/(T_(1)T_(2))]`.