If the rate constant at two different temperature t1 and t2 are k1 and k2 respectively with an activation energy ea than prove- ea = r [ln (k2/ k1)] [t1t2/t2

Abhijeet Gaurav

Arrhenius Equation The equation was first proposed by Dutch chemist, J.H. Van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation. The Arrhenius equation is based on the Collision theory. It is not an equation that is born out of pure math that we can derive. It is an empirical equation that fits experimental data in most of the situations. The Arrhenius equation looks like this, k = A e -Ea/RT where, K = Rate constant A = Frequency or Pre-exponential Factor Ea = Activation Energy R = Gas Constant T = Temperature Kelvin Increasing the temperature increases the fraction of molecules, which collide with energies greater than the activation energy Ea. Temperature dependence of Rate of Reaction in Arrhenius Equation In Arrhenius equation, the factor e -Ea/RT corresponds to the fraction of molecules colliding with activation energies more than Ea. Taking natural logarithms of both sides of the equation I, we get, ln k = -Ea/RT + ln A Therefore, from the Arrhenius equation, we can find that increasing the temperature or decreasing the activation energy will result in an increase in the rate of the reaction and an exponential increase in the rate constant. In a graph of activation energy vs rate of reaction, slope = -Ea/R and intercept = ln A. At temperature T1, equation II will be ln k1 = -Ea/RT1 + ln A …………………(III) At temperature T2 , equation II will be ln k2 = -Ea/RT2 + ln A …………………(IV) (k1 and k2 are the rate constants at temperature T1 and T2) Subtracting equation III from equation IV, we get ln k2 – ln k1 = Ea/RT1 – Ea/RT2 ∴ ln k2 / k1 = (Ea /R)[1/T1 – 1/T2] ∴ log k2 / k1 = (Ea /2.303R)[(T2 – T1)/T1T2] Hence Proved.