Derive Arrhenius equation from Van’t Hoff Equation. | Chemical Kinetics | Physical Chemistry

Download Notes from: Chemistry/Chemical Kinetics/ The van’t Hoff equation relates the change in the equilibrium constant left( { K }_{ eq } right) of a chemical reaction to the change in temperature left( T right) . This Van’t Hoff’s relation is: boxed { frac { dleft( ln { K } right) }{ dT } = frac { triangle E }{ R{ T }^{ 2 } } } ... (1) where triangle E is energy of activation, R is gas constant, T is temperature and K is the equilibrium constant for the reaction. Consider a reversible reaction, A B begin{matrix} { k }_{ 1 } Longleftrightarrow { k }_{ 2 } end{matrix} C D Equilibrium constant K can be taken as frac { { k }_{ 1 } }{ { k }_{ 2 } } , where { k }_{ 1 } and { k }_{ 2 } are the velocity constants for the forward and back ward reactions. If { E }_{ 1 } and { E }_{ 2 } are the activation energies of the reactant and the product, then substituting these values in the above Van’t Hoff’s equation we get, fra