## Variation of Heat of Reaction with Temperature

## Kirchoff's Equation

Variation of heat of reaction with temperature is called Kirchoff's equation. This equation was developed by G.R. Kirchhoff in 1858.

Let us consider a reaction A → B

If this reaction is carried out at constant pressure, the heat of reaction of this reaction at any temperature.

ΔH = H_{B} − H_{A}

where H_{A} and H_{B} are the enthaplies of reactant and products respectively.

Differentiating the above equation wrt temperature at constant pressure we get-

where, (C_{p})_{A} and (C_{p})_{B} are the heat capacities of reactants and products respectively.

We see that the change in heat of reaction per degree change in temperature is the difference in heat capacities of products and reactants
(ΔC_{P}) produced that the reaction is carried out at constant pressure.

Integrating the above equation between T_{1} and T_{2} we get-

where, ΔH_{A} and ΔH_{B} are the enthalpies of reactants and products at temperature T_{1} and T_{2} respectively.

If the reaction takes place at constant volume, then the heat of reaction-

ΔE = E_{B} − E_{A}

where E_{A} and E_{B} are the internal energies of reactants and products respectively.

Differentiating the above equation wrt temperature at constant volume, we get-

where, (C_{V})_{A} and (C_{V})_{B} are the heat capacities of reactants and products respectively.

We see that the change in heat of reaction per degree change in temperature is the difference in heat capacities of products and reactants
(ΔC_{V}) produced that the reaction is carried out at constant volume.

Integrating the above equation between T_{1} and T_{2} we get-

where, ΔH_{A} and ΔH_{B} are the enthalpies of reactants and products at temperature T_{1} and T_{2} respectively.

From equation 1 and equation 2, it is obvious that if the molar heat capacities of reactants and products are same (i.e. ΔC_{V} or ΔC_{P} = 0), the heat of reaction will not change at all with temperature.