Kirchoff's Equation

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 T₁ and T₂ we get-

where, ΔH_A and ΔH_B are the enthalpies of reactants and products at temperature T₁ and T₂ 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 T₁ and T₂ we get-

where, ΔH_A and ΔH_B are the enthalpies of reactants and products at temperature T₁ and T₂ 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.