Question

Variation of the heat of reaction with temperature is given by Kirchhoff’s equation. Which of the following is not the equation for Kirchhoff’s?
A). $\Delta {H_2} = \Delta {H_1} + \Delta {C_y}\left( {{T_2} - {T_1}} \right)$
B). $dG = TdS + VdP$
C). $\dfrac{{\Delta {H_2} - \Delta {H_1}}}{{\Delta T}} = \Delta {C_P}$
D). $\dfrac{{d\left( {\Delta H} \right)}}{{\Delta T}} = \Delta {C_P}$

Answer 1

Hint: The law of Kirchhoff describes the enthalpy of a temperature change reaction variation. Enthalpy of any material usually rises with temperature, which rises the enthalpies of both the products and the reactants. When the growth of the product and reactant enthalpy is different, the overall enthalpy of the reaction will change.

Complete step-by-step solution:
The heat capacity at constant pressure equals the enthalpy change divided by temperature changes.
$ \Rightarrow {c_p} = \dfrac{{\Delta H}}{{\Delta T}}$ (equation 1)
Therefore, where the temperature does not change the heat capacity, enthalpy changes will depend on the temperature and the heat capacity difference. The increase in the enthalpy is proportional to the change in temperature and heat capacity in products and reactants. A weighted total is mostly used to calculate heat capacity changes to include the ratio of the molecules involved since all molecules have varying heat capacity in different states.
$ \Rightarrow {H_{{T_f}}} = {H_{{T_i}}} + \int\limits_{{T_i}}^{{T_f}} {{c_p}dT} $ (equation 2)
If the temperature of the heat capacity is independent of the temperature, equation 1 can be estimated as-
${H_{{T_f}}} = {H_{{T_i}}} + {c_p}\left( {{T_f} - {T_i}} \right)$ (equation 3)
Where ${c_p}$ is considered to be the heat capacity which is assumed to be constant.
Where, ${H_{{T_i}}}$ and ${H_{{T_f}}}$ are considered to be the enthalpy at the respective temperatures.
Hence, Option A is the actual equation of Kirchhoff’s while options C and D are its form. Thus, it is clear that option B is the correct option as it is not a Kirchhoff’s equation.

Note: Equation 3 can be used only for small (< 100 K) increase in temperatures because the heat capacity is not constant over a larger temperature change. It is possible to predict enthalpy changes at certain temperatures using standard enthalpy data since many biochemical applications exist.