Question

The variation of heat of reaction with temperature at constant pressure is given by the ____________ law.
(a) Antoine’s law
(b) Kelvin’s law
(c) Kirchhoff’s law
(d) None of these

Answer 1

Hint: We already know that enthalpy of any substance increases with increase in temperature. This means that both the products and the reactant’s' enthalpies increase. The overall enthalpy of the reaction will change if the increase in the enthalpy of products and reactants is different.

Complete step by step solution:
The equation which indicates Effect of temperature on the heat of reaction is known as Kirchhoff's equation.
This can be better understood by the following reaction.
The enthalpy change for the reaction
\[aA\, + \,bB \to cC\, + \,dD\]
Is given by
\[\Delta H\, = \,\Sigma {H_{products}} - \Sigma {H_{reac\tan ts}} = (c{H_C}\, + \,d{H_D}) - \left( {a{H_A} + b{H_B}} \right)\]
On differentiating the given equation with respect to temperature and keeping pressure constant, we get,
\[{\left[ {\dfrac{{\partial (\Delta H)}}{{\partial T}}} \right]_P} = c{\left( {\dfrac{{\partial {H_C}}}{{\partial T}}} \right)_P} + d{\left( {\dfrac{{\partial {H_D}}}{{\partial T}}} \right)_P} - {\left( {\dfrac{{\partial {H_A}}}{{\partial T}}} \right)_P} - {\left( {\dfrac{{\partial {H_B}}}{{\partial T}}} \right)_P}\]
  \[ = c{C_{P,C}} + d{C_{P,D}} - a{C_{P,A}} - b{C_{P,B}} = \Delta {C_P}\] since, \[{C_P} = {\left( {\dfrac{{\partial H}}{{\partial T}}} \right)_P}\]
where, $\Delta {C_P}$ = Sum of heat capacities of product - Sum of heat capacities of reactants

Thus, we can sum this up as:
Kirchhoff’s equation expresses the temperature dependence of the thermal quantities associated with a chemical reaction through the difference in heat capacities between products and reactants.
Hence, Option (C) Kirchhoff’s law is the correct answer to the given question.

Additional Information:
Let us learn briefly about the other laws provided as options.
Antoine’s Law: It states the empirical correlation between vapor pressure and temperature of pure substances. It enables us to predict the vapor pressure of pure liquids and sublimable solids.
Kelvin’s Law: describes the change in vapor pressure due to a curved liquid–vapor interface, like the surface of a droplet. Thus, the vapor pressure of a curved surface is more than that of a flat surface.

Note: Kirchhoff’s equation has many biochemical applications because it allows us to predict enthalpy changes at other temperatures by using standard enthalpy data. If the temperature range is not small then the heat capacities will vary with temperature.