Q.13 The given equation
(d(ΔH)/dT)p = ΔCp
where H, T and Cp are the enthalpy, temperature and heat capacity at constant pressure, respectively, is called
(A) Clausius–Clapeyron equation
(B) Hess’s law
(C) Kirchhoff’s equation
(D) Trouton’s rule
Introduction
In thermodynamics, understanding how enthalpy changes with
temperature is essential for analyzing chemical reactions.
One important relation connects the temperature dependence of enthalpy with
heat capacity at constant pressure. This relation is commonly tested in
chemistry competitive examinations.
Given Equation
The given equation is:
(d(ΔH) / dT)p = ΔCp
where:
- H = Enthalpy
- T = Temperature
- Cp = Heat capacity at constant pressure
Correct Answer
(C) Kirchhoff’s equation
Kirchhoff’s equation states that the rate of change of enthalpy change with
respect to temperature at constant pressure is equal to the change in heat
capacity.
Explanation of All Options
(A) Clausius–Clapeyron Equation
This equation relates vapour pressure with temperature and is used in
phase equilibrium problems. It involves enthalpy of vaporization, not
heat capacity.
Hence, this option is incorrect.
(B) Hess’s Law
Hess’s law states that enthalpy change of a reaction is independent of
the path followed. It does not involve temperature derivatives or heat
capacity.
This option is incorrect.
(C) Kirchhoff’s Equation
Kirchhoff’s equation directly relates enthalpy change with heat capacity
at constant pressure:
d(ΔH) / dT = ΔCp
This option is correct.
(D) Trouton’s Rule
Trouton’s rule states that entropy of vaporization is nearly constant
for many liquids. It deals with entropy, not enthalpy-temperature
relations.
This option is incorrect.
Summary
| Option | Law | Result |
|---|---|---|
| A | Clausius–Clapeyron Equation | Incorrect |
| B | Hess’s Law | Incorrect |
| C | Kirchhoff’s Equation | Correct |
| D | Trouton’s Rule | Incorrect |
Conclusion
The equation (d(ΔH) / dT)p = ΔCp
is known as Kirchhoff’s equation. It plays a crucial role in
thermodynamics by explaining how enthalpy varies with temperature using heat
capacity data.
