Question

Consider the following liquid – vapour equilibrium Liquid $\rightleftharpoons$ Vapour. Which of the following relations is correct.
A. $\dfrac{{d\ln G}}{{d{T^2}}} = \dfrac{{\Delta H}}{{R{T^2}}}$
B. $\dfrac{{d\ln P}}{{dT}} = \dfrac{{ - \Delta H}}{{RT}}$
C. $\dfrac{{d\ln P}}{{d{T^2}}} = \dfrac{{ - \Delta H}}{{{T^2}}}$
D. $\dfrac{{d\ln P}}{{dT}} = \dfrac{{\Delta H}}{{R{T^2}}}$

Answer 1

This question gives the knowledge about the Clausius Clapeyron relation. Clausius Clapeyron relation is a way of representing the various discontinuous phase transitions between the two phases of matter of single constituents.

Complete step by step answer:
The Clausius Clapeyron relation is a way of representing the various discontinuous phase transitions between the two phases of matter of single constituents. This relation is generally derived from the Gibbs Helmholtz equation.
The Clausius Clapeyron equation on considering liquid – vapour equilibrium is written as follows:
Liquid $\rightleftharpoons$ Vapour
$\dfrac{{d\ln P}}{{dT}} = \dfrac{{\Delta H}}{{R{T^2}}}$

Therefore, option $D$ is the correct option.

Additional information: The Clausius Clapeyron relation is a way of representing the various discontinuous phase transitions between the two phases of matter of single constituents.
The applications of Clausius Clapeyron equation are as follows:
$1$. It helps in determining the latent heat of vaporization.
$2$. Clausius Clapeyron equation is used to determine the freezing point or boiling point. If the boiling point or the freezing point of a liquid at a particular pressure is known it is used to determine the other pressure using Clausius Clapeyron equation.
$3$. It helps in determining the vapor pressure at different temperatures.
$4$. It helps in determining the molal elevation constant.
$5$. Clausius Clapeyron equation is used to determine the molal depression constant.
$6$. It is also used to determine the latent heat of fusion.

Note:
The Clausius Clapeyron relation is a way of representing the various discontinuous phase transitions between the two phases of matter of single constituents. Gibbs Helmholtz equation is used to derive the Clausius Clapeyron equation.This equation gives the relation between the pressure and temperature.