Question

Consider the following liquid vapor equilibrium
$Liquid\rightleftharpoons Vapor$
Which of the following relations is correct?
(A).$\dfrac{d\ln P}{dT}=-\dfrac{\Delta H}{RT}$
(B).$\dfrac{d\ln P}{d{{T}^{2}}}=\dfrac{-\Delta H}{{{T}^{2}}}$
(C).$\dfrac{d\ln P}{dT}=\dfrac{\Delta H}{R{{T}^{2}}}$
(D).$\dfrac{d\ln P}{d{{T}^{2}}}=\dfrac{\Delta H}{RT}$

Answer 1

Hint: The clausius – clapeyron equation allows us to estimate the vapor pressure at another temperature. If the vapor pressure is known at the same temperature then we can calculate the enthalpy of vaporization.

Complete answer:
The clausius – clapeyron equation is used to find the relationship between the pressure and the temperature for the conditions of the equilibrium between the two phases. The two phases for the clausius – clapeyron equation could be vapor or solid for sublimation or it can be solid or liquid for melting.
We can write that: $\dfrac{d\ln P}{dT}=\dfrac{\Delta H}{R{{T}^{2}}}$
The rate at which the natural logarithm of the vapor pressure of a liquid changes with the temperature and it is determined by the molar enthalpy of vapourization of the liquid, the ideal gas of the system or the temperature.

Hence the correct answer is option (C).

Additional information:
Equilibrium is defined as the condition during the course of a reversible chemical reaction in which there is no net change in the amounts of the reactants and the amount of product after a time. The equilibrium constant is defined as the product of concentration of product to the product of concentration of reactants each raise to the power of their respective stoichiometric coefficient.

Note:
Sublimation is a process in which the substance changes directly from solid to gas without converting into liquid or we can say that it is a process of direct transfer of molecules from the solid to gaseous state and vapourization is a process in which a substance changes from liquid to a gas.