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NEET CHEMISTRYSolutionsMedium

Question

Consider the following liquid-vapor equilibrium: Liquid ⇌ Vapour. Which of the following relations is correct?

A

\frac{d \ln P}{dT} = \frac{-\Delta H_v}{RT}

B

\frac{d \ln P}{dT} = \frac{-\Delta H_v}{T^2}

C

\frac{d \ln P}{dT} = \frac{\Delta H_v}{RT^2}

D

\frac{d \ln G}{dT^2} = \frac{-\Delta H_v}{RT^2}

Step-by-Step Solution

The relationship between vapor pressure (PP) and temperature (TT) for a liquid-vapor equilibrium is given by the Clausius-Clapeyron equation.

  1. Concept: For the equilibrium Liquid⇌VapourLiquid \rightleftharpoons Vapour, the equilibrium constant KpK_p is equal to the vapor pressure PP (assuming pure liquid).
  2. Temperature Dependence: The variation of the equilibrium constant with temperature is given by the van't Hoff equation: dln⁡KdT=ΔH∘RT2\frac{d \ln K}{dT} = \frac{\Delta H^\circ}{RT^2}.
  3. Substitution: Substituting K=PK = P and ΔH∘=ΔHvap\Delta H^\circ = \Delta H_{vap} (Enthalpy of vaporization, ΔHv\Delta H_v), we get: dln⁡PdT=ΔHvRT2\frac{d \ln P}{dT} = \frac{\Delta H_v}{RT^2}

This equation quantitatively describes how vapor pressure increases with temperature for an endothermic process (vaporization).

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Solutions. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYSolutionsconsiderfollowingliquidvaporequilibriumliquid

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