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Question #44518

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The Question

An aqueous solution of ethanol (\ce{C2H5OH}) exhibits a positive deviation from Raoult's Law, forming a minimum-boiling azeotrope at a specific liquid mole fraction $x_E$ and temperature $T_{az}$ under a constant pressure $P$ . Let $\Delta H_{vap, sys}$ and $\Delta S_{vap, sys}$ represent the integral enthalpy and entropy of vaporization of the azeotropic mixture. Let $\gamma_E$ and $\gamma_W$ be the activity coefficients of ethanol and water in the liquid phase, and $P_E^\circ$ and $P_W^\circ$ be their respective pure component vapor pressures at $T_{az}$ . Assuming the vapor phase behaves ideally, which of the following sets of thermodynamic relations is strictly valid during the reversible, isobaric vaporization of this azeotrope?

Options

A.
$\Delta S_{vap, sys} = \frac{\Delta H_{vap, sys}}{T_{az}}$ , \quad $\left(\frac{\partial T_b}{\partial x_E}\right)_P = 0$ , \quad $\frac{\gamma_E}{\gamma_W} = \frac{P_W^\circ}{P_E^\circ}$
B.
$\Delta S_{vap, sys} = \frac{\Delta H_{vap, sys}}{T_{az}} + \Delta S_{mix}$ , \quad $\left(\frac{\partial T_b}{\partial x_E}\right)_P > 0$ , \quad $\frac{\gamma_E}{\gamma_W} = \frac{P_E^\circ}{P_W^\circ}$
C.
$\Delta S_{vap, sys} = \frac{\Delta H_{vap, sys} - \Delta H_{mix}}{T_{az}}$ , \quad $\left(\frac{\partial T_b}{\partial x_E}\right)_P = 0$ , \quad $\frac{\gamma_E}{\gamma_W} = \frac{P_E^\circ}{P_W^\circ}$
D.
$\Delta S_{vap, sys} = \frac{\Delta H_{vap, sys}}{T_{az}}$ , \quad $\left(\frac{\partial T_b}{\partial x_E}\right)_P < 0$ , \quad $\gamma_E = \gamma_W = 1$

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Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Raoult’s Law Ideal vs Non-Ideal|Entropy of Phase Change|Enthalpy Definition

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Chemical Exception' of azeotropic mixtures behaving as pseudo-pure substances.

Students often conflate the integral properties of mixing ( $\Delta H_{mix} > 0$ , $\Delta S_{mix} > 0$ ) with the localized phase transition properties at the azeotrope.

The trap assumes that because the solution is non-ideal, the entropy of vaporization must be modified by $\Delta S_{mix}$ or $\Delta H_{mix}$ .

Furthermore, it tests the rigorous application of Raoult's Law at the azeotrope to derive the inverse relationship between activity coefficients and pure vapor pressures, catching students who guess the direct ratio or assume ideality.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Raoult’s Law Ideal vs Non-Ideal
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free