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GATE 2024 Chemical Engineering, Q32 · Thermodynamics

The correct answer is 0.44 to 0.46.

Question

Consider a binary mixture of components A and B at temperature T and pressure P. Let V̄_A and V̄_B be the partial molar volumes of A and B, respectively. At a certain mole fraction of A, xA,(∂VˉA/∂xA)T,P=22cm3/molx_{A}, (\partial V̄_{A}/\partial x_{A})_{T,P} = 22 cm³/mol and (∂VˉB/∂xA)T,P=−18cm3/mol.(\partial V̄_{B}/\partial x_{A})_{T,P} = −18 cm³/mol. The value of xA,x_{A}, rounded off to 2 decimal places, is ________

Official answer: 0.44 to 0.46

Why

GATE 2024 official key: 0.44 to 0.46. Gibbs-Duhem: xA(∂VˉA/∂xA)+xB(∂VˉB/∂xA)=0⇒22xA−18(1−xA)=0⇒40xA=18⇒xA=0.45.x_{A}(\partial V̄_{A}/\partial x_{A}) + x_{B}(\partial V̄_{B}/\partial x_{A}) = 0 \Rightarrow 22x_{A} − 18(1−x_{A}) = 0 \Rightarrow 40x_{A} = 18 \Rightarrow x_{A} = 0.45.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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