The GATE Grind

GATE 2021 MT – Question 16

Metallurgical Thermodynamics · Solutions and chemical potential · 1 mark · Multiple choice

Elements A and B have the same crystal structure. For a dilute solution of B in A, which is true? Here $\Delta H_{mix}$ is mixing enthalpy, $a_B$ activity and $X_B$ mole fraction of B.

  1. If $\Delta H_{mix}=0$, then $a_B<X_B$
  2. If $\Delta H_{mix}=0$, then $a_B>X_B$
  3. If $\Delta H_{mix}>0$, then $a_B<X_B$
  4. If $\Delta H_{mix}<0$, then $a_B<X_B$

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Show answer and explanation

Correct answer: (D) If $\Delta H_{mix}<0$, then $a_B<X_B$

Explanation

In the standard regular-solution interpretation, negative mixing enthalpy means unlike neighbors are favored and the solute shows negative deviation from ideality.

Thus γB<1 and aB=γBxB<xB, **D**.

The enthalpy-to-activity inference uses the usual regular-solution approximation; enthalpy alone does not determine excess Gibbs energy in complete generality.