Project ForgeSign up free
Process Calculations
Laws of Thermodynamics
GATE 2012
Hard

Consider a binary liquid mixture at constant temperature T and pressure P. If the enthalpy change of mixing, ΔH=5x1x2, where x1 and x2 are the mole fractions of species 1 and 2 respectively, and the entropy change of mixing ΔS=−R[x1lnx1+x2lnx2] (with R=8.314 J/mol.K), then the minimum value of the Gibbs free energy change of mixing at 300K occurs when

  • Ax1=0
  • Bx1=0.2
  • Cx1=0.4
  • x1=0.5

Explanation

ΔGmix=ΔH−TΔS=5x1x2+RT[x1lnx1+x2lnx2], a function symmetric under x1↔x2. By symmetry, x1=0.5 is a critical point. Checking the second derivative there: d²G/dx1²=−10+RT[1/x1+1/(1−x1)]=−10+2494.2×4≈9967>0, confirming a genuine minimum (the entropy term's curvature dominates the enthalpy term's).

Source: GATE CH 2012 (2012)

This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.

Start revising free