Project ForgeProcess Calculations
Vapor-Liquid Equilibrium
GATE 2009
Hard
For a binary mixture at constant temperature and pressure, given lnγ1=−1+2x1−x1², which ONE of the following relations for lnγ2 is thermodynamically consistent (satisfies the Gibbs-Duhem equation)?
- Alnγ2=(1/2)x1²
- Blnγ2=x1²
- Clnγ2=−(1/2)x1²
- lnγ2=−x1²
Explanation
Gibbs-Duhem: x1(dlnγ1/dx1)+x2(dlnγ2/dx1)=0. Given dlnγ1/dx1=2−2x1=2x2, so x1(2x2)+x2(dlnγ2/dx1)=0 ⟹ dlnγ2/dx1=−2x1. Integrating with lnγ2=0 at x1=0 (pure component 2 reference): lnγ2=−x1².
Source: GATE CH 2009 (2009)
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.