Project ForgeProcess Calculations
Laws of Thermodynamics
GATE 2010
Hard
At constant T and P, the molar density of a binary mixture is given by ρ=1+x2, where x2 is the mole fraction of component 2. The partial molar volume at infinite dilution for component 1, V̄1^∞, is
- 0.75
- B1.0
- C2.0
- D4.0
Explanation
Total volume V=(n1+n2)/ρ=(n1+n2)²/(n1+2n2) (since ρ=1+n2/(n1+n2)). V̄1=∂V/∂n1=f(2g−f)/g², with f=n1+n2, g=n1+2n2. At infinite dilution (n1→0): f=n2, g=2n2, giving V̄1=n2(4n2−n2)/(2n2)²=3n2²/4n2²=0.75.
Source: GATE CH 2010 (2010)
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