Discussion
The ideal solution made up of 5.00 mol (mole fraction = 0.606) benzene and 3.25 mol (mole fraction = 0.394) toluene, the free energy of mixing (ΔGmix) is equal to −13 kJ mol−1. The corresponding values for the their equimolar solution will be ;
Answer: D
The value for the equimolar solution is more negative than −13 kJ mol−1.
For an ideal solution the Gibbs energy of mixing is entirely entropic:
\[ \Delta G_{mix} = nRT\,(x_{1}\ln x_{1} + x_{2}\ln x_{2}) \]
The bracket is most negative at x1 = x2 = 0.5, where it equals ln 0.5 = −0.693, compared with −0.671 at the given composition (0.606 and 0.394). For the same amount of liquid, the equimolar mixture therefore has the more negative ΔGmix.
ΔGmix depends on composition, ruling out option B, it is not a pure number like 'unity', and 'less negative' (C) has the dependence the wrong way round.
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