Question
Which one of the following is incorrect for ideal solution?
A.
$$\Delta {H_{{\text{mix}}}} = 0$$
B.
$$\Delta {U_{{\text{mix}}}} = 0$$
C.
$$\Delta P = {P_{{\text{obs}}.}} - {P_{{\text{calculated by Raoult's law}}}} = 0$$
D.
$$\Delta {G_{{\text{mix}}}} = 0$$
Answer :
$$\Delta {G_{{\text{mix}}}} = 0$$
Solution :
Key Idea For this problem, the following expression can be used.
$$\eqalign{
& \Delta {G_{{\text{mix}}}} = \Delta {H_{{\text{mix}}}} - T\Delta {S_{{\text{mix}}}} \cr
& {\text{For an ideal gas}} \cr
& \Delta {H_{{\text{mix}}}} = 0;\,\,\Delta {U_{{\text{mix}}}} = 0;\,\,\Delta {S_{{\text{mix}}}} \ne 0 \cr} $$
Putting all these values in the expression,
$$\Delta {G_{{\text{mix}}}} = \Delta {H_{{\text{mix}}}} - T\Delta {S_{{\text{mix}}}}$$ $$ \Rightarrow \Delta {G_{{\text{mix}}}} = 0 - T\Delta {S_{{\text{mix}}}}$$
$$\therefore \,\,\Delta {G_{{\text{mix}}}} \ne 0$$
Thus, option (D) is incorrect.