Question

Which one of the following is incorrect for an ideal solution?
(A) \[\Delta P = {P_{obs}} - P_{calculated\,by\,Raoult's\,law} = 0\]
(B) \[\Delta {G_{mix}} = 0\]
(C) \[\Delta {H_{mix}} = 0\]
(D) \[\Delta {U_{mix}} = 0\]

Answer 1

Hint: For an ideal gas, the enthalpy of the solution gets closer to zero and shows an ideal behaviour. Also, the volume remains the same on mixing the solution. For vapour pressure, one must know Raoult’s law. The entropy always increases for an ideal gas and so the Gibbs free energy is negative.

Complete step-by-step answer:
An ideal solution is a homogeneous mixture of compounds under which the interactions between the solute and solvent molecules are the same as those between the molecules itself of each substance. For example, benzene and toluene have very similar molecular structures and so they are ideal.
We know that \[\Delta {U_{mix}} = \Delta {H_{mix}} - P\Delta {V_{mix}}\]from the first law of thermodynamics
For an ideal gas, the solution enthalpy reached approximately to zero and the volume mixing is also zero for an ideal gas. During mixing, no heat should be either evolved or absorbed and there should be no expansion or contraction during mixing.
\[\Delta {H_{mix}} = 0,\Delta {V_{mix}} = 0\]
\[\therefore \Delta {U_{mix}} = 0\]
Again, for an ideal gas, as per Raoult’s law, the partial vapour pressure of a solvent in a solution is equal to the vapour pressure of a pure solvent multiplied by its mole fraction.
We have \[{P_A} = {x_A}P_A^o,{P_B} = {x_B}P_B^o\]
Therefore, \[\Delta P = {P_{obs}} - {P_{calculated\,by\,Raoult's\,law}} = 0\]
For ideal gas, the Gibbs free energy can be written as:
\[\Delta {G_{mix}} = \Delta {H_{mix}} - T\Delta {S_{mix}}\]
\[\Delta {S_{mix}} \ne 0\]for an ideal gas
Thus, \[\Delta {G_{mix}} \ne 0\]

Hence, the correct option is (B).

Note: An ideal gas is also defined as one where all collisions between atoms or molecules are perfectly elastic and where no attractive intermolecular forces exist. We can imagine it as a chain of colliding perfectly hard spheres, which are not communicating with each other.