Question

Which one is not equal to zero for an ideal solution?
(A) \[ - \Delta {V_{mix}}\]
(B) \[ - \Delta P = {P_{Observed}} - {P_{Roult}}\]
(C) \[ - \Delta {H_{mix}}\]
(D) \[ - \Delta {S_{mix}}\]

Answer 1

Hint: A solution in which the gas phase exhibits thermodynamic properties analogous to those of the mixture of ideal gases is known as an ideal solution or ideal mixture. The ideal gases will follow all the gas laws such as Charles law, Boyle's law, Avogadro law.

Complete Solution :
- A mixture in which the molecules of different species are distinguishable, however unlike the ideal gas, the molecules in the solution exert forces on one another is known as an ideal solution or an ideal mixture. When the forces between the molecules are the same for all the molecules, independent of species then a solution is known as an ideal solution.
- An ideal solution can be prepared by mixing a solute and a solvent which consist of similar molecular structure and size. Let us assume X and Y be two substances and mix them. We will see that there are several intermolecular forces that exist between them is such that-
X and X experience intermolecular forces of attraction.
Y and Y experience intermolecular forces of attraction.
X and Y experience intermolecular forces of attraction.

Here, the intermolecular forces of attraction are the same for all types of interactions between the molecule, hence it gives us an ideal solution.
- An ideal solution or ideal mixture possesses the following characteristics-
- Volume change by mixing of solutes must be zero.
\[{V_{Solute}} + {V_{Solvent}} = {V_{Solution}};\Delta {V_{mix}} = 0\]

- Heat change on mixing the solution must be zero, that is heat should neither be evolved or absorbed.
\[\Delta {H_{mix}} = 0\]
- There should be no chemical reaction between the components of the solution, that is the solute and solvent.
\[Solute + Solvent \to Solution\]
- Solute molecules must not dissociate intro their respective ions in the ideal solution.
- Solute molecules must not associate with other ions in the ideal solution.
- Ideal solutions must obey Raoult's law at all concentrations without exception. The observed pressure is equal to the pressure calculated from Raoult’s law, then the solution is known to be an ideal solution.
\[{P_{Observed}} = {P_{Raoult}}\]
\[\Delta P = {P_{Solute}} - {P_{Solvent}} = 0\]
So, the correct answer is “Option D”.

Additional Information:
Some examples of ideal solutions are given below-
- Benzene and toluene
- Carbon tetrachloride and silicon tetrachloride
- n-hexane and n-heptane

Note: Let us now see Raoult’s law in detail. Raoult’s law states that ‘the relative lowering of the vapour pressure of a solvent by dissolving a non-volatile electrolyte is equal to the mole fraction of the solute’.
Therefore, it is given by
\[{p_i} = p_i^0{x_i}\]