Question

For an ideal solution, the correct option is:
 (A) ${\mathrm{\Delta }}_{mix}S=0$ at constant T and P
 (B) ${\mathrm{\Delta }}_{mix}V\ne 0$ at constant T and P
 (C) ${\mathrm{\Delta }}_{mix}H=0$ at constant T and P
 (D) ${\mathrm{\Delta }}_{mix}G=0$ at constant T and P

Answer 1

Hint: In an ideal solution the components interact with each other in the same way they interact among themselves. The component molecules have similar structure and size. They also obey Raoult's Law.

Complete step by step answer:
-First we will understand what an ideal solution is.
It is a solution in which the thermodynamic properties exhibited by the gas phase are the same or analogous to those of a mixture of ideal gases. A mixture in which the molecules of different constituents are distinguishable and the molecules exert forces on each other will be ideal only if the forces are the same for all the molecules independent of the constituents.
In simple words we can say that any homogeneous solution in which the molecules of the components (solute and solvents) interact with each other in exactly the same way the molecules of the same component interact among themselves, is known as an ideal solution.
We can obtain an ideal solution by mixing 2 components having similar molecular structure and size.
-An ideal solution obeys Raoult's Law. According to the Raoult’s Law “For a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.”
So, for component 1: $P_1\alpha X_1$
                                                    $P_1=P_1^{\circ }{X}_1$ (1)
Where $P_1^{\circ }$ will be the vapour pressure of pure component 1 at the same temperature.
Similarly for component 2 $P_2=P_2^{\circ }{X}_2$ (2)
Where $P_2^{\circ }$ will be the vapour pressure of pure component 2 at the same temperature.
According to Dalton’s Law of partial pressure, the total pressure of a solution will be equal to the sum of the partial pressure of the components.
                                             $P_{total}=P_1+P_2$ (3)
Putting values from (1) and (2) in (3):
  $P_{total}=P_1^{\circ }{X}_1+P_2^{\circ }{X}_2$
                          = $(1-X_2)P_1^{\circ }+P_2^{\circ }{X}_2$ (Since $X_1+X_2=1$)
                          = $P_1^{\circ }+(P_2^{\circ }-P_1^{\circ })X_2$

-The conditions for any solution to be ideal are:
(1) The solution should obey Raoult's Law at every concentration.
(2) $\mathrm{\Delta }{H}_{mix}=0$, which means that heat is neither evolved or absorbed during the dissolution.
(3) $\mathrm{\Delta }{V}_{mix}=0$, which means that total volume of solution is equal to sum of the volumes of the components.
(4) The interactions between both A-A, B-B and A-B are the same, so both A and B are similar in shape, size and structure.
(5) $\mathrm{\Delta }{S}_{mix}>0$, which means that entropy increases.
(6) $\mathrm{\Delta }{G}_{mix}<0$, the process will be spontaneous.
(7) Both the components can be easily separated via simple fractional distillation.
-Some examples of ideal solutions are: toluene and benzene, ethyl iodide and ethyl bromide, n-heptane and n- hexane, bromobenzene and chlorobenzene, etc.
So, the correct answer is “Option C”.

Note: In an ideal gas the collisions occurring between the constituent atoms or molecules are completely elastic and there are no attractive intermolecular forces. So, they can be considered as a series of spheres which collide with each other perfectly but they do not communicate with each other.