Animated Solution for Chemistry - Solutions: At $35^{\circ }\text{C}$, the vapour pressure of ${\text{CS}}_2$ is $512\text{ mm Hg}$ and that of acetone is $344\text{ mm Hg}$. A solution of ${\text{CS}}_2$ in acetone has a total vapour pressure of $600\text{ mm Hg}$. The false statement amongst the following is

Ideal vs. Reality

Imagine you have two separate beakers: one filled with pure acetone and the other with pure carbon disulfide (${\text{CS}}_2$). At $35^{\circ }\text{C}$, the vapour pressure of pure acetone is $344\text{ mm Hg}$, and that of pure ${\text{CS}}_2$ is $512\text{ mm Hg}$.

According to Raoult's Law, if we mix these two liquids to form an ideal solution, the total vapour pressure should simply be a weighted average of their individual pure vapour pressures. Mathematically, the ideal total pressure $p_{\text{id}}$ is given by:

Because mole fractions $x_A$ and $x_B$ must add up to $1$, the ideal total pressure must strictly lie between $344\text{ mm Hg}$ and $512\text{ mm Hg}$. However, the problem states that the observed total vapour pressure of the mixture is a whopping $600\text{ mm Hg}$!

Since $600\text{ mm Hg}$ is significantly higher than the maximum possible ideal pressure ($512\text{ mm Hg}$), this solution exhibits a massive positive deviation from Raoult's Law. This immediately tells us that statement (a) is true: Raoult's law is indeed not obeyed by this system.

Why does the pressure shoot up so dramatically? It all comes down to molecular interactions. In pure acetone, the molecules are held together by relatively strong dipole-dipole interactions. In pure ${\text{CS}}_2$, the molecules are held together by dispersion forces.

When we mix them, the new $A-B$ interactions (between acetone and ${\text{CS}}_2$) are weaker than the original $A-A$ and $B-B$ interactions. Because the molecules don't attract each other as strongly in the mixture, they find it much easier to escape into the vapour phase. This increased escaping tendency is exactly what causes the vapour pressure to spike to $600\text{ mm Hg}$. Therefore, statement (b) is also a true fact.

Because the molecules in the mixture are experiencing weaker attractive forces, they tend to stay slightly further apart from each other compared to when they were in their pure states. This physical "pushing away" means that the total volume of the mixture will actually expand!

For any solution showing a positive deviation, the change in volume upon mixing is positive ($\Delta V_{\text{mix}}>0$). So, if we mix $100\text{ mL}$ of ${\text{CS}}_2$ and $100\text{ mL}$ of acetone, the final volume will be strictly greater than $200\text{ mL}$. Statement (c) claims the volume will be less than $200\text{ mL}$, making it the false statement we are looking for.

Finally, let's look at the thermodynamics. Breaking the strong initial $A-A$ and $B-B$ bonds requires a significant input of energy. Forming the new, weaker $A-B$ bonds releases only a small amount of energy. The net result is that energy must be absorbed from the surroundings. The process is endothermic ($\Delta H_{\text{mix}}>0$), meaning statement (d) is perfectly true.