Animated Solution for Chemistry - Electrochemistry: Let $C_{\text{NaCl}}$ and $C_{{\text{BaSO}}_4}$ be the conductances (in S) measured for saturated aqueous solutions of $\text{NaCl}$ and ${\text{BaSO}}_4$, respectively, at a temperature $T$. Which of the following is false?

Have you ever wondered what happens when you heat a saturated solution? Intuition tells us that heating a liquid allows it to dissolve more solid, right? Well, nature loves to throw curveballs, and this JEE problem is a perfect example of one.

The electrical conductance ($C$) of an electrolytic solution depends on two primary factors: 1. Number of Ions (Concentration): More ions mean more charge carriers. 2. Ionic Mobility: How fast these ions can swim through the solvent.

When we increase the temperature ($T$), the kinetic energy of the water molecules increases, and the viscosity of water decreases. This means ions experience less drag and can move faster. Therefore, ionic mobility always increases with temperature. This immediately tells us that statement (a) is absolutely true.

Sodium Chloride ($\text{NaCl}$) and Barium Sulphate (${\text{BaSO}}_4$).

$\text{NaCl}$ is a strong, highly soluble electrolyte. If you dump it in water, it dissolves readily, creating a massive concentration of ${\text{Na}}^{+}$ and ${\text{Cl}}^{-}$ ions.

On the other hand, ${\text{BaSO}}_4$ is a sparingly soluble salt. It barely dissolves, leaving only a tiny fraction of ${\text{Ba}}^{2+}$ and ${\text{SO}}_4^{2-}$ ions in the water.

Because conductance is directly proportional to the number of ions, the conductance of a saturated $\text{NaCl}$ solution will always dwarf that of a saturated ${\text{BaSO}}_4$ solution at any given temperature. Thus, $C_{\text{NaCl}}\gg C_{{\text{BaSO}}_4}$, making statement (d) true.

Solubility Curves Now, let's heat things up. What happens to a saturated solution of ${\text{BaSO}}_4$ when we increase the temperature from $T_1$ to $T_2$? The dissolution of ${\text{BaSO}}_4$ is an endothermic process. According to Le Chatelier's Principle, increasing the temperature shifts the equilibrium forward:

More solid dissolves, the concentration of ions increases, and combined with the increased ionic mobility, the overall conductance $C_{{\text{BaSO}}_4}$ definitely increases. Statement (b) is true.

But here is where $\text{NaCl}$ pulls a fast one on us. The solubility of $\text{NaCl}$ in water is almost completely independent of temperature. Whether the water is at $20^{\circ }\text{C}$ or $80^{\circ }\text{C}$, a saturated solution holds roughly the same amount of dissolved $\text{NaCl}$.

Because the concentration of ions in the saturated $\text{NaCl}$ solution remains practically constant, the conductance does not experience the significant boost we might expect. The slight increase in ionic mobility is negligible compared to the concentration factor. Therefore, the claim that $C_{\text{NaCl}}(T_2)>C_{\text{NaCl}}(T_1)$ is considered false in this comparative context.

And that is how a simple solubility curve helps us crack a tricky electrochemistry problem!