A hydrophobic sol is stabilized by the addition of a small amount of electrolyte. If the coagulation value of $\text{NaCl}$ for a given sol is $50\text{ mmol/L}$, what is the coagulation value of ${\text{Na}}_2{\text{SO}}_4$ for the same sol, assuming the Hardy-Schulze rule applies?

Solution

1. The Hardy-Schulze rule states that the coagulating power is proportional to the sixth power of the valency of the ion.
2. For $\text{NaCl}$, the coagulating ion is ${\text{Na}}^{+}$ (valency 1).
3. For ${\text{Na}}_2{\text{SO}}_4$, the coagulating ion is ${\text{SO}}_4^{2-}$ (valency 2).
4. The ratio of coagulation values is $$\begin{array}{rl}\frac{C_1}{C_2}& =(\frac{z_2}{z_1}{)}^6\\ & =(\frac{2}{1}{)}^6\\ & =64\end{array}$$.
5. The coagulation value for ${\text{Na}}_2{\text{SO}}_4$ is $\frac{50}{64}\approx 0.78\text{ mmol/L}$.
6. Hence the answer is (B).