Question

A sample of water has a hardness expressed as $77.5$ ppm $C{a}^{2+}$. This sample is passed through an ion exchange column and $C{a}^{2+}$ is replaced by $H^{+}$. Select correct statement(s).

• A. pH of the water after it has been so treated is $2.4$.
• B. Every $C{a}^{2+}$ ion is replaced by one $H^{+}$ ion.
• C. Every $C{a}^{2+}$ ion is replaced by two $H^{+}$ ions.
• D. pH of the solution remains unchanged.

Answer 1

Answer: (A), (C)

pH of the water after it has been so treated is $2.4$.
Every $C{a}^{2+}$ ion is replaced by two $H^{+}$ ions.

The ion exchange equilibrium is as shown below:
$C{a}^{2+}+R{H}_2\to CaR+2H^{+}$
$77.5$ ppm $C{a}^{2+}$ corresponds to $77.5$ g $C{a}^{2+}$ per ${10}^6$ mL .
This is equal to $77.5\times {10}^{-6}g{L}^{-1}C{a}^{2+}$.

This is also equal to $\frac{77.5\times {10}^{3-}}{40}mol{L}^{-1}C{a}^{2+}$ or $\frac{77.5\times {10}^{3-}\times 2}{40}mol{L}^{-1}{H}^{+}$.

Hence, the hydrogen ion concentration is $\left[H^{+}\right]=3.875\times {10}^{-3}$
The $pH$ of the solution is $pH=-log{H}^{+}=-log3.875\times {10}^{-3}=-2.4$
Thus, the options, A and C are correct.