Question

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (molecular weight = $206$). What would be the maximum uptake of $Ca^{2+}$ ions by the resin when expressed in mole per gram resin

• A. $\frac{1}{103}$
• B. $\frac{1}{206}$
• C. $\frac{2}{309}$
• D. $\frac{1}{412}$

Answer 1

The Correct Option is D

To determine the maximum uptake of \(Ca^{2+}\) ions by the resin, we need to understand the ion exchange process involved in water softening using this resin.

1. The resin used has the formula \(C_8H_7SO_3Na\), with a molecular weight of 206 g/mol. This resin is a sodium salt and can exchange its \(Na^+\) ions with other cations in the water.
2. In water softening, \(Ca^{2+}\) ions are exchanged with \(Na^+\) ions in the resin. The chemical reaction for this ion exchange process can be represented as: \[ 2 \, \text{C}_8\text{H}_7\text{SO}_3\text{Na} + \text{Ca}^{2+} \rightarrow (\text{C}_8\text{H}_7\text{SO}_3)_2\text{Ca} + 2 \, \text{Na}^+ \] This equation shows that two moles of the resin are required to exchange with one mole of \(Ca^{2+}\) ions.
3. Given that the molecular weight of the resin is 206 g/mol, the mass required for exchanging one mole of \(Ca^{2+}\) is: \[ 2 \times 206 = 412 \, \text{g/mol} \] Thus, the uptake of \(Ca^{2+}\) ions per gram of resin is the reciprocal of 412 g/mol.
4. Therefore, the maximum uptake of \(Ca^{2+}\) ions by the resin, when expressed in mole per gram resin, is: \[ \frac{1}{412} \, \text{mole/g} \]

This reasoning clearly indicates that the correct answer is \( \frac{1}{412} \), which corresponds to the calculation and understanding of the ion exchange process of the resin with \(Ca^{2+}\) ions.