The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (Mol

Question

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (Mol. Wt. 206). The maximum uptake of $Ca^{2+}$ ions by the resin when expressed in mole per gram resin is based on the reaction:
$$ 2C_8H_7SO_3Na + Ca^{2+} \rightarrow (C_8H_7SO_3)_2Ca + 2Na^+ $$

Accepted Answer

1. **Analyze Stoichiometry:** From the balanced chemical equation, 2 moles of the resin ($C_8H_7SO_3Na$) react with 1 mole of calcium ions ($Ca^{2+}$) to maintain charge neutrality (replacing two $+1$ ions with one $+2$ ion).
2. **Calculate Mass of Resin:**
   - Molar Mass of Resin = $206 	ext{ g mol}^{-1}$.
   - Mass of 2 moles of Resin = $2 	imes 206 	ext{ g} = 412 	ext{ g}$.
3. **Calculate Uptake:**
   - The uptake is defined as the moles of $Ca^{2+}$ absorbed per gram of resin.
   - Uptake = $\frac{	ext{Moles of } Ca^{2+}}{	ext{Mass of Resin}}$
   - Uptake = $\frac{1 	ext{ mol}}{412 	ext{ g}}$
   - Uptake = $\frac{1}{412} 	ext{ mol g}^{-1}$.

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