The molecular formula of a commercial resin used for exchanging ions in water softening is${\mathrm{C}}_8{\mathrm{H}}_7{\mathrm{SO}}_3\mathrm{Na}$ (molecular weight : 206). What would be the maximum uptake of${\mathrm{Ca}}^{2+}$ ions by the resin when expressed in mole per gram resin?

The exchanging reaction is $2{\mathrm{C}}_8{\mathrm{H}}_7{\mathrm{SO}}_3\mathrm{Na}+{\mathrm{Ca}}^{2+}\to {\left({\mathrm{C}}_8{\mathrm{H}}_7{\mathrm{SO}}_3\right)}_2\mathrm{Ca}+2{\mathrm{Na}}^{+}$ For one mole of ${\mathrm{Ca}}^{2+}$ ions, two moles of resin is required. Thus, the maximum uptake of ${\mathrm{Ca}}^{2+}$ ions will be $1\mathrm{mol}{\mathrm{Ca}}^{2+}/2\mathrm{mol}$ resin =1 mole ${\mathrm{Ca}}^{2+}/(2 \mathrm{x} 206) \mathrm{g}$ resin$\equiv (1/412)\mathrm{mol}{\mathrm{Ca}}^{2+}/\mathrm{g}$ of resin