Question

The molecular formula of a commercial resin used for the exchanging ions in water softening is ${{\text{C}}_{\text{8}}}{{\text{H}}_{\text{7}}}\text{S}{{\text{O}}_{\text{3}}}\text{Na}$ (Molecular weight 206). What would be the maximum uptake $\text{C}{{\text{a}}^{\text{2+}}}$ ions by the resin when expressed in mole per gram resin?
(A) $\dfrac{1}{412}$
(B) $\dfrac{1}{103}$
(C) $\dfrac{1}{206}$
(D) $\dfrac{2}{309}$

Answer 1

Hint: The ion exchange resin has a wide application in water softening. The ${{\text{C}}_{\text{8}}}{{\text{H}}_{\text{7}}}\text{S}{{\text{O}}_{\text{3}}}\text{Na}$ is an acidic cation exchange resin. It has an ion exchange site at the $\text{-S}{{\text{O}}_{\text{3}}}\text{Na}$ group. The sodium ion replaces the calcium ion in the solution and removes the hardness of the water. The number of ions exchange in moles per gram of the resin is known as the exchange capacity of resin. It is usually the finding out the relation between the ions exchange on the surface of the resin.

Complete step by step answer:
The hard water is water that has a high dissolved mineral. It has a high concentration of \[\text{C}{{\text{a}}^{\text{2+}}}\] and \[\text{M}{{\text{g}}^{\text{2+}}}\] ions.
Here, we have hard water which contains the \[\text{C}{{\text{a}}^{\text{2+}}}\] ions. We are using an ion exchange resin to remove the calcium ions from the water. The ${{\text{C}}_{\text{8}}}{{\text{H}}_{\text{7}}}\text{S}{{\text{O}}_{\text{3}}}\text{Na}$ resin interacts with the calcium ions from the water, the two resin molecules form a bond with the\[\text{C}{{\text{a}}^{\text{2+}}}\] in exchange of 2 \[\text{N}{{\text{a}}^{\text{+}}}\] ions.
The chemical reaction for the maximum uptake of $\text{C}{{\text{a}}^{\text{2+}}}$ in grams per resin is given as:
\[\text{2}{{\text{C}}_{\text{8}}}{{\text{H}}_{\text{7}}}\text{S}{{\text{O}}_{\text{3}}}\text{Na + C}{{\text{a}}^{\text{2+}}}\text{ }\to {{\left( {{\text{C}}_{\text{8}}}{{\text{H}}_{\text{7}}}\text{S}{{\text{O}}_{\text{3}}} \right)}_{\text{2}}}\text{Ca + 2N}{{\text{a}}^{\text{+}}}\text{ }\]

From this reaction, we can observe that 1 mole of calcium is taken up by 2 moles of resin. The molecular weight of the resin is 206.
Hence, 1 mole of resin consists of 206 grams of resin.
Since 2 moles of resin are involved in the reaction, we can derive that,

The total mass of resin involved in the water softening is equal to,
$\text{Mass of 2 moles of resin = }206\text{ }\times \text{ 2g = 412g}$
This indicates that, the 1 moles of $\text{C}{{\text{a}}^{\text{2+}}}$ uptakes the $\text{412g}$ of resin.
We are interested to find out the moles,
$\begin{align}
  & 1\text{ mole of C}{{\text{a}}^{\text{2+}}}\text{ = 2 mole of resin = }\dfrac{1\text{ gram of resin}}{412\text{ g mo}{{\text{l}}^{\text{-1}}}} \\
 & \therefore \text{ 1 mol of C}{{\text{a}}^{\text{2+}}}\text{ = }=\dfrac{\text{1}}{\text{412}}\text{mol} \\
\end{align}$
Therefore, the number of moles of calcium ion that is removed by 1g of resin is
$\text{ }\dfrac{1}{412}\text{mol}$
So, the correct answer is “Option A”.

Note: Note that, the ion exchange resin has exchangeable sites. It can be anionic or cationic. The above resin is cation exchange resin. The ions are exchanged in such a manner that the charge on the ion in the solution and on the resin must be nullified. That is, here sodium has a charge of $+1$ while for calcium it is $+2$ . Thus to maintain the charge neutrality two sodium ions are exchanged with one calcium ion.