Question

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

Answer 1

Ion exchange resins are used to remove ions like calcium and magnesium which causes hardness to the water. We have to convert the grams of the ion exchanger into moles by using the following formula.
$\text{one of the moles of the compound=}\dfrac{\text{weight of the compound}}{\text{molecular weight of the compound}}$

Complete step by step answer:
- We have to calculate the number moles of the calcium that are attached to1 gm of the ion exchanger resin.
- The molecular formula of the given resin is ${{C}_{8}}{{H}_{7}}S{{O}_{3}}Na$ .
- It is given that the molecular weight of the ion exchange resin is 206.
- We can calculate the number of moles of the resin by using the following formula.

& \text{number of moles of the resin=}\frac{\text{weight of the resin}}{\text{molecular weight of the resin}} \\\ & \text{number of moles of the resin}=\dfrac{1}{206}mol \\\ \end{aligned}$$ \- Means 1 gm of resin is equal to $\dfrac{1}{206}$ moles. \- Now the reaction between resin and calcium looks like the below equation. $$2{{C}_{8}}{{H}_{7}}S{{O}_{3}}Na+C{{a}^{2+}}\to ({{C}_{8}}{{H}_{7}}S{{O}_{3}})Ca+2N{{a}^{+}}$$ \- From the above chemical reaction we can say that 2 moles of ion exchange reacts with one moles of calcium and one mole od=f calcium replaces two moles of sodium from the ion exchange resin. \- Therefore 2 moles of resin combines with 1 mole of $C{{a}^{2+}}$ . \- 1 mole of resin will combine with $\dfrac{1}{2}$ mole of $C{{a}^{2+}}$ . $\dfrac{1}{206}$ moles of resin will combine with = $\dfrac{\text{1}}{\text{206}}\text{ }\\!\\!\times\\!\\!\text{ }\dfrac{\text{1}}{\text{2}}\text{=}\dfrac{\text{1}}{\text{412}}\text{moles of C}{{\text{a}}^{\text{2+}}}$ **So, the correct answer is “Option D”.** **Note:** There are two types of ion exchangers used in water purification to remove the hardness causing salts. They are cation exchanger and anion exchanger. Cation exchanger has a negative charge and anion exchanger has a positive charge.