The molecular formula of a commercial resin used for exchanging ions in water softening is `C_(8)H_(7)SO_(3)Na(mol. Wt. 206)` . What would be the maximum uptake of `Ca^(2+)` ions by the resin when expressed in mole per gram resin?

Options

A. `(1)/(206)`
B. `(1)/(412)`
C. `(2)/(309)`
D. `(1)/(103)`

Explanation

To determine the maximum uptake of \( \text{Ca}^{2+} \) ions by the resin expressed in moles per gram of resin, we can follow these steps:

### Step 1: Understand the Ion Exchange Reaction
The resin has the formula \( \text{C}_8\text{H}_7\text{SO}_3\text{Na} \). In the ion exchange process, the sodium ion (\( \text{Na}^+ \)) in the resin is exchanged for calcium ions (\( \text{Ca}^{2+} \)). The reaction can be represented as:
\[ \text{C}_8\text{H}_7\text{SO}_3\text{Na} + \text{Ca}^{2+} \rightarrow \text{C}_8\text{H}_7\text{SO}_3\text{Ca} + \text{Na}^+ \]

### Step 2: Determine the Molar Mass of the Resin
The molar mass of the resin is given as 206 g/mol. This means that 1 mole of the resin weighs 206 grams.

### Step 3: Calculate the Moles of Resin in 1 Gram
To find the number of moles of resin in 1 gram, we use the formula:
\[ \text{Moles of resin} = \frac{\text{mass of resin (g)}}{\text{molar mass of resin (g/mol)}} \]
Substituting the values:
\[ \text{Moles of resin} = \frac{1 \text{ g}}{206 \text{ g/mol}} \approx 0.00485 \text{ mol} \]

### Step 4: Determine the Maximum Uptake of \( \text{Ca}^{2+} \)
Since each mole of resin can exchange one mole of \( \text{Ca}^{2+} \) ions, the maximum uptake of \( \text{Ca}^{2+} \) ions by the resin is equal to the number of moles of resin calculated in Step 3.

Thus, the maximum uptake of \( \text{Ca}^{2+} \) ions in moles per gram of resin is:
\[ \text{Maximum uptake of } \text{Ca}^{2+} = 0.00485 \text{ mol/g} \]

### Final Answer
The maximum uptake of \( \text{Ca}^{2+} \) ions by the resin is approximately \( 0.00485 \text{ mol/g} \).

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