21.6 g of silver coin is dissolved in `HNO_(3)`. When NaCl is added to this solution, all silver is precipitated as AgCl. The weight of AgCl is found to be 14.35g then % silver in coin is:
`Ag + HNO_(3) overset(NaCl)to AgCl`

Options

A. 0.5
B. 0.75
C. 1
D. 0.15

Answer

To find the percentage of silver in the silver coin, we can follow these steps:

### Step 1: Determine the moles of AgCl formed
We know that the weight of AgCl precipitated is 14.35 g. To find the moles of AgCl, we use the formula:

\[ \text{Moles of AgCl} = \frac{\text{Weight of AgCl}}{\text{Molar mass of AgCl}} \]

The molar mass of AgCl (Silver Chloride) can be calculated as follows:
- Molar mass of Ag = 107.87 g/mol
- Molar mass of Cl = 35.45 g/mol

Thus, the molar mass of AgCl is:
\[ \text{Molar mass of AgCl} = 107.87 + 35.45 = 143.32 \text{ g/mol} \]

Now, substituting the values:
\[ \text{Moles of AgCl} = \frac{14.35 \text{ g}}{143.32 \text{ g/mol}} \approx 0.100 \text{ mol} \]

### Step 2: Determine the moles of silver (Ag) in AgCl
From the reaction, we know that 1 mole of AgCl contains 1 mole of Ag. Therefore, the moles of Ag will also be 0.100 mol.

### Step 3: Calculate the mass of silver (Ag)
Now, we can calculate the mass of silver using the moles of Ag:
\[ \text{Mass of Ag} = \text{Moles of Ag} \times \text{Molar mass of Ag} \]
\[ \text{Mass of Ag} = 0.100 \text{ mol} \times 107.87 \text{ g/mol} \approx 10.787 \text{ g} \]

### Step 4: Calculate the percentage of silver in the coin
Now, we can find the percentage of silver in the silver coin using the formula:
\[ \text{Percentage of Ag} = \left( \frac{\text{Mass of Ag}}{\text{Total mass of coin}} \right) \times 100 \]
\[ \text{Percentage of Ag} = \left( \frac{10.787 \text{ g}}{21.6 \text{ g}} \right) \times 100 \approx 50\% \]

### Final Answer
The percentage of silver in the silver coin is approximately **50%**.

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