A silver coin weighing 11.34 g was dissolved in nitric acid When sodium chloride was added to the solution all the silver (present as `AgNO_(3)`) precipitated as silver chloride. The mass of the precipitated silver chloride was 14.35 g. Calculate the percentage of silver in the coin.

Options

A. 48%
B. 95.2%
C. 90%
D. 80%

Answer

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

### Step 1: Determine the moles of silver chloride (AgCl) formed.
The mass of the precipitated silver chloride is given as 14.35 g. We need to calculate the number of moles of AgCl using the formula:

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

The molar mass of AgCl is calculated as follows:
- Silver (Ag) = 107.87 g/mol
- Chlorine (Cl) = 35.45 g/mol
- Molar mass of AgCl = 107.87 + 35.45 = 143.32 g/mol

Now, substituting the values:

\[ \text{Moles of AgCl} = \frac{14.35 \, \text{g}}{143.32 \, \text{g/mol}} \approx 0.1000 \, \text{mol} \]

### Step 2: Determine the moles of silver (Ag) in the coin.
From the stoichiometry of the reaction, we know that 1 mole of Ag produces 1 mole of AgCl. Therefore, the moles of silver (Ag) will be equal to the moles of AgCl:

\[ \text{Moles of Ag} = \text{Moles of AgCl} = 0.1000 \, \text{mol} \]

### Step 3: Calculate the mass of silver (Ag) in the coin.
To find the mass of silver, we can use the formula:

\[ \text{Mass of Ag} = \text{Moles of Ag} \times \text{Molar mass of Ag} \]

Substituting the values:

\[ \text{Mass of Ag} = 0.1000 \, \text{mol} \times 107.87 \, \text{g/mol} \approx 10.79 \, \text{g} \]

### Step 4: Calculate the percentage of silver in the coin.
Now, we can calculate the percentage of silver in the coin using the formula:

\[ \text{Percentage of Ag} = \left( \frac{\text{Mass of Ag}}{\text{Mass of coin}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage of Ag} = \left( \frac{10.79 \, \text{g}}{11.34 \, \text{g}} \right) \times 100 \approx 95.2\% \]

### Final Answer:
The percentage of silver in the coin is approximately **95.2%**.

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