A silver coin weighing 2.5 gm was dissolved in `HNO_3` and then further treated with excess HCI. The mass of `Ag CI` formed was 2.99 gm. The percentage of silver in the coin will be:

Options

A. 0.75
B. 0.9
C. 0.35
D. 0.1

Answer

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

### Step 1: Write the reactions
1. **Dissolving Silver Coin in HNO3**:
\[ \text{Ag} + 4 \text{HNO}_3 \rightarrow \text{AgNO}_3 + 2 \text{H}_2\text{O} + \text{NO}_2 \]

2. **Formation of Silver Chloride (AgCl)**:
\[ \text{AgNO}_3 + \text{HCl} \rightarrow \text{AgCl} + \text{HNO}_3 \]

### Step 2: Calculate moles of AgCl formed
- Given mass of AgCl = 2.99 g
- Molar mass of AgCl = Atomic mass of Ag (107.8 g/mol) + Atomic mass of Cl (35.5 g/mol) = 143.3 g/mol

Now, calculate the moles of AgCl:
\[ \text{Moles of AgCl} = \frac{\text{mass}}{\text{molar mass}} = \frac{2.99 \, \text{g}}{143.3 \, \text{g/mol}} \approx 0.0208 \, \text{mol} \]

### Step 3: Determine moles of silver (Ag)
From the stoichiometry of the reactions:
- 1 mole of Ag produces 1 mole of AgCl.
- Therefore, moles of Ag = moles of AgCl = 0.0208 mol.

### Step 4: Calculate the mass of silver (Ag)
Using the atomic mass of silver:
\[ \text{Mass of Ag} = \text{moles} \times \text{atomic mass} = 0.0208 \, \text{mol} \times 107.8 \, \text{g/mol} \approx 2.242 \, \text{g} \]

### Step 5: Calculate the percentage of silver in the coin
Given the mass of the silver coin = 2.5 g:
\[ \text{Percentage of silver} = \left( \frac{\text{mass of Ag}}{\text{mass of coin}} \right) \times 100 = \left( \frac{2.242 \, \text{g}}{2.5 \, \text{g}} \right) \times 100 \approx 89.68\% \]

### Final Answer
The percentage of silver in the coin is approximately **89.68%**.

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