A 5.82 g silver coin is dissolved in nitric acid. When sodium chloride is added to the solution, all the silver gets precipitated as AgCl. The percentage of silver in the coin is :

Options

A. `60.3 %`
B. `80 %`
C. `93.1 %`
D. `70 %`

Explanation

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

### Step 1: Determine the mass of silver chloride (AgCl) precipitated.
The problem states that the mass of precipitated silver chloride is 7.2 grams.

### Step 2: Calculate the molar mass of AgCl.
The molar mass of AgCl can be calculated as follows:
- Atomic mass of silver (Ag) = 108 g/mol
- Atomic mass of chlorine (Cl) = 35.5 g/mol

So, the molar mass of AgCl = 108 g/mol + 35.5 g/mol = 143.5 g/mol.

### Step 3: Calculate the mass of silver (Ag) in the precipitate.
Using the mass of AgCl and the ratio of the molar masses, we can find the mass of silver in the precipitate:
\[ \text{Mass of Ag} = \left(\frac{\text{Atomic mass of Ag}}{\text{Molar mass of AgCl}}\right) \times \text{Mass of AgCl} \]
Substituting the values:
\[ \text{Mass of Ag} = \left(\frac{108 \, \text{g/mol}}{143.5 \, \text{g/mol}}\right) \times 7.2 \, \text{g} \]

Calculating this gives:
\[ \text{Mass of Ag} = \left(\frac{108}{143.5}\right) \times 7.2 \approx 5.42 \, \text{g} \]

### Step 4: Calculate the percentage of silver in the coin.
Now that we have the mass of silver, we can calculate the percentage of silver in the coin:
\[ \text{Percentage of Ag} = \left(\frac{\text{Mass of Ag}}{\text{Mass of the coin}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of Ag} = \left(\frac{5.42 \, \text{g}}{5.82 \, \text{g}}\right) \times 100 \]

Calculating this gives:
\[ \text{Percentage of Ag} \approx 93.1\% \]

### Final Answer:
The percentage of silver in the coin is **93.1%**.

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