5.82 g of a silver coin were dissolved in strong nitric acid and excess of NaCI solution was added. The silver chloride precipitated was dried and weighed 7.20 g. Calculate the percentage of silver in the coin

Explanation

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

### Step 1: Identify the given data
- Mass of the silver coin = 5.82 g
- Mass of silver chloride (AgCl) precipitate = 7.20 g

### Step 2: Determine the molar masses
- Molar mass of AgCl = 143.5 g/mol
- Molar mass of silver (Ag) = 108 g/mol

### Step 3: Calculate the mass of silver in the silver chloride
Using the relationship between the mass of silver chloride and the mass of silver, we can set up the following proportion:
\[ \text{If } 143.5 \text{ g of AgCl contains } 108 \text{ g of Ag, then } 7.20 \text{ g of AgCl contains } x \text{ g of Ag.} \]
This can be expressed mathematically as:
\[ x = \left(\frac{108 \text{ g Ag}}{143.5 \text{ g AgCl}}\right) \times 7.20 \text{ g AgCl} \]

### Step 4: Perform the calculation
Calculating the mass of silver:
\[ x = \left(\frac{108}{143.5}\right) \times 7.20 \]
\[ x = 0.751 \times 7.20 \approx 5.41 \text{ g of Ag} \]

### Step 5: Calculate the percentage of silver in the coin
Now we can calculate the percentage of silver in the coin using the formula:
\[ \text{Percentage of silver} = \left(\frac{\text{mass of silver}}{\text{mass of silver coin}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of silver} = \left(\frac{5.41 \text{ g}}{5.82 \text{ g}}\right) \times 100 \]
\[ \text{Percentage of silver} \approx 93.1\% \]

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

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