If 965 coulombs of electricity is passed through a metal cup dipped in silver(l) salt solution, in order to plate it with silver. Then the amount of silver deposited on its surface is (Given : the molar mass of `Ag = 108 g mol^(-1), 1F = 96500` coulombs)

Options

A. `1.08 g`
B. `1.002 g`
C. `108 g`
D. `9.89 g`

Answer

To solve the problem of determining the amount of silver deposited when 965 coulombs of electricity is passed through a silver salt solution, we can follow these steps:

### Step 1: Understand Faraday's First Law of Electrolysis
According to Faraday's first law, the amount of substance deposited at an electrode is directly proportional to the quantity of electricity passed through the electrolyte. This can be mathematically expressed as:
\[ m = \frac{Z \cdot Q}{F} \]
where:
- \( m \) = mass of the substance deposited (in grams)
- \( Z \) = equivalent weight of the substance (in grams per equivalent)
- \( Q \) = total charge passed (in coulombs)
- \( F \) = Faraday's constant (approximately 96500 coulombs per mole)

### Step 2: Determine the Equivalent Weight of Silver
The equivalent weight of a metal can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{\text{Valency}} \]
For silver (Ag):
- Molar mass of silver = 108 g/mol
- Valency of silver = 1

So, the equivalent weight of silver is:
\[ \text{Equivalent Weight of Ag} = \frac{108 \, \text{g/mol}}{1} = 108 \, \text{g/equiv} \]

### Step 3: Calculate the Amount of Silver Deposited
Now, we can substitute the values into the formula:
- Charge \( Q = 965 \, \text{C} \)
- Equivalent weight \( Z = 108 \, \text{g/equiv} \)

Using the formula:
\[ m = \frac{Z \cdot Q}{F} \]
Substituting the values:
\[ m = \frac{108 \, \text{g/equiv} \cdot 965 \, \text{C}}{96500 \, \text{C/equiv}} \]

### Step 4: Simplify the Calculation
Now, simplifying the equation:
\[ m = \frac{108 \cdot 965}{96500} \]
Calculating the numerator:
\[ 108 \cdot 965 = 104940 \]
Now divide by 96500:
\[ m = \frac{104940}{96500} \approx 1.09 \, \text{g} \]

### Step 5: Conclusion
The amount of silver deposited on the surface of the metal cup is approximately:
\[ \boxed{1.09 \, \text{g}} \]