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 how much silver is deposited when 965 coulombs of electricity is passed through a silver salt solution, we will use Faraday's first law of electrolysis. Here’s the step-by-step solution:

### Step 1: Understand the Formula
According to Faraday's first law of electrolysis, the amount of substance deposited (W) is given by the formula:
\[ W = Z \cdot I \cdot t \]
where:
- \( W \) = weight of the substance deposited (in grams)
- \( Z \) = electrochemical equivalent (in grams per coulomb)
- \( I \) = current (in amperes)
- \( t \) = time (in seconds)

However, we can also express \( Z \) in terms of molar mass and Faraday's constant:
\[ Z = \frac{M}{nF} \]
where:
- \( M \) = molar mass of the substance (in grams per mole)
- \( n \) = number of moles of electrons transferred (valency)
- \( F \) = Faraday's constant (approximately 96500 coulombs per mole of electrons)

### Step 2: Identify Given Values
From the problem, we have:
- Molar mass of silver (Ag), \( M = 108 \, \text{g/mol} \)
- Charge passed, \( Q = 965 \, \text{C} \)
- Faraday's constant, \( F = 96500 \, \text{C/mol} \)
- For silver, \( n = 1 \) (since silver is in +1 oxidation state)

### Step 3: Calculate Electrochemical Equivalent (Z)
Using the formula for \( Z \):
\[ Z = \frac{M}{nF} = \frac{108 \, \text{g/mol}}{1 \times 96500 \, \text{C/mol}} \]

Calculating \( Z \):
\[ Z = \frac{108}{96500} \approx 0.00112 \, \text{g/C} \]

### Step 4: Calculate the Weight of Silver Deposited (W)
Now, we can use the charge passed to find the weight of silver deposited:
\[ W = Z \cdot Q \]
Substituting the values:
\[ W = 0.00112 \, \text{g/C} \times 965 \, \text{C} \]

Calculating \( W \):
\[ W \approx 1.08 \, \text{g} \]

### Conclusion
The amount of silver deposited on the surface of the metal cup is approximately **1.08 grams**.