Calculate the mass of silver deposited from silver nitrate solution by a current of 2 amperes flowing for 30 minutes (equivalent mass of silver is 108).

Answer

To calculate the mass of silver deposited from a silver nitrate solution by a current of 2 amperes flowing for 30 minutes, we can use the formula:

\[ W = Z \times I \times T \]

Where:
- \( W \) = mass of silver deposited (in grams)
- \( Z \) = electrochemical equivalent of silver (in grams per coulomb)
- \( I \) = current (in amperes)
- \( T \) = time (in seconds)

### Step 1: Calculate the Electrochemical Equivalent (Z)

The electrochemical equivalent \( Z \) can be calculated using the formula:

\[ Z = \frac{\text{Equivalent mass}}{F} \]

Where:
- Equivalent mass of silver = 108 g
- Faraday's constant \( F \) = 96500 C/mol

Substituting the values:

\[ Z = \frac{108 \, \text{g}}{96500 \, \text{C/mol}} \]

### Step 2: Convert Time from Minutes to Seconds

Given that the time is 30 minutes, we need to convert this to seconds:

\[ T = 30 \, \text{minutes} \times 60 \, \text{seconds/minute} = 1800 \, \text{seconds} \]

### Step 3: Substitute Values into the Formula

Now we can substitute the values into the formula for \( W \):

\[ W = Z \times I \times T \]

Where:
- \( I = 2 \, \text{A} \)
- \( T = 1800 \, \text{s} \)

Substituting the value of \( Z \):

\[ W = \left(\frac{108}{96500}\right) \times 2 \times 1800 \]

### Step 4: Calculate the Mass of Silver Deposited (W)

Now, we can calculate \( W \):

1. Calculate \( Z \):

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

2. Substitute \( Z \) into the equation:

\[ W = 0.00112 \times 2 \times 1800 \]

3. Calculate:

\[ W = 0.00112 \times 3600 \]
\[ W \approx 4.032 \, \text{g} \]

Thus, the mass of silver deposited is approximately **4.02 grams**.

### Summary of Steps
1. Calculate the electrochemical equivalent \( Z \).
2. Convert time from minutes to seconds.
3. Substitute values into the formula \( W = Z \times I \times T \).
4. Calculate the mass of silver deposited.