Three electrolytic cell `A,B`, and `C` contaning solutions of `ZnSO_(4), AgNO_(3)`, and `CuSO_(4)`, respectively, are connected in series. A steady current of `1.5A` was passed through them until `1.45 g` of silver deposited at the cathode of cell `B`. How long did the current flow ? What mass of copper and zinc were deposited ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the total charge required to deposit 1.45 g of silver (Ag) at the cathode of cell B.

1. **Determine the molar mass of silver (Ag)**:
- Molar mass of Ag = 108 g/mol.

2. **Calculate the number of moles of silver deposited**:
\[ \text{Moles of Ag} = \frac{\text{mass of Ag}}{\text{molar mass of Ag}} = \frac{1.45 \, \text{g}}{108 \, \text{g/mol}} \approx 0.0134 \, \text{mol} \]

3. **Determine the charge required to deposit this amount of silver**:
- According to Faraday's law, 1 mole of Ag requires 1 mole of electrons (1 Faraday = 96500 C).
- Therefore, the charge (Q) required is:
\[ Q = \text{moles of Ag} \times 96500 \, \text{C/mol} = 0.0134 \, \text{mol} \times 96500 \, \text{C/mol} \approx 1295.6 \, \text{C} \]

### Step 2: Calculate the time the current flowed using the formula \( Q = I \times t \).

1. **Given current (I)**:
- I = 1.5 A.

2. **Rearranging the formula to find time (t)**:
\[ t = \frac{Q}{I} = \frac{1295.6 \, \text{C}}{1.5 \, \text{A}} \approx 863.7 \, \text{s} \]

### Step 3: Calculate the mass of copper (Cu) deposited in cell C.

1. **Determine the molar mass of copper (Cu)**:
- Molar mass of Cu = 63.5 g/mol.

2. **Determine the charge required for copper deposition**:
- The reaction for copper is \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \). Thus, 1 mole of Cu requires 2 moles of electrons.
- Therefore, the charge required for 1 mole of Cu is:
\[ Q_{\text{Cu}} = 2 \times 96500 \, \text{C} = 193000 \, \text{C} \]

3. **Calculate the mass of copper deposited**:
- Using the ratio of charge:
\[ \text{Mass of Cu} = \frac{\text{mass of Cu}}{Q_{\text{Cu}}} \times Q = \frac{63.5 \, \text{g}}{193000 \, \text{C}} \times 1295.6 \, \text{C} \approx 0.426 \, \text{g} \]

### Step 4: Calculate the mass of zinc (Zn) deposited in cell A.

1. **Determine the molar mass of zinc (Zn)**:
- Molar mass of Zn = 65.3 g/mol.

2. **Determine the charge required for zinc deposition**:
- The reaction for zinc is \( \text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \). Thus, 1 mole of Zn requires 2 moles of electrons.
- Therefore, the charge required for 1 mole of Zn is:
\[ Q_{\text{Zn}} = 2 \times 96500 \, \text{C} = 193000 \, \text{C} \]

3. **Calculate the mass of zinc deposited**:
- Using the ratio of charge:
\[ \text{Mass of Zn} = \frac{\text{mass of Zn}}{Q_{\text{Zn}}} \times Q = \frac{65.3 \, \text{g}}{193000 \, \text{C}} \times 1295.6 \, \text{C} \approx 0.438 \, \text{g} \]

### Final Answers:
- Time the current flowed: **863.7 seconds**
- Mass of copper deposited: **0.426 g**
- Mass of zinc deposited: **0.438 g**