3g of metal ions were discharged at cathode using a current of 3 amperes for 2 hours from aqueous cupric sulphate solution. Calculate the current efficiency. At wt . of Cu is 63.5 .

Answer

To solve the problem step by step, we will calculate the current efficiency based on the given data.

### Step 1: Identify the given data
- Weight of metal discharged (w) = 3 g
- Current (I) = 3 A
- Time (t) = 2 hours
- Atomic weight of Cu = 63.5 g/mol

### Step 2: Convert time from hours to seconds
Since the current is given in amperes (A), we need to convert the time from hours to seconds for consistency in units.
- 1 hour = 3600 seconds
- Therefore, 2 hours = 2 × 3600 = 7200 seconds

### Step 3: Calculate the equivalent weight of copper
The equivalent weight (E) of copper can be calculated using the formula:
\[ E = \frac{\text{Atomic weight}}{n} \]
Where n is the number of electrons transferred per ion. For Cu²⁺ to Cu, n = 2.
- Therefore,
\[ E = \frac{63.5}{2} = 31.75 \, \text{g/equiv} \]

### Step 4: Calculate the theoretical weight of copper that should have been deposited
Using Faraday's law of electrolysis, the weight of the metal deposited can be calculated using the formula:
\[ w = \frac{E \cdot I \cdot t}{96500} \]
Where:
- w = weight of metal deposited (g)
- E = equivalent weight (g/equiv)
- I = current (A)
- t = time (s)
- 96500 = Faraday's constant (C/equiv)

Substituting the values:
\[ w = \frac{31.75 \cdot 3 \cdot 7200}{96500} \]

### Step 5: Calculate the weight of copper deposited
Calculating the above expression:
\[ w = \frac{31.75 \cdot 3 \cdot 7200}{96500} = \frac{684600}{96500} \approx 7.09 \, \text{g} \]

### Step 6: Calculate the current efficiency
Current efficiency can be calculated using the formula:
\[ \text{Current Efficiency} = \frac{\text{Actual weight of metal deposited}}{\text{Theoretical weight of metal deposited}} \times 100 \]
Substituting the values:
\[ \text{Current Efficiency} = \frac{3 \, \text{g}}{7.09 \, \text{g}} \times 100 \]

### Step 7: Final calculation
Calculating the current efficiency:
\[ \text{Current Efficiency} \approx \frac{3}{7.09} \times 100 \approx 42.2\% \]

### Conclusion
The current efficiency is approximately **42.2%**.

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