If same quantity of electricity is passed through `CuCI` and `CuSO_(4)` the ratio of the weights of `Cu` deposited from `CuSO_(4)` and `CuCI` is:-

Options

A. `2:1`
B. `1:2`
C. `1:1`
D. `4:1`

Explanation

To solve the problem of finding the ratio of the weights of copper (Cu) deposited from copper(II) chloride (CuCl) and copper(II) sulfate (CuSO4) when the same quantity of electricity is passed through both solutions, we can use Faraday's second law of electrolysis. Here’s a step-by-step solution:

### Step 1: Understand Faraday's Second Law
Faraday's second law states that the mass of a substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity passed and the equivalent mass of the substance.

### Step 2: Define the Equivalent Mass
The equivalent mass (E) of a metal can be calculated using the formula:
\[ E = \frac{\text{Molar mass}}{\text{Valency}} \]

### Step 3: Calculate Equivalent Mass for CuSO4
For copper(II) sulfate (CuSO4):
- Molar mass of Cu = 63.5 g/mol
- Valency of Cu in CuSO4 = 2

Thus, the equivalent mass (E1) of copper in CuSO4 is:
\[ E1 = \frac{63.5 \text{ g/mol}}{2} = 31.75 \text{ g/equiv} \]

### Step 4: Calculate Equivalent Mass for CuCl
For copper(I) chloride (CuCl):
- Molar mass of Cu = 63.5 g/mol
- Valency of Cu in CuCl = 1

Thus, the equivalent mass (E2) of copper in CuCl is:
\[ E2 = \frac{63.5 \text{ g/mol}}{1} = 63.5 \text{ g/equiv} \]

### Step 5: Set Up the Ratio of Masses Deposited
Let W1 be the mass of copper deposited from CuSO4 and W2 be the mass of copper deposited from CuCl. According to Faraday's second law:
\[ \frac{W1}{W2} = \frac{E1}{E2} \]

### Step 6: Substitute the Equivalent Masses
Substituting the values we calculated:
\[ \frac{W1}{W2} = \frac{31.75}{63.5} \]

### Step 7: Simplify the Ratio
To simplify the ratio:
\[ \frac{W1}{W2} = \frac{31.75}{63.5} = \frac{31.75 \div 31.75}{63.5 \div 31.75} = \frac{1}{2} \]

### Conclusion
Thus, the ratio of the weights of copper deposited from CuSO4 to CuCl is:
\[ \frac{W1}{W2} = 1 : 2 \]

### Final Answer
The correct option is **1 : 2**.

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