A certain current liberates `0.5g` of hydrogen in 2 hours. How many grams of copper can be liberated by the same current flowing for the same time in a copper sulphate solution ?

Options

A. `12.7g`
B. `15.9g`
C. `31.8g`
D. `63.5g`

Explanation

To solve the problem of how many grams of copper can be liberated by the same current flowing for the same time in a copper sulfate solution, we can use Faraday's second law of electrolysis. Here’s a step-by-step solution:

### Step 1: Understand the relationship between the substances liberated
According to Faraday's second law of electrolysis, the weight of a substance liberated at an electrode during electrolysis is directly proportional to its equivalent weight when the same quantity of electricity is passed through different electrolytic solutions.

### Step 2: Set up the equation
Let:
- \( W_H \) = weight of hydrogen liberated = 0.5 g
- \( W_C \) = weight of copper deposited (what we want to find)
- \( E_H \) = equivalent weight of hydrogen
- \( E_C \) = equivalent weight of copper

From Faraday's second law, we have:
\[ \frac{W_H}{E_H} = \frac{W_C}{E_C} \]

### Step 3: Calculate the equivalent weights
1. **Equivalent weight of hydrogen (H)**:
- Molecular weight of hydrogen (H₂) = 2 g/mol
- Equivalent weight of hydrogen = \(\frac{Molar\ weight}{n} = \frac{2}{2} = 1\) g/equiv

2. **Equivalent weight of copper (Cu)**:
- Atomic weight of copper = 63.5 g/mol
- For copper, it typically forms Cu²⁺ ions, so \( n = 2 \).
- Equivalent weight of copper = \(\frac{63.5}{2} = 31.75\) g/equiv

### Step 4: Substitute the values into the equation
Now substituting the known values into the equation:
\[ \frac{0.5}{1} = \frac{W_C}{31.75} \]

### Step 5: Solve for \( W_C \)
Cross-multiplying gives:
\[ W_C = 0.5 \times 31.75 \]
Calculating this:
\[ W_C = 15.875 \text{ g} \]

### Step 6: Round to the appropriate significant figures
Rounding 15.875 g gives approximately 15.9 g.

### Conclusion
Thus, the weight of copper that can be liberated by the same current flowing for the same time in a copper sulfate solution is approximately **15.9 grams**.