Two voltameters containing copper sulphate and acidulated water respectively are connected in series and the same current is passed for some time. If the amounts of copper and hydrogen obtained at cathode are 0.3177 g and `1.008 xx 10^(-2)` g respectively, calculate the of copper. (Eq. mass of hydrogen = 1.008).

Answer

To solve the problem, we will use the concept of equivalent mass and the relationship between the mass of substances deposited during electrolysis when the same current is passed through different solutions.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of copper deposited (m_Cu) = 0.3177 g
- Mass of hydrogen evolved (m_H) = 1.008 x 10^(-2) g
- Equivalent mass of hydrogen (E_H) = 1.008 g

2. **Calculate the Number of Equivalents of Hydrogen:**
The number of equivalents of hydrogen can be calculated using the formula:
\[ \text{Number of equivalents of H} = \frac{\text{mass of H}}{\text{equivalent mass of H}} = \frac{1.008 \times 10^{-2}}{1.008} \]
Simplifying this gives:
\[ \text{Number of equivalents of H} = 0.01 \]

3. **Set Up the Relationship for Copper:**
Since the same current is passed through both voltameters, the number of equivalents of copper deposited will be equal to the number of equivalents of hydrogen evolved. Therefore:
\[ \text{Number of equivalents of Cu} = \text{Number of equivalents of H} = 0.01 \]

4. **Calculate the Equivalent Mass of Copper:**
Using the relationship for copper:
\[ \text{Number of equivalents of Cu} = \frac{\text{mass of Cu}}{\text{equivalent mass of Cu}} \]
Substituting the known values:
\[ 0.01 = \frac{0.3177}{\text{equivalent mass of Cu}} \]

5. **Rearranging to Find Equivalent Mass of Copper:**
Rearranging the equation gives:
\[ \text{equivalent mass of Cu} = \frac{0.3177}{0.01} = 31.77 \text{ g} \]

### Final Answer:
The equivalent mass of copper is **31.77 g**.

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