The ratio of mass of hydrogen and megnesium deopisted by the same amount of electricity from `H_(2)SO_(4)` and `MgSO_(4)` is

Options

A. `1:8`
B. `1:12`
C. `1:16`
D. `1:32`

Explanation

To find the ratio of the mass of hydrogen and magnesium deposited by the same amount of electricity from \( H_2SO_4 \) and \( MgSO_4 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Equivalent Weight**:
The mass deposited during electrolysis is directly proportional to the equivalent weight of the substance. Therefore, we can use the equivalent weights of hydrogen and magnesium to find the mass ratio.

2. **Calculate the Equivalent Weight of Hydrogen**:
- The atomic weight of hydrogen (H) is 1.
- The valency factor of hydrogen (as it forms \( H^+ \)) is 1.
- Therefore, the equivalent weight of hydrogen (E_H) is:
\[ E_H = \frac{\text{Atomic Weight}}{\text{Valency}} = \frac{1}{1} = 1 \]

3. **Calculate the Equivalent Weight of Magnesium**:
- The atomic weight of magnesium (Mg) is 24.
- The valency factor of magnesium (as it forms \( Mg^{2+} \)) is 2.
- Therefore, the equivalent weight of magnesium (E_Mg) is:
\[ E_Mg = \frac{\text{Atomic Weight}}{\text{Valency}} = \frac{24}{2} = 12 \]

4. **Set Up the Mass Ratio**:
- Let \( M_1 \) be the mass of hydrogen deposited and \( M_2 \) be the mass of magnesium deposited.
- The mass ratio \( \frac{M_1}{M_2} \) is equal to the ratio of their equivalent weights:
\[ \frac{M_1}{M_2} = \frac{E_H}{E_Mg} = \frac{1}{12} \]

5. **Conclusion**:
- The ratio of the mass of hydrogen to the mass of magnesium deposited by the same amount of electricity is:
\[ M_1 : M_2 = 1 : 12 \]

### Final Answer:
The ratio of mass of hydrogen to magnesium deposited is \( 1 : 12 \).

---