How much silver will be obtained by that quantity of current which displaces 5.6 litre of `H_(2)` ?

Options

A. 54g
B. 13.5 g
C. 20 g
D. 108 g

Answer

To solve the problem of how much silver will be obtained by the quantity of current that displaces 5.6 liters of H₂, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the number of moles of H₂**:
- At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters.
- To find the number of moles of H₂ in 5.6 liters, we use the formula:
\[ \text{Number of moles of } H_2 = \frac{\text{Volume of } H_2}{\text{Molar volume at STP}} = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}} = 0.25 \text{ moles} \]

2. **Calculate the equivalent of H₂**:
- The equivalent weight of H₂ is 2 grams (since 1 mole of H₂ displaces 2 equivalents).
- Therefore, the number of gram equivalents of H₂ can be calculated as:
\[ \text{Gram equivalents of } H_2 = 0.25 \text{ moles} \times 2 \text{ g/equiv} = 0.5 \text{ gram equivalents} \]

3. **Relate the gram equivalents of H₂ to silver**:
- According to Faraday's laws of electrolysis, 1 equivalent of a substance will produce 1 equivalent of another substance. In this case, 1 equivalent of H₂ will produce 1 equivalent of silver (Ag).
- Thus, the gram equivalents of silver produced will also be 0.5.

4. **Calculate the mass of silver obtained**:
- The molar mass of silver (Ag) is approximately 108 grams per mole.
- Therefore, the mass of silver obtained can be calculated as:
\[ \text{Mass of silver} = \text{Gram equivalents of silver} \times \text{Molar mass of silver} = 0.5 \text{ equivalents} \times 108 \text{ g/equiv} = 54 \text{ grams} \]

### Final Answer:
The mass of silver obtained is **54 grams**.

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