The mass of Hydrogen at S.T.P. that is present in a vessel which can hold 4 grams of oxygen under similar conditions is

Options

A. 1gm
B. 0.5gm
C. 0.25gm
D. 0.125gm

Explanation

To solve the problem of finding the mass of hydrogen present in a vessel that can hold 4 grams of oxygen at standard temperature and pressure (S.T.P.), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Molar Masses**:
- The molar mass of oxygen (O₂) is 32 g/mol.
- The molar mass of hydrogen (H₂) is 2 g/mol.

2. **Calculate the Number of Moles of Oxygen**:
- Use the formula for the number of moles:
\[ \text{Number of moles of O}_2 = \frac{\text{mass of O}_2}{\text{molar mass of O}_2} \]
- Given the mass of oxygen is 4 grams:
\[ \text{Number of moles of O}_2 = \frac{4 \text{ g}}{32 \text{ g/mol}} = 0.125 \text{ moles} \]

3. **Use the Stoichiometry of the Reaction**:
- According to the balanced chemical reaction for the formation of water (H₂ + O₂ → H₂O), 1 mole of O₂ reacts with 2 moles of H₂.
- Therefore, the number of moles of hydrogen required is:
\[ \text{Number of moles of H}_2 = 2 \times \text{Number of moles of O}_2 = 2 \times 0.125 = 0.25 \text{ moles} \]

4. **Calculate the Mass of Hydrogen**:
- Use the formula for mass:
\[ \text{Mass of H}_2 = \text{Number of moles of H}_2 \times \text{molar mass of H}_2 \]
- Substitute the values:
\[ \text{Mass of H}_2 = 0.25 \text{ moles} \times 2 \text{ g/mol} = 0.5 \text{ g} \]

### Final Answer:
The mass of hydrogen present in the vessel is **0.5 grams**.

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