4.6 g Na is dissolved in 1 litre of water. Then how much `H_(2)` gas will be evolved ?

Options

A. 2.24 L
B. 1.12 L
C. 4.48 L
D. 11.2 L

Answer

To solve the problem of how much \( H_2 \) gas will be evolved when 4.6 g of sodium (Na) is dissolved in 1 liter of water, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Chemical Reaction**:
When sodium reacts with water, the reaction can be represented as:
\[ 2 \text{Na} + 2 \text{H}_2\text{O} \rightarrow 2 \text{NaOH} + \text{H}_2 \]
This shows that 2 moles of sodium produce 1 mole of hydrogen gas.

2. **Calculate the Moles of Sodium**:
The number of moles of sodium can be calculated using the formula:
\[ \text{Moles of Na} = \frac{\text{Mass of Na}}{\text{Molar Mass of Na}} \]
Given that the mass of sodium is 4.6 g and the molar mass of sodium (Na) is approximately 23 g/mol:
\[ \text{Moles of Na} = \frac{4.6 \, \text{g}}{23 \, \text{g/mol}} = 0.2 \, \text{moles} \]

3. **Determine the Moles of Hydrogen Gas Produced**:
From the balanced equation, we know that 2 moles of sodium produce 1 mole of hydrogen gas. Therefore, the moles of \( H_2 \) produced from 0.2 moles of sodium can be calculated as follows:
\[ \text{Moles of } H_2 = \frac{0.2 \, \text{moles of Na}}{2} = 0.1 \, \text{moles of } H_2 \]

4. **Calculate the Volume of Hydrogen Gas at STP**:
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Thus, the volume of 0.1 moles of \( H_2 \) can be calculated as:
\[ \text{Volume of } H_2 = 0.1 \, \text{moles} \times 22.4 \, \text{L/mole} = 2.24 \, \text{liters} \]

### Final Answer:
The volume of hydrogen gas evolved is **2.24 liters** at STP.

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