The volume occupied by 22.4 g of a gas (`"vap. Density" = 11.2`) at NTP is

Options

A. 22.4 litre
B. 11.2 litre
C. 44.8 litre
D. 1 litre

Explanation

To find the volume occupied by 22.4 g of a gas with a vapor density of 11.2 at NTP (Normal Temperature and Pressure), we can follow these steps:

### Step 1: Calculate the Molecular Mass of the Gas
The vapor density (VD) is defined as the ratio of the molecular mass of the gas (M) to the molecular mass of hydrogen (H₂), which is 2 g/mol.

\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{\text{Molecular Mass of H}_2} \]

Given that the vapor density is 11.2, we can set up the equation:

\[ 11.2 = \frac{M}{2} \]

To find the molecular mass (M), we rearrange the equation:

\[ M = 11.2 \times 2 = 22.4 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of the Gas
Next, we need to calculate the number of moles (n) of the gas using the formula:

\[ n = \frac{\text{mass}}{\text{molecular mass}} \]

Given that the mass is 22.4 g and the molecular mass is 22.4 g/mol:

\[ n = \frac{22.4 \text{ g}}{22.4 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Use the Ideal Gas Law to Calculate Volume
We can use the Ideal Gas Law, which is given by:

\[ PV = nRT \]

Where:
- P = pressure (1 atm at NTP)
- V = volume (what we want to find)
- n = number of moles (1 mole)
- R = ideal gas constant (0.0821 L·atm/(K·mol))
- T = temperature (273 K at NTP)

Rearranging the equation to solve for volume (V):

\[ V = \frac{nRT}{P} \]

Substituting the known values:

\[ V = \frac{1 \text{ mole} \times 0.0821 \text{ L·atm/(K·mol)} \times 273 \text{ K}}{1 \text{ atm}} \]

Calculating the volume:

\[ V = 0.0821 \times 273 = 22.4 \text{ L} \]

### Conclusion
The volume occupied by 22.4 g of the gas at NTP is **22.4 liters**.

### Final Answer
The correct option is **22.4 liters**.

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