M gram of a substance when vapourised occupies of `5.6` litre at NTP. The molar mass (in g/mol) of the substance will be :

Options

A. `2M`
B. `4M`
C. `8M`
D. `16M`

Answer

To find the molar mass of a substance that occupies 5.6 liters at Normal Temperature and Pressure (NTP), we can use the relationship between the volume of gas and the number of moles, as well as the molar mass.

### Step-by-Step Solution:

1. **Understanding NTP Conditions:**
At NTP (Normal Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters.

2. **Volume Given:**
The problem states that the substance occupies 5.6 liters at NTP.

3. **Calculating Moles of the Substance:**
To find the number of moles (n) of the substance, we can use the formula:
\[ n = \frac{\text{Volume of gas}}{\text{Molar volume at NTP}} = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}} \]
\[ n = \frac{5.6}{22.4} = 0.25 \text{ moles} \]

4. **Relating Mass and Moles:**
The mass of the substance (m) in grams is related to the number of moles and the molar mass (M) by the formula:
\[ m = n \times M \]
Rearranging this gives us:
\[ M = \frac{m}{n} \]

5. **Substituting Values:**
Now, substituting the value of n we calculated:
\[ M = \frac{m}{0.25} \]
\[ M = 4m \]

6. **Conclusion:**
Therefore, the molar mass of the substance is \(4m\) grams per mole.

### Final Answer:
The molar mass of the substance will be \(4m\) g/mol.