`10 dm^(3)` of `N_(2)` gas and `10 dm^(3)` of gas `X` contain the same number of molecules at the same temperature, the gas `(X)` may be

Options

A. `CO`
B. `CO_(2)`
C. `H_(2)`
D. `NO`

Explanation

To solve the problem, we need to determine which gas \( X \) has the same number of molecules as \( N_2 \) when both are contained in the same volume (10 dm³) at the same temperature.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation \( PV = nRT \), where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

2. **Identify Given Conditions**:
- The volume of both gases is \( 10 \, \text{dm}^3 \).
- The temperature is the same for both gases.
- Since the volume and temperature are the same, the number of moles \( n \) is directly proportional to the pressure \( P \).

3. **Relate Moles to Molecular Mass**:
The number of moles \( n \) can be expressed as:
\[ n = \frac{m}{M} \]
where \( m \) is the mass of the gas and \( M \) is the molar mass. For the same number of molecules (or moles) in the same volume and temperature, the gases must have the same molar mass.

4. **Calculate the Molar Mass of \( N_2 \)**:
The molar mass of nitrogen gas \( N_2 \) is calculated as follows:
\[ M_{N_2} = 14 \, \text{g/mol} \times 2 = 28 \, \text{g/mol} \]

5. **Identify Possible Gases with the Same Molar Mass**:
We need to find a gas \( X \) that also has a molar mass of \( 28 \, \text{g/mol} \). Let's calculate the molar masses of some common gases:
- Carbon monoxide \( CO \):
\[ M_{CO} = 12 \, \text{g/mol} + 16 \, \text{g/mol} = 28 \, \text{g/mol} \]
- Carbon dioxide \( CO_2 \):
\[ M_{CO_2} = 12 \, \text{g/mol} + 32 \, \text{g/mol} = 44 \, \text{g/mol} \]
- Nitric oxide \( NO \):
\[ M_{NO} = 14 \, \text{g/mol} + 16 \, \text{g/mol} = 30 \, \text{g/mol} \]

6. **Conclusion**:
The only gas that has the same molar mass as \( N_2 \) (28 g/mol) is carbon monoxide \( CO \). Therefore, gas \( X \) is \( CO \).

### Final Answer:
The gas \( X \) may be \( CO \) (carbon monoxide).