In two vessels of 1 litre each at athe same temperature 1g of `H_(2)` and 1g of `CH_(4)` are taken. For these gases:

Options

A. `V_("rms")` values will be same
B. Kinetic energy per mol will be same
C. Total kinetic energy will same
D. Pressure will be same

Explanation

To solve the problem, we need to analyze the given information about the two gases, hydrogen (H₂) and methane (CH₄), in terms of their properties at the same temperature and in equal volumes.

### Step-by-Step Solution:

1. **Identify the Molar Masses**:
- The molar mass of H₂ (hydrogen) is approximately 2 g/mol.
- The molar mass of CH₄ (methane) is approximately 16 g/mol.

2. **Calculate the Number of Moles**:
- For H₂:
\[ \text{Number of moles of H₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ moles} \]
- For CH₄:
\[ \text{Number of moles of CH₄} = \frac{1 \text{ g}}{16 \text{ g/mol}} = 0.0625 \text{ moles} \]

3. **Calculate the Root Mean Square (RMS) Velocity**:
- The formula for RMS velocity is:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
- For H₂:
\[ v_{rms(H₂)} = \sqrt{\frac{3RT}{2}} \]
- For CH₄:
\[ v_{rms(CH₄)} = \sqrt{\frac{3RT}{16}} \]
- Since the molar masses are different, the RMS velocities will also differ.

4. **Calculate the Kinetic Energy per Mole**:
- The kinetic energy per mole is given by:
\[ KE = \frac{3}{2}RT \]
- This value is the same for both gases since it depends only on temperature (T) and the gas constant (R), not on the type of gas.

5. **Total Kinetic Energy**:
- The total kinetic energy for each gas can be calculated as:
\[ \text{Total KE} = \text{Number of moles} \times \text{KE per mole} \]
- For H₂:
\[ \text{Total KE(H₂)} = 0.5 \text{ moles} \times \frac{3}{2}RT \]
- For CH₄:
\[ \text{Total KE(CH₄)} = 0.0625 \text{ moles} \times \frac{3}{2}RT \]
- Since the number of moles is different, the total kinetic energies will also be different.

6. **Pressure Comparison**:
- Using the ideal gas law \( PV = nRT \):
- Since both gases are in 1 liter vessels at the same temperature, the pressure will depend on the number of moles.
- Therefore, the pressure will be different for H₂ and CH₄ because the number of moles is different.

### Conclusion:
- The correct statements are:
- The kinetic energy per mole is the same for both gases.
- The total kinetic energy is different due to the difference in moles.
- The pressures in the vessels will also be different.