Hydrogen gas and oxygen gas have volume `1 cm^(3)` each at N.T.P. select incorrect statement/statements

Options

A. Number of molecues is same in both the gases
B. The rms velocity of molecules of both the gases is the same.
C. The internal energy of each gas is the same.
D. The average velocity of molecules of each gas is the same.

Explanation

To solve the question regarding the incorrect statements about hydrogen gas and oxygen gas at N.T.P. (Normal Temperature and Pressure), we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Conditions**:
- Both hydrogen and oxygen gases have a volume of 1 cm³ each at N.T.P.
- At N.T.P., the temperature is 0°C (273.15 K) and the pressure is 1 atm.

2. **Number of Molecules**:
- Since both gases occupy the same volume at the same temperature and pressure, we can use the ideal gas law to determine that the number of molecules in each gas is the same.
- **Statement**: The number of molecules is the same in both gases.
- **Conclusion**: This statement is **correct**.

3. **RMS Speed**:
- The root mean square (RMS) speed of gas molecules is given by the formula:
\[ V_{RMS} = \sqrt{\frac{3RT}{M}} \]
- Here, \( R \) is the universal gas constant, \( T \) is the temperature, and \( M \) is the molar mass of the gas.
- Hydrogen has a molar mass of 2 g/mol, while oxygen has a molar mass of 32 g/mol.
- Since the temperature is the same, the RMS speeds will differ due to the different molar masses.
- **Statement**: The RMS speed of molecules of both gases is the same.
- **Conclusion**: This statement is **incorrect**.

4. **Internal Energy**:
- The internal energy \( U \) of an ideal gas is given by:
\[ U = \frac{f}{2}RT \]
- For diatomic gases (both hydrogen and oxygen), the degrees of freedom \( f \) are the same (5 for diatomic).
- Since both gases are at the same temperature and have the same degrees of freedom, their internal energies will also be the same.
- **Statement**: The internal energy of each gas is the same.
- **Conclusion**: This statement is **correct**.

5. **Average Velocity**:
- The average velocity of gas molecules is related to temperature but not to molar mass.
- Since both gases are at the same temperature, their average velocities will also be the same.
- **Statement**: The average velocity of molecules of each gas is the same.
- **Conclusion**: This statement is **correct**.

### Summary of Statements:
- **Correct Statements**: Number of molecules is the same, internal energy is the same, average velocity is the same.
- **Incorrect Statement**: RMS speed of molecules of both gases is the same.

### Final Answer:
The incorrect statement is: "The RMS speed of molecules of both gases is the same."