Consider a mixture of oxygen and hydrogen kept at room temperature, As compared to a hydrogen molecule an oxygen molecule hits the wall

Options

A. (a)with greater average speed
B. (b)with smaller average speed
C. (c)with greater average kinetic energy
D. (d)with smaller average kinetic energy.

Answer

To solve the problem, we need to analyze the behavior of oxygen and hydrogen molecules in a mixture at room temperature, focusing on their average speed and kinetic energy.

### Step-by-Step Solution:

1. **Understanding Average Speed**:
The average speed \( V_{avg} \) of gas molecules is given by the formula:
\[ V_{avg} = \sqrt{\frac{8kT}{\pi m}} \]
where \( k \) is the Boltzmann constant, \( T \) is the absolute temperature, and \( m \) is the molar mass of the gas.

2. **Comparing Molar Masses**:
- The molar mass of hydrogen (H₂) is approximately 2 g/mol.
- The molar mass of oxygen (O₂) is approximately 32 g/mol.

3. **Relationship Between Average Speed and Molar Mass**:
Since both gases are at the same temperature, we can express the ratio of their average speeds:
\[ \frac{V_{avg, O_2}}{V_{avg, H_2}} = \sqrt{\frac{m_{H_2}}{m_{O_2}}} \]
Substituting the molar masses:
\[ \frac{V_{avg, O_2}}{V_{avg, H_2}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4} \]
This indicates that:
\[ V_{avg, O_2} = \frac{1}{4} V_{avg, H_2} \]

4. **Conclusion About Average Speed**:
Since the average speed of oxygen is one-fourth that of hydrogen, we conclude that the oxygen molecule hits the wall with a smaller average speed. Thus, the correct answer for this part is:
**B part: with smaller average speed.**

5. **Understanding Kinetic Energy**:
The kinetic energy \( KE \) of a gas molecule is given by:
\[ KE = \frac{3}{2} k T \]
This formula shows that the kinetic energy depends only on the temperature \( T \) and not on the type of gas.

6. **Conclusion About Kinetic Energy**:
Since both gases are at the same temperature, the kinetic energy of both hydrogen and oxygen molecules will be the same. Therefore, the options regarding kinetic energy (C and D) are incorrect.

### Final Answer:
The oxygen molecule hits the wall with a smaller average speed (Option B).