In a mixture of oxygen and hydrogen at room temperature find out compare to a hydrogen molecule, an oxygen molecule hits the wall

Options

A. With greater average speed
B. With smaller avarage speed
C. With greater average kinetic energy
D. With smaller average kinetic energy

Explanation

To solve the problem of comparing the behavior of oxygen and hydrogen molecules when they hit a wall in a mixture at room temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to compare the average speed and kinetic energy of oxygen (O₂) and hydrogen (H₂) molecules when they collide with a wall.

2. **Identify Relevant Equations**:
The root mean square (rms) speed of a gas molecule can be expressed as:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas.

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

4. **Analyze the Relationship**:
From the rms speed formula, we see that the rms speed is inversely proportional to the square root of the molar mass:
\[ v_{rms} \propto \frac{1}{\sqrt{M}} \]
This means that as the molar mass increases, the rms speed decreases.

5. **Compare the Speeds**:
Since the molar mass of oxygen is greater than that of hydrogen, we can conclude:
\[ v_{rms, H_2} > v_{rms, O_2} \]
Therefore, hydrogen molecules will have a higher average speed compared to oxygen molecules.

6. **Kinetic Energy Comparison**:
The average kinetic energy of a gas molecule is given by:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant. Since both gases are at the same temperature (room temperature), their average kinetic energies will be the same:
\[ KE_{H_2} = KE_{O_2} \]

7. **Conclusion**:
- The average speed of hydrogen molecules is greater than that of oxygen molecules.
- The average kinetic energy of both gases is the same since they are at the same temperature.

### Final Answer:
- Compared to hydrogen molecules, oxygen molecules hit the wall with a lower average speed, but both have the same average kinetic energy.