The average kinetic energy per mole of hydrogen at given temperature is

Options

A. equal of that of oxygen
B. 16 times that of oxygen
C. `1//16` times that of oxygen
D. `1//8` times that of oxygen

Explanation

To find the average kinetic energy per mole of hydrogen at a given temperature, we can use the formula for the average kinetic energy of a gas:

### Step-by-Step Solution:

1. **Understanding the Formula**: The average kinetic energy (KE) per mole of an ideal gas can be expressed as:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the universal gas constant and \( T \) is the absolute temperature in Kelvin.

2. **Identifying the Gas Constant**: The value of the universal gas constant \( R \) is approximately:
\[ R = 8.314 \, \text{J/(mol·K)} \]

3. **Substituting the Values**: Since the question states that the average kinetic energy of hydrogen at a given temperature is being compared to that of oxygen, we can use the same temperature \( T \) for both gases. The average kinetic energy for hydrogen at temperature \( T \) can be calculated as:
\[ KE_{H_2} = \frac{3}{2} RT \]

4. **Comparison with Oxygen**: The average kinetic energy for oxygen (\( O_2 \)) at the same temperature \( T \) will also be:
\[ KE_{O_2} = \frac{3}{2} RT \]

5. **Conclusion**: Since the average kinetic energy depends only on the temperature and not on the type of gas, the average kinetic energy per mole of hydrogen at a given temperature is equal to that of oxygen at the same temperature. Therefore, the average kinetic energy per mole of hydrogen is the same as that of oxygen at the same temperature.

### Final Answer:
The average kinetic energy per mole of hydrogen at a given temperature is equal to that of oxygen at the same temperature.