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 follow these steps:

### Step 1: Understand the formula for average kinetic energy
The average kinetic energy (KE) per mole of an ideal gas is given by the formula:
\[ KE = \frac{F}{2} RT \]
where:
- \( F \) is the degrees of freedom of the gas,
- \( R \) is the universal gas constant (approximately \( 8.314 \, \text{J/(mol·K)} \)),
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Determine degrees of freedom for hydrogen
For diatomic gases like hydrogen (H₂), the degrees of freedom \( F \) is typically 5 (3 translational + 2 rotational).

### Step 3: Substitute values into the formula
Using the formula for average kinetic energy:
\[ KE_{H_2} = \frac{5}{2} RT \]
This shows that the average kinetic energy per mole of hydrogen depends on the temperature \( T \) and the universal gas constant \( R \).

### Step 4: Compare with oxygen
The problem states that the average kinetic energy of hydrogen is equal to 16 times that of oxygen at the same temperature. However, since the average kinetic energy per mole of any ideal gas at a given temperature is the same, we can conclude that:
\[ KE_{H_2} = KE_{O_2} \]
This means that the average kinetic energy per mole of hydrogen is equal to that of oxygen at the same temperature.

### Conclusion
Thus, the average kinetic energy per mole of hydrogen at a given temperature is equal to that of oxygen, confirming that it does not depend on the type of gas but only on the temperature.

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

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