Which of the following ideal gases has higher value of average kinetic energy per mole at the same temperature - `N_2,CO_2,O_2` ?

Options

A. `N_2`
B. `CO_2`
C. `O_2`
D. All have equal value of KE

Answer

To solve the question of which of the gases (N₂, CO₂, O₂) has a higher value of average kinetic energy per mole at the same temperature, we can follow these steps:

### Step 1: Understand the formula for average kinetic energy
The average kinetic energy (KE) of an ideal gas is given by the formula:
\[ KE = \frac{3}{2} k T \]
where:
- \( k \) is the Boltzmann constant,
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Analyze the dependence on temperature
From the formula, we can see that the average kinetic energy depends only on the temperature \( T \) and the Boltzmann constant \( k \).

### Step 3: Consider the conditions given in the question
The question states that all gases (N₂, CO₂, O₂) are at the same temperature. Since the average kinetic energy is directly proportional to the temperature, if the temperature is the same for all gases, the average kinetic energy will also be the same for each gas.

### Step 4: Conclusion
Since all gases are at the same temperature, their average kinetic energies will be equal. Therefore, the answer to the question is that all gases have the same average kinetic energy per mole at the same temperature.

### Final Answer
All gases (N₂, CO₂, O₂) have equal values of average kinetic energy per mole at the same temperature.

---