Which of the following expressions correctly represents the relationship between the average molar kinetic energies `(KE)` of `CO` and `N_(2)` molecules at the same temperature?

Options

A. `bar(KE)_(CO)ltbar(KE)_(N_(2))`
B. `bar(KE)_(CO)gtbar(KE)_(N_(2))`
C. `bar(KE)_(CO)=bar(KE)_(N_(2))`
D. Cannot be predicted unless volumes of the gases are given

Explanation

To solve the problem of determining the relationship between the average molar kinetic energies (KE) of CO and N₂ molecules at the same temperature, we can follow these steps:

### Step 1: Understand the formula for kinetic energy
The average kinetic energy (KE) of one mole of an ideal gas is given by the equation:
\[ KE = \frac{3}{2} RT \]
where \( R \) is the universal gas constant and \( T \) is the absolute temperature in Kelvin.

### Step 2: Apply the formula to both gases
Since we are comparing the average kinetic energies of CO and N₂ at the same temperature, we can express the kinetic energy for both gases:
- For CO:
\[ KE_{CO} = \frac{3}{2} RT \]
- For N₂:
\[ KE_{N_2} = \frac{3}{2} RT \]

### Step 3: Compare the kinetic energies
Since both gases are at the same temperature (T), we can see that:
\[ KE_{CO} = KE_{N_2} \]
This implies that the average molar kinetic energies of CO and N₂ are equal when measured at the same temperature.

### Conclusion
Thus, the correct expression representing the relationship between the average molar kinetic energies of CO and N₂ at the same temperature is:
\[ KE_{CO} = KE_{N_2} \]