At the same temperature, the average molar kinetic energy of N₂ and CO is

The correct option is KE₁ = KE₂.

To understand why this is correct, let's look at the relationship between the average molar kinetic energy of a gas and its temperature.

According to the kinetic molecular theory of gases, the average translational kinetic energy ($E_k$) per mole of any ideal gas is directly proportional to its absolute temperature.

The formula for the average molar kinetic energy of a gas is given by:
$E_k=\frac{3}{2}RT$
where:
- $R$ is the universal gas constant.
- $T$ is the absolute temperature in Kelvin.

From this equation, we can see that the average molar kinetic energy depends solely on the temperature ($T$) of the gas, and it is completely independent of the identity, chemical formula, or molar mass of the gas molecules.

Since the problem states that both nitrogen ($N_2$, represented by ${\mathrm{KE}}_1$) and carbon monoxide ($\mathrm{CO}$, represented by ${\mathrm{KE}}_2$) are at the same temperature, their average molar kinetic energies must be equal.

Therefore, we have:
${\mathrm{KE}}_1={\mathrm{KE}}_2$