If two gases are at the same temperature, which of the following statements is true regarding their molecular speeds?

At the same temperature, the average kinetic energy of gas molecules is equal, regardless of their molecular weights. The kinetic energy for a gas molecule can be expressed using the equation ( KE = \frac{1}{2}mv^2 ), where ( m ) is the mass of the molecule and ( v ) is its speed. Since the temperature is related to the average kinetic energy, if we consider molecules with different weights, lighter molecules will move faster to maintain the same average kinetic energy as heavier molecules.

In this context, a gas molecule with a lower molecular weight is indeed able to achieve a higher speed than a gas molecule with a higher molecular weight at the same temperature. This relationship can also be understood through the derived root-mean-square speed formula, ( v_{rms} = \sqrt{\frac{3RT}{M}} ), where ( R ) is the universal gas constant, ( T ) is the temperature in Kelvin, and ( M ) is the molar mass. The equation clearly indicates that as the molar mass ( M ) increases, the root-mean-square speed decreases, reinforcing the idea that lighter molecules travel faster.