Which of the following gases would have molecules with the greatest average kinetic energy at 25°C?

• A. All have the same average kinetic energy
• B. Helium (He)
• C. Oxygen (O_2)
• D. Nitrogen (N_2)

Answer: (A)

Verified step by step guidance

1. Recall that the average kinetic energy of gas molecules depends only on the temperature and is independent of the type of gas. This is a key concept from the kinetic molecular theory.
2. Write down the formula for the average kinetic energy per molecule: \(\text{KE}_{avg} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in kelvin.
3. Convert the given temperature from Celsius to kelvin using \(T(K) = T(^\circ C) + 273.15\). For 25°C, this becomes \$25 + 273.15 = 298.15$ K.
4. Note that since \(k_B\) is a constant and \(T\) is the same for all gases, the average kinetic energy \(\text{KE}_{avg}\) will be the same for helium, oxygen, and nitrogen at 25°C.
5. Conclude that all gases at the same temperature have the same average kinetic energy regardless of their molecular masses or identities.