According to the kinetic molecular theory, what is the average translational kinetic energy of a nitrogen molecule (N_2) at standard temperature and pressure (STP, 273 K)?

• A. k_B T
• B. RT
• C. 3/2 k_B T
• D. 1/2 m v^2

Answer: (C)

Verified step by step guidance

1. Recall that according to the kinetic molecular theory, the average translational kinetic energy of a gas molecule is related to the temperature by the formula \(\frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in kelvin.
2. Identify the given temperature at STP, which is \(T = 273\) K, and note that \(k_B\) is a constant with a known value (approximately \$1.38 \times 10^{-23}$ J/K).
3. Understand that the average translational kinetic energy does not depend on the type of gas molecule (such as \(N_2\)) but only on the temperature, according to the kinetic molecular theory.
4. Write down the expression for the average translational kinetic energy: \(E_{avg} = \frac{3}{2} k_B T\).
5. To find the numerical value, you would multiply \(\frac{3}{2}\) by the Boltzmann constant \(k_B\) and the temperature \(T\), but since the problem asks for the expression, the answer is \(\frac{3}{2} k_B T\).