Question

Helium is two times heavier than H2. The average kinetic energy per molecule for helium at 300K is

• A. twice as H2
• B. same as H2
• C. half as H2
• D. one fourth of H2

Hint:

In the kinetic theory, the average kinetic energy per molecule is dependent only on temperature, not the molecular mass.

Answer 1

The Correct Option is B

1. Key Concept: According to the Kinetic Theory of Gases, the average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas and depends only on the temperature.
2. Formula: The average translational kinetic energy per molecule of any ideal gas is given by: \[ \bar{KE} = \frac{3}{2} k_B T \] where \(k_B\) is the Boltzmann constant and \(T\) is the absolute temperature in Kelvin.
3. Analysis: The formula shows that the average kinetic energy per molecule depends solely on the temperature (\(T\)). It does not depend on the type of gas, the mass of the molecules, or the molar mass.
4. Given Information:
   • Gas 1: Helium (He)
   • Gas 2: Hydrogen (H₂)
   • Temperature: 300 K (same for both gases)
   • Mass Information: Helium is two times heavier than H₂ (Molar mass of He ≈ 4 g/mol, Molar mass of H₂ ≈ 2 g/mol). This information is irrelevant for the average kinetic energy per molecule.
5. Comparison: Since both Helium and H₂ are at the same temperature (300 K), their average kinetic energy per molecule must be the same. \[ \bar{KE}_{\text{Helium}} = \frac{3}{2} k_B (300) \] \[ \bar{KE}_{\text{H}_2} = \frac{3}{2} k_B (300) \] Therefore, \( \bar{KE}_{\text{Helium}} = \bar{KE}_{\text{H}_2} \).

The correct option is (b) same as H₂.

Answer 2

The average kinetic energy per molecule of an ideal gas is given by: 

$$ E_k = \frac{3}{2} kT $$ where:
$k$ = Boltzmann constant,
$T$ = absolute temperature.

Key point: The formula does not depend on the mass or type of gas molecule. It only depends on temperature.

So at the same temperature ($300\,\text{K}$), the average kinetic energy per molecule of helium and hydrogen ($\text{H}_2$) will be the same. 

Correct answer: (b) same as H₂

Answer 3

According to the kinetic theory of gases, the average kinetic energy per molecule is proportional to the temperature and is independent of the type of gas: \[ KE = \frac{3}{2} k_B T \] Thus, at the same temperature, the average kinetic energy per molecule for helium is the same as that for hydrogen (H2).