Molecular kinetic theory model Quiz

1. Which of these is NOT an assumption of the kinetic theory of an ideal gas?

• A. Collisions are elastic
• B. The volume of the molecules is negligible
• C. There are strong attractive forces between molecules
• D. The motion of the molecules is random

2. An ideal gas has $c_{rms} = 500$ m s⁻¹ and molecular mass $5.0 \times 10^{-26}$ kg. What is the mean kinetic energy of a molecule?

• A. 6.3 × 10⁻²¹ J
• B. 1.3 × 10⁻²⁰ J
• C. 2.5 × 10⁻²³ J
• D. 1.3 × 10⁻²³ J

3. The kelvin temperature of an ideal gas is doubled. What happens to the mean kinetic energy of a molecule?

• A. It is unchanged
• B. It increases by a factor of $\sqrt{2}$
• C. It increases by a factor of 4
• D. It doubles

4. What is the internal energy of 2.0 mol of an ideal gas at 300 K? ($R = 8.31$ J mol⁻¹ K⁻¹)

• A. 7.5 × 10³ J
• B. 3.7 × 10³ J
• C. 5.0 × 10³ J
• D. 1.5 × 10⁴ J

5. In the derivation of $pV = \frac{1}{3}Nmc^2$, why is $\overline{c_x^2}$ replaced by $\frac{1}{3}\overline{c^2}$?

• A. The molecules only move in the x direction
• B. The molecules move randomly, so no direction is preferred
• C. The collisions are inelastic
• D. The gas has a fixed volume