Question

1. consider a 1.0 - l container of neon gas at stp. will the average kinetic energy, average velocity, and frequency of collisions of gas molecules with the walls of the container increase, decrease, or remain the same under each of the following conditions? a. the temperature is increased to 100°c. b. the temperature is decreased to - 50°c. c. the volume is decreased to 0.5 l. d. the number of moles of neon is doubled.

Explanation:

Step1: Recall kinetic - molecular theory

The average kinetic energy of gas molecules is directly proportional to the temperature ($K_{avg}=\frac{3}{2}RT$), average velocity $v_{avg}=\sqrt{\frac{8RT}{\pi M}}$, and the frequency of collisions is related to temperature, pressure, and number of moles.

Step2: Analyze case a

When the temperature is increased to 100°C from STP (0°C).

• Average kinetic energy: Since $K_{avg}\propto T$, it increases.
• Average velocity: Since $v_{avg}\propto\sqrt{T}$, it increases.
• Frequency of collisions: With increased temperature and assuming constant volume, pressure increases (by $PV = nRT$). So the frequency of collisions increases.

Step3: Analyze case b

When the temperature is decreased to - 50°C from STP.

• Average kinetic energy: Since $K_{avg}\propto T$, it decreases.
• Average velocity: Since $v_{avg}\propto\sqrt{T}$, it decreases.
• Frequency of collisions: With decreased temperature and assuming constant volume, pressure decreases. So the frequency of collisions decreases.

Step4: Analyze case c

When the volume is decreased to 0.5 L.

• Average kinetic energy: Temperature is constant (assuming no heat - exchange during compression), so it remains the same.
• Average velocity: Temperature is constant, so it remains the same.
• Frequency of collisions: With decreased volume, pressure increases (by $PV=nRT$, $n$ and $T$ constant). So the frequency of collisions increases.

Step5: Analyze case d

When the number of moles of neon is doubled.

• Average kinetic energy: Temperature is constant (assuming no heat - exchange during addition of gas), so it remains the same.
• Average velocity: Temperature is constant, so it remains the same.
• Frequency of collisions: With more moles, pressure increases (by $PV = nRT$, $V$ and $T$ constant). So the frequency of collisions increases.

Answer:

a. Average kinetic energy: increases; Average velocity: increases; Frequency of collisions: increases
b. Average kinetic energy: decreases; Average velocity: decreases; Frequency of collisions: decreases
c. Average kinetic energy: remains the same; Average velocity: remains the same; Frequency of collisions: increases
d. Average kinetic energy: remains the same; Average velocity: remains the same; Frequency of collisions: increases