Question

exam 3 fall 2025
your initials nt
(vi) (10 points) the following (figure 3) graph shows the gas speed distributions for a
n₂, o₂, he, and ar gases, at same temperature. which curve corresponds to the
ar gas?
figure 3:
o a o b o c o d
(vii) (10 points) according to the kinetic molecular theory of gases:
o gas particles have attractive and repulsive forces between them
o gas particles have a finite volume
o gas particles engage in elastic collisions between each other and the walls of the
container (similar to billiard balls)
o as the temperature increases, the average kinetic energy of the gas decreases
o all of the above

Explanation:

For question (VI), according to the Maxwell - Boltzmann distribution, at the same temperature, the root - mean - square speed \(v_{rms}=\sqrt{\frac{3RT}{M}}\) (where \(R\) is the gas constant, \(T\) is the temperature, and \(M\) is the molar mass of the gas). The molar mass of \(He\) is \(M_{He} = 4\space g/mol\), \(M_{N_2}=28\space g/mol\), \(M_{O_2} = 32\space g/mol\), \(M_{Ar}=40\space g/mol\). Since \(v_{rms}\propto\frac{1}{\sqrt{M}}\), \(Ar\) has the largest molar mass among them, so it has the smallest \(v_{rms}\). The peak of the distribution curve for the gas with the smallest \(v_{rms}\) is at the lowest speed.

For question (VII), according to the Kinetic Molecular Theory of gases:

• Gas particles have no attractive and repulsive forces between them (ideal gas assumption).
• Gas particles have a negligible volume (not a finite volume in the ideal gas model).
• Gas particles engage in elastic collisions between each other and the walls of the container (similar to billiard balls).
• As the temperature increases, the average kinetic energy of the gas \(E_{k}=\frac{3}{2}kT\) (where \(k\) is the Boltzmann constant) increases.

Answer:

VI. a
VII. Gas particles engage in elastic collisions between each other and the walls of the container (similar to billiard balls)