Question

question 1
select all the correct answers.
a gas with a small molar mass at a particular temperature...
will have a slower diffusion rate than a gas with a large molar mass at the same temperature
will have a higher particle velocity than a gas with a large molar mass at the same temperature
will have the same particle velocity as a gas with a large molar mass at the same temperature
will have the same average kinetic energy as a gas with a large molar mass at the same temperature

Explanation:

Step1: Recall Kinetic Molecular Theory (KMT)

KMT states that at the same temperature, all gases have the same average kinetic energy ($KE_{avg} = \frac{3}{2}kT$, where $k$ is Boltzmann constant and $T$ is temperature). Also, $KE = \frac{1}{2}mv^2$, so for a gas with smaller molar mass ($m$), velocity ($v$) must be higher to keep $KE$ same. Diffusion rate is related to velocity (Graham's law: rate $\propto \frac{1}{\sqrt{\text{molar mass}}}$), so smaller molar mass means faster diffusion.

Step2: Analyze each option

• Option 1: Slower diffusion? No, smaller molar mass means faster diffusion (Graham's law). Eliminate.
• Option 2: Higher particle velocity? Yes, from $KE = \frac{1}{2}mv^2$, same $KE$ (same $T$) and smaller $m$ implies larger $v$.
• Option 3: Same particle velocity? No, as shown above, velocity depends on molar mass. Eliminate.
• Option 4: Same average kinetic energy? Yes, KMT says same $T$ means same $KE_{avg}$.

Answer:

B. will have a higher particle velocity than a gas with a large molar mass at the same temperature, D. will have the same average kinetic energy as a gas with a large molar mass at the same temperature