Question

the diagram above shows the distribution of molecular speed in a sample of gas at two different temperatures, $t_1$ and $t_2$. which of the following is a correct interpretation of the information provided by the diagram?

a the average speed of the molecules is greater at $t_1$ than at $t_2$

b the taller peak corresponds to the higher temperature, $t_1$.

c there are fewer molecules of gas at $t_2$ than at $t_1$.

d the average kinetic energy of the molecules is greater at $t_2$ than at $t_1$.

Explanation:

The distribution of molecular speeds in a gas is related to temperature. Higher - temperature gases have a broader distribution of speeds and a higher average kinetic energy. The peak of the distribution shifts to higher speeds and becomes flatter as the temperature increases. In the given graph, $T_2$ has a broader and flatter distribution compared to $T_1$, indicating that the average kinetic energy of the molecules is greater at $T_2$ since average kinetic energy is proportional to temperature ($KE_{avg}=\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature). The number of molecules is not determined by the shape of the distribution but by the amount of gas present, which is not indicated by the graph. The taller peak corresponds to the lower - temperature gas ($T_1$) as more molecules have speeds close to the most probable speed at lower temperatures.

Answer:

D. The average kinetic energy of the molecules is greater at $T_2$ than at $T_1$.