Kinetic Molecular Theory Question 5

Of the following gases, which has the greatest average molecular speed at 298 K?

$ \ce{Cl2} $

$ \ce{NO} $

$ \ce{HCN} $

$ \ce{PH3} $

Approach

Temperature is a measure of the average kinetic energy of a system. All of the gasses in the question have the same kinetic energy. Kinetic energy is proportional to mass and velocity.

$$ KE = \frac{1}{2}mv^2 $$

Mass and velocity are inversely proportional. Therefore, we want to find the gas with the lowest molar mass which corresponds to the highest average molecular speed.

$\ce{HCN}$ has the lowest molar mass at 27 g.