Chemistry - Ideal Gas Question with Solution | TestHub

(a) True: The ratio of the most probable speed ($u_{mp}$) to the root-mean-square speed ($u_{rms}$) is a constant:

$$\frac{u_{mp}}{u_{rms}}=\sqrt{\frac{2}{3}}$$

(b) True: The mean kinetic energy (KE) of a gas molecule is given by $\frac{3}{2}kT$, which is independent of the molecular mass ($M$).

(c) True: The relationship between the speeds is $u_{rms}>u_{av}>u_{mp}$. This can be expressed as:

$$\sqrt{3}>\sqrt{\frac{8}{\pi }}>\sqrt{2}times\sqrt{\frac{RT}{M}}$$

(d) False: The average speed ($u_{av}$) is approximately $1.60\sqrt{\frac{RT}{M}}$, while the root-mean-square speed ($u_{rms}$) is approximately $1.73\sqrt{\frac{RT}{M}}$. Therefore, $u_{av}$ is always less than $u_{rms}$. The untrue statement is (d). This confirms Answer (d).