Consider a sample of oxygen behaving like an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The root mean square (rms) velocity of an ideal gas is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.The average velocity of an ideal gas is given by

Vedclass · Accepted Answer

$\sqrt{\frac{3 \pi}{8}}$

Vedclass · Answer

(C) The root mean square (rms) velocity of an ideal gas is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.The average velocity of an ideal gas is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.To find the ratio of rms velocity to average velocity,we divide the two expressions:$\frac{v_{rms}}{v_{avg}} = \frac{\sqrt{\frac{3RT}{M}}}{\sqrt{\frac{8RT}{\pi M}}}$.Simplifying the expression,the terms $R$,$T$,and $M$ cancel out:$\frac{v_{rms}}{v_{avg}} = \sqrt{\frac{3RT}{M} 	imes \frac{\pi M}{8RT}} = \sqrt{\frac{3\pi}{8}}$.Thus,the ratio is $\sqrt{\frac{3\pi}{8}}$.

Consider a sample of oxygen behaving like an ideal gas. At $300 \, K$,the ratio of root mean square (rms) velocity to the average velocity of gas molecules would be: (Molecular weight of oxygen is $32 \, g/mol$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$)

Similar Questions

At what temperature does the $r.m.s.$ speed of air molecules become double that at $N.T.P.$?

The $rms$ speed of a gas at room temperature of $27^{\circ}C$ is found to be $412 \ m/s$. The gas is:

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$).

The root mean square speed of smoke particles of mass $5 \times 10^{-17} \, kg$ in their Brownian motion in air at $NTP$ is approximately $....... \, mm \, s^{-1}$. [Given $k = 1.38 \times 10^{-23} \, J \, K^{-1}$ and $T = 293 \, K$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module