A flask contains argon and chlorine in the ra | vedclass

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

Question

(C) The root mean square speed of a gas molecule is given by the formula $v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas const

Vedclass · Accepted Answer

$\frac{\sqrt{7}}{2}$

Vedclass · Answer

(C) The root mean square speed of a gas molecule is given by the formula $v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass of the gas.Since the temperature $T$ is the same for both gases in the mixture, the ratio of their root mean square speeds depends only on their molar masses.The ratio is given by $\frac{v_{	ext{rms}}^{	ext{Ar}}}{v_{	ext{rms}}^{	ext{Cl}}} = \frac{\sqrt{3RT/M_{	ext{Ar}}}}{\sqrt{3RT/M_{	ext{Cl}}}} = \sqrt{\frac{M_{	ext{Cl}}}{M_{	ext{Ar}}}}$.Given the atomic mass of argon $M_{	ext{Ar}} = 40.0 	ext{u}$ and the molecular mass of chlorine $M_{	ext{Cl}} = 70.0 	ext{u}$.Substituting these values, we get $\frac{v_{	ext{rms}}^{	ext{Ar}}}{v_{	ext{rms}}^{	ext{Cl}}} = \sqrt{\frac{70}{40}} = \sqrt{\frac{7}{4}} = \frac{\sqrt{7}}{2}$.Therefore, the correct option is $C$.

Similar Questions

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \ m \ s^{-1}$, then the rms speed of Helium molecules at the same temperature is

The root mean square speed of hydrogen molecules at $300 \ K$ is $1930 \ m/s.$ Then the root mean square speed of oxygen molecules at $900 \ K$ will be ....... $m/s$.

When the temperature of an ideal gas is increased from $27^\circ C$ to $227^\circ C$,its $r.m.s.$ speed changes from $400 \ m/s$ to $V_s$. The value of $V_s$ is ........ $m/s$.

If $m'$ represents the mass of each molecule of a gas and $T'$ its absolute temperature,then the root mean square speed of the gas molecule is proportional to

If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module