At 27,^oC,the rms velocity of H_2 gas is 100, | vedclass

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

Question

(B) The formula for $rms$ velocity is $V_{rms} = \sqrt{\frac{3RT}{M_w}}$.Given for $H_2$: $T_1 = 27 + 273 = 300\, K$,$M_{w1} = 2\, g/mol$,$V_{rms1} =

Vedclass · Accepted Answer

$\frac{50}{\sqrt{2}}$

Vedclass · Answer

(B) The formula for $rms$ velocity is $V_{rms} = \sqrt{\frac{3RT}{M_w}}$.Given for $H_2$: $T_1 = 27 + 273 = 300\, K$,$M_{w1} = 2\, g/mol$,$V_{rms1} = 100\, m/s$.Given for $O_2$: $T_2 = 327 + 273 = 600\, K$,$M_{w2} = 32\, g/mol$.Taking the ratio: $\frac{V_{rms2}}{V_{rms1}} = \sqrt{\frac{T_2}{T_1} 	imes \frac{M_{w1}}{M_{w2}}}$.Substituting the values: $\frac{V_{rms2}}{100} = \sqrt{\frac{600}{300} 	imes \frac{2}{32}} = \sqrt{2 	imes \frac{1}{16}} = \sqrt{\frac{1}{8}} = \frac{1}{2\sqrt{2}}$.$V_{rms2} = 100 	imes \frac{1}{2\sqrt{2}} = \frac{50}{\sqrt{2}}\, m/s$.

At $27\,^oC$,the $rms$ velocity of $H_2$ gas is $100\, m/s$. Find the $rms$ velocity of $O_2$ gas at $327\,^oC$.

Similar Questions

If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300 \ m/s$,what will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on the Kelvin scale?

If the pressure of a gas is doubled while keeping the temperature constant,what will happen to the root mean square $(RMS)$ speed of the gas molecules?

According to the kinetic theory of gases,the $r.m.s.$ velocity of gas molecules is directly proportional to:

The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} C$ in a vessel is $61 \ m/s$. The molecular weight of the gas is nearly:
$[R = 8.31 \ J \ mol^{-1} \ K^{-1}]$

If the root mean square velocity of a hydrogen molecule at a given temperature and pressure is $2 \,km/s$, the root mean square velocity of oxygen at the same condition in $km/s$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module