At what temperature does an oxygen molecule h | vedclass

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

Question

(B) The root mean square (r.m.s.) velocity of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Here,$R$ is the universal gas c

Vedclass · Accepted Answer

$320$

Vedclass · Answer

(B) The root mean square (r.m.s.) velocity of a gas molecule is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Here,$R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.For hydrogen $(H_2)$,the molar mass $M_{H_2} = 2 	imes 10^{-3} \ kg/mol$ and temperature $T_{H_2} = 20 \ K$.For oxygen $(O_2)$,the molar mass $M_{O_2} = 32 	imes 10^{-3} \ kg/mol$.We are given that the r.m.s. velocities are equal: $v_{rms(H_2)} = v_{rms(O_2)}$.Therefore,$\sqrt{\frac{3RT_{H_2}}{M_{H_2}}} = \sqrt{\frac{3RT_{O_2}}{M_{O_2}}}$.Squaring both sides and simplifying: $\frac{T_{H_2}}{M_{H_2}} = \frac{T_{O_2}}{M_{O_2}}$.Substituting the values: $\frac{20}{2} = \frac{T_{O_2}}{32}$.$10 = \frac{T_{O_2}}{32} \implies T_{O_2} = 320 \ K$.

At what temperature does an oxygen molecule have the same r.m.s. velocity as a hydrogen molecule at $20 \ K$ (in $K$)?

Similar Questions

The $rms$ speed of helium gas at $27\,^{\circ}C$ and $1\,atm$ pressure is $900\,ms^{-1}$. Then the $rms$ speed of helium molecules at temperature $27\,^{\circ}C$ and $2\,atm$ pressure is ...... $m/s$.

Select the incorrect statement about Maxwell's speed distribution.

The speeds of $5$ gas molecules are $2, 3, 4, 5,$ and $6$ units respectively. What is the $rms$ speed of these molecules?

The root mean square speed of the molecules of a diatomic gas is $v$. When the temperature is doubled,the molecules dissociate into two atoms. The new root mean square speed of the atom is

The temperature of a gas is $-80^{\circ} C$. To what temperature should the gas be heated so that the r.m.s. speed is increased by $2$ times (in $^{\circ} C$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module