Respuesta :
Answer : The rms speed of the molecules in a sample of [tex]H_2[/tex] gas at 300 K will be four times larger than the rms speed of [tex]O_2[/tex] molecules at the same temperature, and the ratio [tex]\mu _{rms}(H_2)/\mu _{rms}(O_2)[/tex] constant with increasing temperature.
Explanation :
Formula used for root mean square speed :
[tex]\mu _{rms}=\sqrt{\frac{3RT}{M}}[/tex]
where,
[tex]\mu _{rms}[/tex] = rms speed of the molecule
R = gas constant
T = temperature
M = molar mass of the gas
At constant temperature, the formula becomes,
[tex]\mu _{rms}=\sqrt{\frac{1}{M}}[/tex]
And the formula for two gases will be,
[tex]\frac{\mu _{H_2}}{\mu _{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}}[/tex]
Molar mass of [tex]O_2[/tex] = 32 g/mole
Molar mass of [tex]H_2[/tex] = 2 g/mole
Now put all the given values in the above formula, we get
[tex]\frac{\mu _{H_2}}{\mu _{O_2}}=\sqrt{\frac{32g/mole}{M_{2g/mole}}}=4[/tex]
Therefore, the rms speed of the molecules in a sample of [tex]H_2[/tex] gas at 300 K will be four times larger than the rms speed of [tex]O_2[/tex] molecules at the same temperature.
And the ratio [tex]\mu _{rms}(H_2)/\mu _{rms}(O_2)[/tex] constant with increasing temperature because rms speed depends only on the molar mass of the gases at same temperature.
