At what temperature will the rms speed of hydrogen be the same as that of oxygen at $25^{\circ} C$ ?

Open in App

Solution

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$
Let the temperature be $T$ .
$v_{r m s} (H)$ = $v_{r m s} (O)$
$\sqrt{\frac{3 R T}{M_{H}}} = \sqrt{\frac{3 R T^{'}}{M_{O}}}$
$⟹ \frac{T}{2} = \frac{298}{32}$
$⟹ T = 18.625 K$

Suggest Corrections

Similar questions

Q. At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at

1327^{\circ} C

Q. At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at

1327^{\circ} C

Q. At what temperature the RMS velocity of oxygen will be same as that of methane at

27^{o} C

Q. At what temperature is the rms speed of

H_{2}

molecules the same as that of oxygen molecules at

1327^{\circ} C

The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room Temperature the rms speed of oxygen molecules is $v$ . The rms speed of the hydrogen molecules at the same temperature will be

Join BYJU'S Learning Program

At what temperature will the rms speed of hydrogen be the same as that of oxygen at 25∘C?

vrms=√3RTMLet the temperature be T.vrms(H)=vrms(O)√3RTMH=√3RT′MO⟹T2=29832⟹T=18.625 K

At what temperature will the rms speed of hydrogen be the same as that of oxygen at $25^{\circ} C$ ?

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$
Let the temperature be $T$ .
$v_{r m s} (H)$ = $v_{r m s} (O)$
$\sqrt{\frac{3 R T}{M_{H}}} = \sqrt{\frac{3 R T^{'}}{M_{O}}}$
$⟹ \frac{T}{2} = \frac{298}{32}$
$⟹ T = 18.625 K$