First slide

Rms speed

Question

At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at $47^{0} C$ ?

Moderate

A

20 K
B

80 K
C

-73 K
D

3 K

Solution

For oxygen $v_{0_{2}} = \sqrt{\frac{3 {RT}_{0_{2}}}{M_{O_{2}}}}$ and
$For hydrogen v_{H_{2}} = \sqrt{3 R \frac{T_{H_{2}}}{M_{H_{2}}}}$
According to problem = $\sqrt{\frac{3 {RT}_{O_{2}}}{M_{O_{2}}}} = \sqrt{3 R \frac{T_{H_{2}}}{M_{H_{2}}}}$
$\Rightarrow \frac{{T_{O}}_{_{2}}}{M_{O_{2}}} = \frac{T_{H_{2}}}{M_{H_{2}}} \Rightarrow \frac{47 + 273}{32} = \frac{T_{H_{2}}}{M_{H_{2}}}$
$\Rightarrow T_{H_{2}} = \frac{320}{32} \times 2 = 20 K$

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