Question

At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at 47°C

• A. 20 K
• B. 80 K
• C. – 73 K
• D. 3 K

Answer 1

Answer: (A)

20 K

Answer 2

$v_{rms} = \sqrt{\frac{3RT}{M}} \Rightarrow T \propto M$ $\lbrack\because v_{rms},R \rightarrow \text{constant}\rbrack$

$\Rightarrow \frac{T_{H_{2}}}{T_{O_{2}}} = \frac{M_{H_{2}}}{M_{O_{2}}} \Rightarrow \frac{T_{H_{2}}}{(273 + 47)} = \frac{2}{32} \Rightarrow T_{H_{2}} = 20K.$