Question

At what temperature will the oxygen molecules have the same root mean square speed as hydrogen molecules at 200 K

• A. 800 K
• B. 1600 K
• C. 2400 K
• D. 3200 K

Answer 1

Answer: (D)

3200 K

Answer 2

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

$\Rightarrow \frac{T_{O_{2}}}{T_{H_{2}}} = \frac{M_{O_{2}}}{M_{H_{2}}} \Rightarrow \frac{T_{O_{2}}}{200} = \frac{32}{2} \Rightarrow T_{O_{2}} = 3200K$