Question

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

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

Answer 1

Answer: (A)

For oxygen $v_{O_2}=\sqrt{\frac{3R{T}_{O_2}}{M_{O_2}}}$ and
For hydrogen $v_{H_2}=\sqrt{3R\frac{T_{H_2}}{M_{H_2}}}$
According to problem $=\sqrt{\frac{3R{T}_{O_2}}{M_{O_2}}}$
$=\sqrt{3R\frac{T_{H_2}}{M_{H_2}}}$
$\Rightarrow \frac{T_{O_2}}{M_{O_2}}=\frac{T_{H_2}}{M_{H_2}}$
$\Rightarrow \frac{47+273}{32}=\frac{T_{H_2}}{M_{H_2}}$
$\Rightarrow T_{H_2}=\frac{320}{32}\times 2=20K$