Question

At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at 47⁰C

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

Answer 1

Answer: (A)

20 K

Answer 2

For oxygen $v_{O_{2}} = \sqrt{\frac{3RT_{O_{2}}}{M_{O_{2}}}}$ and For hydrogen

$v_{H_{2}} = \sqrt{3R\frac{T_{H_{2}}}{M_{H_{2}}}}$

According to problem $= \sqrt{\frac{3RT_{O_{2}}}{M_{O_{2}}}} = \sqrt{3R\frac{T_{H_{2}}}{M_{H_{2}}}}$

⇒ $\frac{T_{O_{2}}}{M_{O_{2}}} = \frac{T_{H_{2}}}{M_{H_{2}}}$ ⇒ $\frac{47 + 273}{32} = \frac{T_{H_{2}}}{2}$

⇒ $T_{H_{2}} = \frac{320}{32} \times 2 = 20K$.