Question

The molecules of which of the following gas have highest speed ?

• A. Hydrogen at ${50}^{o}C$
• B. Methane at $298K$
• C. Nitrogen at ${1000}^{o}C$
• D. Oxygen at $0^{o}C$

Answer 1

The correct option is A Hydrogen at ${50}^{o}C$

Speed of gas $\propto \frac{\sqrt{T}}{\sqrt{M}}$ i.e. $\sqrt{\frac{T}{M}}$

where $M$ is the molecular weight of gas.

$\underset{–}{For\left(A\right)}:-\sqrt{\frac{T}{M}}=\sqrt{\frac{(50+273)}{2}}=12.708$

$\underset{–}{For\left(B\right)}:-\sqrt{\frac{T}{M}}=\sqrt{\frac{298}{16}}=4.316$

$\underset{–}{For\left(C\right)}:-\sqrt{\frac{T}{M}}=\sqrt{\frac{(1000+273)}{28}}=6.74$

$\underset{–}{For\left(D\right)}:-\sqrt{\frac{T}{M}}=\sqrt{\frac{273}{32}}=2.92$

$\therefore$ Option $A$ is the correct answer.