Question

At $298\text{K}$, which of the following gases has the lowest average molecular speed ?

• A. $C{H}_4$ at $0.80\text{atm}$
• B. $He$ at $0.40\text{atm}$
• C. $C{O}_2$ at $0.20\text{atm}$
• D. $NO$ at $1.00\text{atm}$

Answer 1

The correct option is C $C{O}_2$ at $0.20\text{atm}$

Average velocity does not depend on the Pressure.
Expression for the average velocity is:

$u_{\text{av}}=\sqrt{\frac{8RT}{\pi M}}\Rightarrow u_{\text{av}}\propto \sqrt{\frac{T}{M}}$
since T is constant
$u_{\text{av}}\propto \sqrt{\frac{1}{M}}$
Larger the molar mass, lower be the average velocity.
$C{O}_2$ has the highest molar mass.
Thus, at $298\text{K}$, $C{O}_2$ will have lowest molecular speed.