Question

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

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

Answer 1

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

$u_{\text{av}}=\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{8PV}{\pi M}}$
(using $PV=nRT$) $Therefore,u_{\text{av}}\propto \sqrt{\frac{P}{M}}$
a) $u_{\text{av}}\left(C{H}_4\right)\propto \sqrt{\frac{0.80}{16}}=0.224$
b) $u_{\text{av}}\left(He\right)\propto \sqrt{\frac{0.40}{4}}=0.10$
c) $u_{\text{av}}\left(C{O}_2\right)\propto \sqrt{\frac{0.20}{44}}=0.067$
d) $u_{\text{av}}\left(NO\right)\propto \sqrt{\frac{1.0}{30}}=0.182$
Thus, at $298\text{K}C{O}_2$ has the lowest average molecular speed.