Question

The number of gas molecules effusing per second unit area through an orifice on the wall of the container is $\frac{1}{4}.N^{\ast }.u_{avg},$ where $N^{\ast }$ is the number of molecules per unit volume. What is this number under STP conditions for nitrogen gas?

• A. $1.53\times {10}^{24}{m}^{-2}{s}^{-1}$
• B. $1.03\times {10}^{22}{m}^{-2}{s}^{-1}$
• C. $3.01\times {10}^{22}{m}^{-2}{s}^{-1}$
• D. $2.121\times {10}^{23}{m}^{-2}{s}^{-1}$

Answer 1

The correct option is D $2.121\times {10}^{23}{m}^{-2}{s}^{-1}$

The average velocity is given by $u_{avg}=\sqrt{\frac{8RT}{\pi m}}$

at $STP,PV=RT$ $\{$ for $n=1\}$

$u_{avg}=\sqrt{\frac{8PV}{\pi m}}$

for nitrogen at STP $m=28$, $V=22.4lt$, $P=1$ atm

$u_{avg}=1.414$ m/s

Now at STP, $N=N_A$ ($1$ mole)
at STP.

No. of gas molecules$=\frac{1}{4}{N}_A\times u_{avg}$

$=\frac{1}{4}\times 6\times {10}^{23}\times 1.414$

$=2.121\times {10}^{23}$ m/s

Option C.