Question

Assuming $N_2$ molecule of spherical shape with radius $2\times {10}^{-9}$ cm, the percentage of empty space in one mole of $N_2$ gas taken at STP is :

• A. $0.1$%
• B. $99.9$%
• C. $90$%
• D. $10$%

Answer 1

The correct option is B $99.9$%

As we know,
Volume of $1$ mole gas at $NTP=22.4litre$
Volume of $1$ mole of $N_2$ molecules $=$ Volume of molecule $\times$ Avagadro's number
$=\frac{4}{3}\pi r^3\times 6.023\times {10}^{23}$
$=\frac{4}{3}\times 3.14\times (2\times {10}^{-10}{)}^3\times 6.023\times {10}^{23}$
$=20.2\times {10}^{-6}{m}^3=20.2c{m}^3$
Empty space $=22400-20.2=22379.8c{m}^3$
The percentage of empty space $=\frac{22379.8}{22400}\times 100=99.9$%