Find the percentage empty space in one mole of nitrogen gas at STP. Given, radius of nitrogen molecule is 2 Å.

Answer

99,9%

Explanation

Here, `r = 2 Å = 2xx 10^(10)m`
Volume of one molecule of nitrogen ` = (4)/(3)pi r^3`
` = (4)/(3)xx(22)/(7)(2xx10^(-10))^3m^3`
Number of molecules in one molecules in
one mole
`V = 6.023 xx10^(23)xx(4)/(3)xx(22)/(7)(2xx10^(10))^3 m^3`
`V = 2.02 xx10^(-5)m^3`
Volume occupied by one mole of gas at NTP
`V' = 22.4 litre = 22.4xx10^(-3) m^3`
`:. Space occupied = (V)/(V') = (2.02xx10^(-5))/(22.4xx10^(-3))~~10^(-3)`
And empty space = `1 - 10^(-3) = 0.999 = 99.9%`