A vessel of volume `V = 5` litre contains `1.4 g` nitrogen and `0.4g` of He at `1500K`. If `30%` of the nitrogen molecules are disassociated into atoms then the gas pressure becomes `(N)/(8)xx10^(5)N//m^(2)`. Find `N` (Assume `T` constant). `[R = (25)/(3)J//molK]`

Answer

33

Explanation

Given mass of `N_(2) = 1.4 g`
mass of `He = 0.4g`
`V = 5` litre
`T = 1500 K =` const
`R = (25)/(3) J//"mole" K`
number of moles of `He = (0.4)/(4) = 0.1` mole
number of moles of `N_(2) = (1.4 xx 70)/(28xx100) = 0.035` mole
number of moles of `N` atoms `=(1.4 xx 30)/(14 xx 100) = 0.03` mole
Pressure of gas is `P = (nRT)/(V)`
`P = ((0.1+0.035+0.03)(25)/(3)xx1500)/(5xx10^(-3))`
`= ((0.165)25xx1500)/(3xx5xx10^(-3))`
`= 4.125 xx 10^(5) N//m^(2) = (33)/(8) xx 10^(5) N//m^(2)`