The henry's law constant for the solubility of `N_2` gas in water at 298 K is `1.0xx10^5` atm . The mole fraction of `N_2 ` in air is 0.8 . The number of moles of `N_2` from air dissolved in 10 moles of water at 298 K and 5 atm pressure is

Options

A. `4.0 xx 10^(-4)`
B. `4.0 xx 10^(-5)`
C. `5.0 xx 10^(-4)`
D. `4.0 xx 10^(-5)`

Answer

A

Explanation

`P_(N_(2)) = 0.8 xx 5 = 4 atm`
From Henry law:
`P_(N_(2)) = K X_(N_(2)) [X_(N_(2))` is small]
`4 = 10^(5) xx X_(N_(2))`
`X_(N_(2)) = 4 xx 10^(05)`
`:' X_(N_(2)) lt lt lt n_(H_(2)O) rArr X_(H_(2)O) = 1`
which means if `n_(H_(2)O) =1` than `n_(N_(2)) = 4 xx 10^(-5)`
`rArr` for 10 mole of `H_(2)O` mole of `N_(2)` present are `10 xx 4 xx 10^(-5) = 4 xx 10^(-4)` mole