For equilibrium
`ZnSO_(4).7H_(2)O(s)hArrZnSO_(4).2H_(2)O(s)+5H_(2)O(g) K_(P)=56.25xx10^(-10) atm^(5)`
and vapour pressure of water is `22.8` torr at `298K.ZnSO_(4).7H_(2)O(s)` is efflorescent (lose water) when relative humidity is `[5sqrt56.25=2.23]`

Options

A. less than `70.620%`
B. less then `74.60%`
C. Above than `74.60%`
D. Above 70.60%`

Answer

B

Explanation

`K_(P)=P_(H_(2)O)^(5)=56.25xx10^(-10)`
`P_(H_(2)O)=(56.25xx10^(-10))^(1//5)`
`=(56.25)^(1//5)xx10^(-2)`
`=2.23xx10^(-2)xx760`
`=17.01` torr
`% "Relative humidity"=("Partial pressure")/("Vapour pressure")xx100`
`=(17.01)/(22.8)xx100=74.60%` (less than `74.60%`)