Under what conditions will `CuSO_4`.`5H_2O` be efflorescent at `25^(@)C`? For the reaction
`CuSO_4.5H_2O_((s)) harr CuSO_4.3H_2O_((s))+2H_2O_((g))`
`K_p` at 298K is `1086 xx 10^(-4)` `atm^2` and vapour pressure of water is 23.8 Torr.

Options

A. If relative humidity `lt` 33.3%, efflorescence takes place
B. If relative humidity `gt` 33.3%, efflorescence takes place
C. The salt does not act as efflorescent at `25^(@)C`
D. The salt effloreses if the vapour pressure of water vapour in atmosphere `lt` 7.92 mm.

Answer

A, D

Explanation

`CuSO_(4).H_(2)O_((s)) harr CUSO_(4).3H_(2)O_((s))+2H_(2)O_((g))`
`K_(P)=P_(H_(2)O)^(2) implies P_(H_(2)O) = sqrt(K_(P))=7.92` mm
Relative humidity = `(P_(H_(2)O))/("vapour pressure of" H_(2)O)`
`=(7.92)/(23.8)=0.333`
% R.H=33.3
`Q lt K`, forward direction
The reaction will proceed only when vapour pressure of moisture in atmosphere is lesser than 7.92mm to show efflorescent nature.