For the equilibrium `CuSO_(4)xx5H_(2)O(s)hArrCuSO_(4)xx3H_(2)O(s) + 2H_(2)O(g)`
`K_(p) = 2.25xx10^(-4)atm^(2)` and vapour pressure of water is `22.8` torr at 298 K. `CuSO_(4)` . `5H_(2)O(s)` is efflorescent (i.e., losses water) when relative humidity is :

Options

A. less than 33.3%
B. above 33.3%
C. less than 66.6%
D. above 66.6%

Answer

A

Explanation

`CuSO_(4).5H_(2)O(s)hArrCuSO_(4).3H_(2)O(s)+2H_(2)O(g)`
`K_(p)=(p_(H_(2)O))^(2)`
`1.086xx10^(-4)=(p_(H_(2)O))^(2)`
`p_(H_(2)O)=sqrt(1.086)xx10^(-2)=1.042xx10^(-2)`
`CuSO_(4).5H_(2)O` is efflorescent when
RH is less than `=(1.042xx10^(-2))/(23.8//760)xx100`
`=(1.042xx760)/(23.8)=33.274%`