Under what pressure conditions `CuSO_(4).5H_(2)O` be efforescent at `25^(@)C`. How good a drying agent is `CuSO_(4).3H_(2)O` at the same temperature? Given
`CuSO_(4).5H_(2)O(s) hArr CuSO_(4).3H_(2)O(s)+2H_(2)O(v)`
`K_(p)=1.086xx10^(-4) atm^(2)` at `35^(@)C`. Vapoure pressure of water at `25^(@)C` is `23.8 mm` of Hg.

Options

A. 3.64 mm Hg
B. 4.84 mm Hg
C. 5.96 mm Hg
D. 7.92 mm Hg

Answer

D

Explanation

An efflorescent salt is one that loses `H_(2)O` to atmosphere
For the reaction,
`CuSO_(4)*5H_(2)O(s) hArr CuSO_(4)*3H_(2)O(s)+2H_(2)O`(vapour)
`K_(p)=(P_(H_(2)O))^(2)=1.086xx10^(-4)"atm"^(2)`
`(P_(H_(2)O))=1.042xx10^(-2)"atm"=8.92`mmHg
`therefore ` Given `P_(H_(2)O)` at `25^(@)C` (i.e. 23.8) mmHg `gt` 7.92 mmHg and thus, reaction will proceed in backward direction, i.e.
`CuSO_(4)*3H_(2)O(s)+2H_(2)O"(vapour)" hArr CuSO_(4)*5H_(2)O(s)`
Thus `CuSO_(4). 5H_(2)O` will not act as efflorescent but on the contrary `CuSO_(2).3H_(2)O` will absorb moisture from the atmosphere under given conditions. The salt `CuSO_(4).5H_(2)O` will effloresce only on a dry when the partial pressure of moisture in the air is less than 7.92 mm or if relative humidity of air at `25^(@)C=7.92//23.8=0.333 or 33.3%`.