At what relative humidity with `Na_(2)SO_(4)` be deliquescent (absorb moisture) when exposed to the air at `0^(@ )C` ? Given
`Na_(2)SO_(4).10H_(2)O(s) hArr Na_(2)SO_(4)(s) +10H_(2)O(g), K_(p)=4.08xx10^(-25)` and vapour pressure of water at `0^(@)C =4.58` Torr ?

Options

A. below 60.5%
B. above 60.5%
C. above 39.5%
D. below 39.5%

Answer

B

Explanation

`Na_(2)SO_(4).10H_(2)O(s)hArr Na_(2)SO_(4)(s)+10H_(2)O(g)`
`K_(p)=4.08xx10^(-25)`
`:. (p_(H_(2)O))^(10)=4.08xx10^(-25)`
`p_(H_(2)O)=(4.08xx10^(-25))^((1)/(10))=x("say")`
`log x =(1)/(10)log (4.08xx10^(-25))`
`=(1)/(10)[log 4.08+log 10^(-25)]`
`=(1)/(10)[log 4.08-25]`
`=(1)/(10)[0.611-25]`
`=0.0611-2.5=bar(3).5611`
`x=` antilog `bar(3).5611=3.64xx10^(-3)`
`Na_(2)SO_(4)(s)` will absorb water if `R_(H)` is more than
`=(3.64xx10^(-3))/(4.58//760)xx100`
`=(0.364xx760)/(4.58)=60.4%`