Determine the osmotic pressure of a solution prepared by dissolving `25mg` of `K_(2)SO_(4)` in `2L` of water at `25^(@)C`, assuming that it is completely dissociated.

Answer

`pi=5.27 xx10^(-3)atm`

Explanation

Volume of solution `=2L,T=25^(@)C=25+273=298K`
Weight of `K_(2)SO_(4)(W_(2))` dissolved `=25mg=0.025g`
`Mw_(2)` of `K_(2)SO_(4)=2xx39+32+16xx4=174g mol^(-1)`
Van't Hoff factor `(i)` for `K_(2)SO_(4) (` complete dissociation `):`
`{:(,KSO_(4),rarr,2K^(o+),+,SO_(4)^(2-),),(Initial ,1,,0,,0,),(Fi nal,0,,2,,1,(T otal ions=2+1=3)):}`
`:. i=3`
`:. pi=i MRT=ixx(n)/(V)RT`
`=ixx(W_(2))/(Mw_(2))xx(1)/(V)xxRT`
`=3xx(0.025g)/(174g mol^(-1))xx(1)/(2L)xx0.821L atm K^(-1) molxx298K`
`=5.27xx10^(-3)atm`