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.

Explanation

Calculation of Van't Hoff factor (i)
`K_(2)SO_(4)` dissociates in water as:
`K_(2)SO_(4)overset(("aq"))to2K^(+)(aq)+SO_(4)^(2-)(aq):alpha=(i-1)/(n-1)`
`alpha("For complete dissiociation")=1, n=3 , 1=(i-1)/(3-1)or i=2+1=3`
Calculation of osmotic pressure `(pi)`
Osmotic pressure `(pi)=i C R T =(iW_(B)RT)/(M_(B)xxV)`
`i=3, W_(B)=25 mg = 0.025 g, M_(B)=2xx29+324 xx16 =174 g mol^(-1), V=2L , T=25^(@)C= 298 K,`
`R=0.0821 L atm K^(-1)mol^(-1)`
`pi=((3)xx(0.025g)xx(0.0821 L atm K^(-1) mol^(-1))xx(298K))/((174 g mol^(-1))xx(2L))`
`=5.27xx10^(-3) atm`.