A solution contins 0 .860 g of `K_(2)SO_(4)` in 500 mL solution . Its osmotic pressure is found to be 0.690 atm at `27^(@)C` . Calculate the value of Van't Hoff factor . (At mass K = 39.0 , S = 32, O = 16 R = 0.082 atm `mol^(-1) K^(-1)`)

Explanation

Let us first calculate observed molar mass
`M_(B) = (w_(B) xx R xxT)/(pi xxV)`
`w_(B) = 0.86g , V = 500 ml = 0.5 L`
`R = 0.082 L atm mol^(-1) K^(-1) , pi = 0.690 atm , T = 300 K `
`M_(B) = (0.860 xx 0.082 xx 300)/(0.690 xx 0.5) = 63.9`
Normal molar mass ` = 2 xx 39+32+4 xx 32 = 174`
Van.t Hoff factor , ` i = ("Normal molar mass")/("Observed molar mass")`
` = 2.83