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

When `K_(2)SO_(4)` is dissolved in water, `K^(+)` and `SO_(4)^(2-)` ions are produced.
`K_(2)SO_(4) rarr 2K^(+) +SO_(4)^(2-)`
Total number of ions produced `=3`
`:. i= 3`
Given,
`w = 25 mg = 0.025 g`
`V = 2L`
`T = 25^(@)C = (25 +273)K = 298K`
Also, we know that:
`R = 0.0821 L atm K^(-1) mol^(-1)`
`M = (2 xx 39) +(1 xx 32) +(4 xx16) = 174 g mol^(-1)`
Applying the following relation,
`pi =i(n)/(v)RT =i(w)/(M)(1)/(v)RT = 3 xx (0.024)/(174) xx (1)/(2) xx 0.0821 xx 298 = 5.27 xx 10^(-3)atm`