`17.4%` (wt.`//`vol.) `K_(2)(SO_(4))` solution at `27^(@)C` isotonic to `5.85%` (wt.`//`vol.) `NaCl` solution at `27^(@)C`. IF `NaCl` is `100%` ionised, what is `%` ionisation of `K_(2)SO_(4)` in aq. solution?

Explanation

For `{:(K_(2)SO_(4),hArr,2K^(+)+,SO_(4)^(2-),),(1,,0,0,),(1-alpha,,2alpha,alpha,):}`
`because pi_(1) = (w)/(m.V)ST (1+2alpha)`
`pi_(1) = (17.4 xx 1000)/(174 xx 100) xx ST (1+2alpha)`
`= ST xx (1+2alpha)`
for `{:(NaCl,hArr,Na^(+)+,Cl^(-),),(1,,0,0,),((1-alpha_(1)),,alpha_(1),alpha_(1),):}`
`:. pi_(2) = (5.85 xx 1000)/(58.5 xx 100) xx ST xx (1+alpha_(1))`
`because alpha_(1) = 1`
`:. pi_(2) = ST xx 2`
Given `pi_(1) = pi_(2)` (isotonic solution)
`:. ST xx 2 = ST xx (1+2alpha)`
or `alpha = 0.5`
or `50%` ionisation of `K_(2)SO_(4)`