Calculate the `[overset(Theta)OH]` of `[NH_(2)C_(2)H_(4)NH_(3)]^(o+)` and `[H_(3)N-C_(2)H_(4)NH_(3)]^(2+)` in `0.15M` ethylene diamine (aq) if
`NH_(2)C_(2)H_(4)NH_(2)+H_(2)O hArr NH_(2)C_(2)H_(4)overset(o+)NH_(3)+overset(Theta)OH (K_(1) = 8.5 xx 10^(-5))`
`NH_(2)C_(2)H_(4)overset(o+)NH_(3) +H_(2)O hArr [NH_(3)C_(2)H_(4)NH_(3)]^(2+) + overset(Theta)OH (K_(2) = 2.7 xx 10^(-8))`

Explanation

Case I: `[OH^(Theta)] = [NH_(2)C_(2)H_(4)NH_(3)]^(o+)`
`=C xx sqrt((K_(b_(1)))/(c)) = sqrt(0.15 xx 8.5 xx 10^(-5)) = 3.57 xx 10^(-3)M`
Case II:
`{:(NH_(2)C_(2)H_(4)NH_(3)^(o+) +H_(2)O hArr,NH_(3)C_(2)H_(4)NH_(3)^(2+)+,OH^(Theta),,),(3.57 xx 10^(-3),0,1.275xx10^(-5),,),([3.57xx10^(-3)-X],X,(X+1.275xx10^(-5)),,):}`
`2.7 xx 10^(-8) = (x.(X+3.57xx10^(-3)))/((3.57xx10^(-3)-X))`
Neglecting `X^(2)`, also `3.57 xx 10^(-3) - X = 3.57 xx 10^(-3)` , (X s very small)
`2.7 xx 10^(-8) = (3.57 xx 10^(-3)X)/(3.57 xx 10^(-3))`
`:.X = 2.7 xx 10^(-8)`
`:. [NH_(2)C_(2)H_(4)NH_(3)]^(2+) = 2.7 xx 10^(-8)M = K_(b_(2))`