Question

Which one of the following electrolytes has the same value
of van't Hoff's factor (i) as that of the Al₂(SO₄)₃ (if all are
100% ionised) ? [2015]
(a) K₃[Fe(CN)₆] (b) Al(NO₃)₃
(c) K₄[Fe(CN)₆] (d) K₂SO₄

Answer 1

answer : option (c) K₄[Fe(CN)₆]

if any dissociation reaction, AnBm ⇒nA+ + mB^-, Van't Hoff factor is given by, i = 1 - α + nα + mα

similarly, for Al₂(SO₄)₃ ⇔2Al³+ + 3(SO4)^2-

i = 1 - α + 2α + 3α = 1 + 4α

if 100% ionised then, α = 1

so, i = 1 + 4 = 5

let's check which option has, i = 5

(a) K₃[Fe(CN)₆] ⇔3K^+ + [Fe(CN)₆]³-

i = 1 + 3α = 1 + 3 = 4

(b) Al(NO3)3 ⇔Al³+ + 3NO3^-

i = 1 + 3α = 1 + 3 = 4

(c) K₄[Fe(CN)₆] ⇔4K^+ + [Fe(CN)₆]³-

i = 1 + 4α = 1 + 4 = 5 ✓

(d) K2SO4 ⇔2K^+ + SO4²-

i = 1 + 2α = 1 + 2 = 3

here it is clear that option (c) K₄[Fe(CN)₆] has Van't Hoff factor ,i = 5 .