Question

Which one of the following salts will have the same value of
van’t Hoff factor (i) as that of K₄[Fe(CN)₆].
(a) Al₂(SO₄)₃ (b) NaCl (c) Al(NO₃)₃ (d) Na₂SO₄

Answer 1

answer : option (a) Al₂(SO₄)₃

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

similarly, for K₄[Fe(CN)₆] ⇔4K^+ + [Fe(CN)₆]³-

i = 1 - α + 4α + α = 1 + 4α

if 100% ionised then, α = 1

so, i = 1 + 4 = 5

let's check which option has, i = 5

(a) Al₂(SO₄)₃ ⇔2Al³+ + 3(SO₄)²-

i = 1 + 4α = 1 + 4 = 5 ✓

(b) NaCl ⇔Na+ + Cl-

i = 1 + α = 1 + 1 = 2

(c) Al(NO3)3 ⇔Al³+ + 3NO3^-

i = 1 + 3α = 1 + 3 = 4

(d) Na2SO4 ⇔2Na^+ + SO4²-

i = 1 + 2α = 1 + 2 = 3

here it is clear that option (a)Al₂(SO₄)₃ has Van't Hoff factor ,i = 5

hence, option (a) is correct choice.