20 % of acetic acid is dissociated when its 5   g is added to 500   mL of water. The depression in freezing point of such water is _ _ _ _ _ × 10 - 3 C ∘ . Atomic mass of C , H and O are 12 ,   1 and 16 a.m.u. respectively. [Given : Molal depression constant and density of water are 1 . 86      K   kg   mol - 1 and 1   g   cm - 3 respectively.

Step-by-step solution

Van't Hoff factor (i) for dissociation of acetic acid can be written as follows, i = 1 + ( n - 1 ) α n = Number of ions α = Degree of dissociation ( i = 1 + 0 . 2 ( 2 - 1 ) = 1 . 2 ΔT f = iK f m ΔT f = Depression   in   freezing   point K f = Molar   depression   constant m = molality ΔT f = 1 . 2 × 1 . 86 × 5 × 1000 60 × 500 ΔT f = 0 . 372 Δ T f = 372 × 10 - 3