When 9.2 10⁻³ ~kg of formic acid is added to 600 ml of water the freezing point of water is depressed. If 30 % of Formic acid undergoes dissociation what would be the freezing point of the solution? ( K _ f of H ₂ O is 1.86 ~K ~kg ~mol ; MM of formic acid: 46 amu )

Step-by-step solution

The molar mass of formic acid (HCOOH) is 46 g/mol . The mass of formic acid is 9.2 10⁻³ kg = 9.2 g . The number of moles of formic acid is n = 9.2 46 = 0.2 mol . The mass of water is 600 ml = 0.6 kg . The molality m is 0.2 0.6 = 1 3 mol/kg . Formic acid dissociates as HCOOH H ⁺ + HCOO ⁻ . For 30 % dissociation, the degree of dissociation = 0.3 . The van't Hoff factor i = 1 + (n-1) , where n=2 . Thus, i = 1 + 0.3(2-1) = 1.3 . The depression in freezing point is T_f = i K_f m = 1.3 1.86 1 3 = 1.3 0.62 = 0.806 K . The