A 0.1 M aqueous solution of a weak monoprotic acid ( HA ) is separated from a 0.12 M aqueous solution of sucrose by a semipermeable membrane. If the two solutions are found to be isotonic at a given temperature, the acid dissociation constant ( K_a ) of the weak acid HA is x 10⁻³ . The value of x is ________.

Step-by-step solution

For the solutions to be isotonic, their osmotic pressures must be equal: _ HA = _ sucrose Using the formula = iCRT , we have: i_ HA C_ HA RT = i_ sucrose C_ sucrose RT Since sucrose is a non-electrolyte, i_ sucrose = 1 . i_ HA 0.1 = 1 0.12 i_ HA = 1.2 For a weak monoprotic acid HA , the dissociation is HA H ^+ + A ^- . The van't Hoff factor is related to the degree of dissociation ( ) by: i = 1 + 1.2 = 1 + = 0.2 The acid dissociation constant K_a is given by Ostwald's dilution law: K_a = C ^2 1 - K_a = 0.1 (0.2)^2