At 298 ~K , the limiting molar conductivity of a weak monobasic acid is 4 10² ~S ~cm ² ~mol ⁻¹ . At 298 ~K , for an aqueous solution of the acid the degree of dissociation is and the molar conductivity is y 10² ~S ~cm ² ~mol ⁻¹ . At 298 ~K , upon 20 times dilution with water, the molar conductivity of the solution becomes 3 y 10² ~S ~cm ² ~mol ⁻¹ The value of y is _________ .

Step-by-step solution

α = λ m λ m ∘ α 1 = y × 10 + 2 4 × 10 2 = y 4           . . . 1 k a = C 1 α 1 2 1 − α 1             . . . 2 After dilution α 2 = 3 y × 10 2 4 × 10 2 = 3 y 4           . . . 3 k a = C 2 α 2 2 1 − α 2             . . . 4 eq. 1 / 3 ⇒   α 1 α 2 = 1 3 eq 2 / 4 ⇒   1 = C 1 α 1 2 1 − α