At 298 ~K , the limiting molar conductivity of a weak monobasic acid is 4 10^ 2 ~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 10^ 2 ~S ~cm ^ 2 ~mol ^ -1 . At 298 ~K , upon 20 times dilution with water, the molar conductivity of the solution becomes 3 y 10^ 2 ~S ~cm ^ 2 ~mol ^ -1 The value of y is _________ .
A. A
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 2 1 − α 1 C 2 α 2 2 α 1 2 1 − α 2 α 2 2 1 − α 1 = C 2 C 1 C 1 = C 2   20 y 1 2 = C 2 C 1 α 1 2 1 − α 2 α 2 2 1 − α 1 = 1 20 20 α 1 2 1 − α 1 = α 2 2 1 − α 2 20 1 − α 1 = 9 1 − 3 α 1 20 − 60 α 1 = 9 − 9 α 1 11 = 51 α 1 α 1 = 11 51 = 0.22 y = 4 α 1 = 4 × 11 51 = 0 .86
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