The conductivity of a saturated solution containing AgA (Ksp = 3 Γ 10^β14) and AgB (Ksp = 1 Γ 10^β14 β Electrochemistry Chemistry Question
Question
The conductivity of a saturated solution containing AgA (Ksp = 3 Γ 10^β14) and AgB (Ksp = 1 Γ 10^β14) is 3.75 Γ 10^β8 Ξ©^β1 cm^β1. If the limiting molar conductivity of Ag^+ and A^β ion is 60 and 80 Ξ©^β1 cm^2 mol^β1, respectively, the limiting molar conductivity of B^β (in Ξ©^β1 cm^2 mol^β1) is
π‘ Solution & Explanation
Let [Ag^+] = x, [A^β] = y, [B^β] = z. By charge balance, x = y + z. Ksp(AgA) = x*y = 3Γ10^β14 and Ksp(AgB) = x*z = 1Γ10^β14. Adding gives x(y+z) = x^2 = 4Γ10^β14, so x = 2Γ10^β7 M. This implies y = 1.5Γ10^β7 M and z = 0.5Γ10^β7 M. Total conductivity ΞΊ = (Ξ»_Ag[Ag^+] + Ξ»_A[A^β] + Ξ»_B[B^β]) / 1000. 3.75Γ10^β8 Γ 1000 = 60(2Γ10^β7) + 80(1.5Γ10^β7) + Ξ»_B(0.5Γ10^β7). 3.75Γ10^β5 = 1.2Γ10^β5 + 1.2Γ10^β5 + Ξ»_B(0.5Γ10^β7). 1.35Γ10^β5 = 0.5Γ10^β7 * Ξ»_B. Ξ»_B = 13500 / 50 = 270 Ξ©^β1 cm^2 mol^β1. Therefore, correct answer is C.