At 300 K, the molar conductivities of the aqueous solutions of three salts at two different concentrations are given below: Salt Concentration (M) Molar conductivity (S cm ^2 mol ⁻¹ ) NaNO ₃ 0.01 111 0.04 101 NaCl 0.01 117 0.04 107 AgNO ₃ 0.01 125 0.04 116 The conductivity of a saturated aqueous solution of AgCl is 1.40 10⁻⁶ S cm ⁻¹ at 300 K. If the solubility of AgCl in water at 300 K is X mol L ⁻¹ , then ₁₀(X⁻¹) is

Step-by-step solution

Using the Debye-Hückel-Onsager equation, _m = ^ _m - b C , we can find the limiting molar conductivity ( ^ _m ) for each salt. For NaNO ₃ : ^ _m - b 0.01 = 111 ^ _m - 0.1b = 111 ^ _m - b 0.04 = 101 ^ _m - 0.2b = 101 Subtracting the two equations gives 0.1b = 10 b = 100 . ^ _m( NaNO ₃) = 111 + 100(0.1) = 121 S cm ^2 mol ⁻¹ . For NaCl : ^ _m - 0.1b = 117 ^ _m - 0.2b = 107 Subtracting gives 0.1b = 10 b = 100 . ^ _m( NaCl ) = 117 + 100(0.1) = 127 S cm ^2 mol ⁻¹ . For AgNO ₃ : ^ _m - 0.1b = 125 ^ _m - 0.2b = 116 Subtrac