The molar conductivity ( _ m ) of a strong electrolyte is measured at two different concentrations. At a concentration of 0.01 , mol ,L⁻¹ , its molar conductivity is 140 , S ,cm² ,mol⁻¹ , and at 0.04 , mol ,L⁻¹ , it is 130 , S ,cm² ,mol⁻¹ . Assuming the electrolyte follows the Debye-Hückel-Onsager equation, the limiting molar conductivity ( _ m ^ ) of the electrolyte in S ,cm² ,mol⁻¹ is _ _ _ _ _ _ .

Step-by-step solution

According to the Debye-Hückel-Onsager equation for strong electrolytes: _ m = _ m ^ - A c Let us set up the equations for the two given concentrations: For c₁ = 0.01 , mol ,L⁻¹ , c₁ = 0.1 ,( mol ,L⁻¹ )^ 1/2 140 = _ m ^ - A(0.1) --- (Equation 1) For c₂ = 0.04 , mol ,L⁻¹ , c₂ = 0.2 ,( mol ,L⁻¹ )^ 1/2 130 = _ m ^ - A(0.2) --- (Equation 2) Subtracting Equation 2 from Equation 1: 140 - 130 = -A(0.1) - (-A(0.2)) 10 = A(0.1) A = 100 , S ,cm² ,mol⁻¹/(mol ,L⁻¹)^ 1/2 Substitute the value of A back into Equation 1: 140 = _ m