For a salt XY , which is a strong electrolyte, the plot of _m versus c has a slope of -90.0 S cm ^2 mol ^ -3/2 L ^ 1/2 at 298 K. At 0.01 M concentration of XY , the value of _m is 145.0 S cm ^2 mol ⁻¹ . The limiting molar conductivity of Y ^- ion ( ^0_ Y^- , in S cm ^2 mol ⁻¹ ) at 298 K will be (Given : ^0_ X^+ =74.0 S cm ^2 mol ⁻¹ )

Step-by-step solution

According to the Debye-Huckel-Onsager equation for strong electrolytes: _m = _m^0 - A c The slope of the plot of _m versus c is -A . Given slope = -90.0 , we have A = 90.0 . At c = 0.01 M, c = 0.1 M ^ 1/2 . Substituting the given values into the equation: 145.0 = _m^0 - 90.0 0.1 145.0 = _m^0 - 9.0 _m^0 = 154.0 S cm ^2 mol ⁻¹ According to Kohlrausch's law of independent migration of ions: _m^0( XY ) = ^0_ X ^+ + ^0_ Y ^- 154.0 = 74.0 + ^0_ Y ^- ^0_ Y ^- = 154.0 - 74.0 = 80.0 S cm ^2 mol ⁻¹ Answer: 80.0