For a strong electrolyte MX ₂ , the plot of molar conductivity ( _m ) versus c yields a straight line with a slope of -100.0 S cm ^2 mol ^ -3/2 L ^ 1/2 at 298 K. The limiting molar conductivities of M ²⁺ and X ^- ions at 298 K are 120.0 S cm ^2 mol ⁻¹ and 60.0 S cm ^2 mol ⁻¹ , respectively. The value of _m for a 0.04 M aqueous solution of MX ₂ at 298 K is:

Step-by-step solution

According to Kohlrausch's law of independent migration of ions, the limiting molar conductivity of MX ₂ is: _m^0( MX ₂) = ^0_ M ²⁺ + 2 ^0_ X ^- _m^0 = 120.0 + 2(60.0) = 240.0 S cm ^2 mol ⁻¹ For a strong electrolyte, the Debye-Huckel-Onsager equation is: _m = _m^0 - A c The slope of the _m versus c plot is -A . Given the slope is -100.0 , we have A = 100.0 . At concentration c = 0.04 M, c = 0.04 = 0.2 M ^ 1/2 . Substituting the values into the equation: _m = 240.0 - (100.0 0.2) _m = 240.0 - 20.0 = 220.0 S cm ^2 mol