The plots of molar conductivity ( _m ) versus the square root of concentration ( c ) for the strong electrolytes HCl , NaA , and NaCl yield straight lines with y-intercepts of 426.0 , 91.0 , and 126.0 S cm ^2 mol ⁻¹ , respectively, at 298 K. If the molar conductivity of a 0.001 M solution of the weak acid HA at the same temperature is 39.1 S cm ^2 mol ⁻¹ , what is its degree of dissociation?

Step-by-step solution

For strong electrolytes, the y-intercept of the _m versus c plot corresponds to the limiting molar conductivity ( _m^0 ). Thus, we have: _m^0( HCl ) = 426.0 S cm ^2 mol ⁻¹ _m^0( NaA ) = 91.0 S cm ^2 mol ⁻¹ _m^0( NaCl ) = 126.0 S cm ^2 mol ⁻¹ According to Kohlrausch's law of independent migration of ions, the limiting molar conductivity of the weak acid HA can be calculated as: _m^0( HA ) = _m^0( HCl ) + _m^0( NaA ) - _m^0( NaCl ) _m^0( HA ) = 426.0 + 91.0 - 126.0 = 391.0 S cm ^2 mol ⁻¹ The degree of dissociation (