Consider two weak acids HX and HY. The limiting molar conductivities of their anions are equal ( ^ _ X^- = ^ _ Y^- ). The difference in their pK_a values is pK_a( HY ) - pK_a( HX ) = 1 . The molar conductivity of a 0.05 M solution of HX is twice the molar conductivity of a solution of HY of concentration C . Assuming the degree of dissociation 1 for both acids, the value of C is x 10⁻² M. The value of x is ____.

Step-by-step solution

Since ^ _ X^- = ^ _ Y^- and ^ _ H^+ is common to both, the limiting molar conductivities of the two acids are equal: ^ _m( HX ) = ^ _m( HY ) . The degree of dissociation is given by = _m ^ _m . Given _m( HX ) = 2 _m( HY ) , we have _X = 2 _Y . From the given pK_a difference: pK_a( HY ) - pK_a( HX ) = 1 - K_a( HY ) + K_a( HX ) = 1 ( K_a( HX ) K_a( HY ) ) = 1 K_a( HX ) K_a( HY ) = 10 For weak acids with 1 , K_a = C ^2 . K_a( HX ) K_a( HY ) = C_X _X^2 C_Y _Y^2 = 0.05 (2 _Y)^2 C_Y _Y^2 = 0.05 4 C_Y = 0.2 C_Y Equating t