At 298 K , the molar conductivity of x % (w/w) MX solution (aqueous) is 123.5 S cm ^2 mol ⁻¹ . The conductance of same solution is 1.9 10⁻³ S . The value of x is _______ 10⁻² . (Given : cell constant = 1.3 cm ⁻¹ ; molar mass of MX is 75 g mol ⁻¹ , density of aqueous solution of MX at 298 K is 1.0 g mL ⁻¹ )

Step-by-step solution

The conductivity (specific conductance), , is given by the product of conductance and cell constant: = G G^* = 1.9 10⁻³ S 1.3 cm ⁻¹ = 2.47 10⁻³ S cm ⁻¹ The molar conductivity, _m , is related to the conductivity and molarity C by the formula: _m = 1000 C Substituting the given values: 123.5 = 2.47 10⁻³ 1000 C 123.5 = 2.47 C C = 2.47 123.5 = 0.02 mol L ⁻¹ Molarity C can also be expressed in terms of mass percentage x (w/w), density d , and molar mass M : C = x d 10 M Substituting the known values ( d = 1.0 g mL ⁻¹ ,