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 )
A. A
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 , M = 75 g mol ^ -1 ): 0.02 = x 1.0 10 75 1.5 = 10x x = 0.15 Expressing x in the required format: x = 15 10^ -2 The value is 15. Answer: 15
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