Molar conductivity of an electrolyte is the conductance of all the ions produced by one gram mole of the electrolyte in solution and is denoted as `Lambda_(m)`.
`Lambda_(m)=(kxx1000)/(c )`
Here k is the specific conductance while c is the molar concentration of the electrolyte. The molar conductance of the strong electrolytes at infinite dilution `(Lambda_(m)^(oo))` can be obtained graphically by extrapolation while the same for weak electrolytes cannot be obtained graphically. It can be calculated theoretically with the help of Kohrausch's. Law.
`Lambda_(m(AxBy))^(oo)=xlambda_(m (A^(y+)))^(oo)+ylambda_(m(B^(x)))^(oo)`
Equivalent conductance of 1 M methanoic acid solution is `10" ohm"^(-1)cm^(2)" equiv"^(-1)` and at infinite dilution it is `200" ohym"^(-1)cm^(2)" equiv"^(-1)`. The pH of methanoic acid solution is :

Options

A. 7
B. 3.3
C. 1.3
D. 6.8.

Answer

C

Explanation

(c ) `alpha=(Lambda_(m)^(c ))/(Lambda_(m)^(prop))=((10" ohm"^(-1) cm^(2) " equiv"^(-1)))/((200" ohm"^(-1) cm^(2)" equiv"^(-1)))=0.05`
`[H^(+)]= C alpha=1Mxx0.05=0.05 M`
`pH=-log [H^(+)]=-log(0.05)`
`=-log(5xx10^(-2))=(2-log 5)`
=2-0.6990=1.3