The conductance of $0.0015\mathrm{ }\mathrm{M}$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $\mathrm{Pt}$electrodes. The distance between the electrodes is $120\mathrm{ }\mathrm{cm}$ with an area of cross-section of $1 {\mathrm{cm}}^2$. The conductance of this solution was found to be $5\times {10}^{-7}\mathrm{S}$ . The $\mathrm{pH}$of the solution is $4$. The value of limiting molar conductivity of this weak monobasic acid in aqueous solution is $\mathrm{ }\mathrm{Z}\mathrm{ }\times \mathrm{ }{10}^2\mathrm{S}\mathrm{ }{\mathrm{cm}}^{-1}{\mathrm{mol}}^{-1}.$ The value of $\mathrm{Z}$is.

Hence, the correct answer is 6.