Find pH and Kw for water with given values of conductivity
We know,

$$\lambda_c = \frac{(\text{Specific Conductivity})}{1000 \times c}$$

$$\alpha\lambda_\infty = \lambda_c$$ 

(where $c$ is concentration in moles per litres of the electrolyte and $\alpha$ is degree of dissociation of the electrolyte)

$\lambda_{\infty}$ of water (the electrolyte) is the sum of $\lambda_{\infty}$ of $\ce{H+}$ and $\ce{OH-}$.

From equations above, one can easily find  the the value of $c\alpha$ is $10^{-7}$, which is the concentration of $\ce{H+}$.