Suggest a way to determine the $\Lambda _{\text{m}}^ \circ $ value of water.

Hint: We have to determine the molar conductivity of water at infinite dilution. The molar conductivity at infinite dilution is denoted by $\Lambda _{\text{m}}^ \circ $. To solve this we apply Kohlrausch’s law. It provides the way to find out the molar conductivity in electrolytic solutions.

Complete step by step solution:
We know that the conductivity of a solution because of all the ions produced by one mole of the electrolyte dissolved in the solution is known as the molar conductivity. The formula for molar conductivity is as follows:
${\Lambda _{\text{m}}} = \dfrac{{\kappa \times {\text{1000}}}}{M}$
Where ${\Lambda _{\text{m}}}$ is the molar conductivity,
$\kappa $ is the electrolytic conductivity,
$M$ is the molarity of the electrolytic solution.
When we dilute the solution i.e. decrease the concentration of the solution the molar conductivity increases. At infinite dilution, the molar conductivity attains a limiting value which is known as molar conductivity at infinite dilution. The molar conductivity at infinite dilution is denoted by $\Lambda _{\text{m}}^ \circ $.
Kohlrausch’s law states that at infinite dilution, each ion migrates independently of its co-ion and makes its contribution to the total molar conductivity. Thus,
$\Lambda _{\text{m}}^ \circ = \lambda _ + ^ \circ + \lambda _ - ^ \circ $
Where ${\Lambda _{\text{m}}}$ is the molar conductivity,
$\lambda _ + ^ \circ $ is the molar conductivity of the cation at infinite dilution,
$\lambda _ - ^ \circ $ is the molar conductivity of the anion at infinite dilution.
The molar conductivity of water at infinite dilution can be obtained by the molar conductivities of the hydrogen ion $\left( {{{\text{H}}^ + }} \right)$ and the hydroxide ion $\left( {{\text{O}}{{\text{H}}^ - }} \right)$ at infinite dilutions. Thus,
$\Lambda _{\text{m}}^ \circ = \lambda _{{{\text{H}}^ + }}^ \circ + \lambda _{{\text{O}}{{\text{H}}^ - }}^ \circ $
Where ${\Lambda _{\text{m}}}$ is the molar conductivity of water,
$\lambda _{{{\text{H}}^ + }}^ \circ $ is the molar conductivity of the hydrogen ion $\left( {{{\text{H}}^ + }} \right)$ at infinite dilution,
$\lambda _{{\text{O}}{{\text{H}}^ - }}^ \circ $ is the molar conductivity of the hydroxide ion $\left( {{\text{O}}{{\text{H}}^ - }} \right)$ at infinite dilution.
Thus, we can conclude that the molar conductivity of water at infinite dilution is equal to the sum of the molar conductivities of hydrogen ion $\left( {{{\text{H}}^ + }} \right)$ and the hydroxide ion $\left( {{\text{O}}{{\text{H}}^ - }} \right)$ at infinite dilutions.

Note: We should always keep in mind that the conductivity of pure water is very low. This is because of the inability of water to exist in ionic form. Distilled water does not conduct electricity and no ions are present in the distilled water.