Molar conductivity:

The molar conductivity of hydrogen and hydroxyl ions at the very small concentrations existing in pure water may be taken as equal to the accepted value at infinite dilutions, those are 0.03498 and 0.01983 S m² mol^-1, respectively at 298 K, and hence the total molar conductivity of 1 mole of hydrogen and hydroxyl ions, at infinite dilution could be 0.05481 S m² mol^-1.

Therefore, Eq. (4.8) can be used to calculate the concentration of hydrogen of hydroxyl ions.

Λ_m = κ

or   c = κ/ Λ_m  ≈  κ/Λ^∝_H+ + Λ^∝_OH-                                 ... (6.14)

The conductivity of pure water is 5.8 × 10-6 S m-1 at 298 K. We can compute concentration c through substituting there values in Eq. (6.12).

c =5.8 ×10 ^-6 S m ^-1/ (0.03498 + 0.01983) S m ² mol ^-1

= 1.06 × 10^-4 mol m^-3

= 1.06 × 10^-7 mol dm^-3

Therefore,

K_w   = c_H + c_{OH -} = (1.06 × 10^-7 mol dm^-3 ) ²

= 1.12 × 10 ^-14(mol dm ^-3 ) ²

Since the activity coefficient of the ions in pure water cannot differ appreciably from unity, this result very close to K_w, the activity ionic product at 398 K. The result in Table 6.2 gives the observed conductivity and values of K_w at several temperatures from 275 K to 323 K (0° to 50° C).