A sample of pure water at a certain temperature has conductivity 6.2x 10^-8 S cm^-1. At this temperature lambda deg(H+) = 349.8 and lambda deg(OH-) = 198.5 S cm^2 mol^-1. The ionic product of water K_w at this temperature is closest to

JEE Advanced levelSingle correct optionDifficulty 3 of 3ec197

A sample of pure water at a certain temperature has conductivity $6.2 \times 1 0^{- 8} S c m^{- 1}$ . At this temperature $λ^{\circ} (H X^{+}) = 349.8$ and $λ^{\circ} (OH X^{-}) = 198.5 S c m^{2} mo l^{- 1}$ . The ionic product of water $K_{w}$ at this temperature is closest to

Water is a very weak electrolyte, so its ions are at effectively infinite dilution:

Λ_{m}^{\circ} (H X_{2} O) = 349.8 + 198.5 = 548.3 S c m^{2} mo l^{- 1}

. Concentration of dissociated water

= [H X^{+}] = [OH X^{-}] = \frac{1000 κ}{Λ _{m}^{\circ}} = \frac{1000 \times 6.2 \times 1 0 ^{- 8}}{548.3} = 1.13 \times 1 0^{- 7} mol L^{- 1}

K_{w} = [H X^{+}] [OH X^{-}] = (1.13 \times 1 0^{- 7})^{2} = 1.28 \times 1 0^{- 14}

. Omitting the factor 1000 gives

1 0^{- 20}