Question

Which of the following statements is/are correct about the ionic product of water?

• A. At 298K , Equilibrium constant of water < ionic product of water
  i.e. $K_c<K_w$
• B. $K_w$ at 373 K $>K_w$ at 298 K
• C. Ionic product of water at ${25}^{\circ }C$ is ${10}^{-14}$
• D. None of the above.

Answer 1

Answer: (A), (B), (C)

Ionic product of water at ${25}^{\circ }C$ is ${10}^{-14}$

Option A : $K_c\times \left[H_{2}O\right]=K_w$, we know that concentration of water at ${25}^{\circ }C$ or 298K is $\frac{1000}{18}M=55.55M\therefore K_c<K_w$

Option B: Effect of temperature on $K_w$:

The ionic product of water $K_w$ increases with increase of temperature. The dissociation of water molecule into it's ions is an endothermic reaction.
$2H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}\left(aq\right)+O{H}^{-}(aq.)\Delta H>0$

By Le Chatelier's principle, increase in the temperature will shift the equilibrium in forward direction. So more ions are formed, and $K_w$ increases.
$K_w\propto T$
So, ionic product is greater at 373 K than at 298 K

Option C:
$K_w$ (at ${25}^{\circ }C)=[H^{+}\left]\right[O{H}^{-}]={10}^{-14}$