Question

At ${90^ \circ }C$ , pure water has $[{H^ + }] = {10^{ - 6}}M$ .The value of ${K_W}$ at ${90^ \circ }C$ is
A. ${10^{ - 6}}$
B. ${10^8}$
C. ${10^{ - 12}}$
D. ${10^{ - 14}}$

Answer 1

Water is a neutral molecule, so the concentration of hydronium ion will be equal to the concentration of hydroxide ion. Moreover the ionic product of water is concentration of hydronium ion into concentration of hydroxide ion.
Formula used:
${K_W} = [{H_3}{O^ + }][O{H^ - }]$

Complete step by step answer:
Water is one of the most common solvents for acid-base reactions. Now, water is a weak acid and a weak base and the hydronium and hydroxide ions exist in very small concentrations relative to that of non-ionized water.
Since, acids and bases react with each other, this signifies that water can react with itself. Yes, it does happen. The water molecules exchange protons with one another to a very small extent and this process is known as the auto ionization or self-ionization of water.
Now, for any sample of pure water, the molar concentration of hydronium and hydroxide ion, must be equal i.e. $[{H_3}{O^ + }] = [O{H^ - }]$ in pure water.
Furthermore, in the given question we have to calculate the value of ${K_W}$ .
So, $[{H_3}{O^ + }] = [O{H^ - }] = {10^{ - 6}}$
Therefore, ionic product of water will be,
${K_W} = [{H_3}{O^ + }][O{H^ - }]$
$= {10^{ - 6}} \times {10^{ - 6}}$
$= {10^{ - 12}}mol\,{L^{ - 1}}$

Hence, option C is correct.

Note:
In neutral solution, the concentration of ${H^ + }$ ion and $O{H^ - }$ ion are equivalent to each other, hence the value of the hydrogen ion and hydroxyl ion are the same. But this is not the case in acidic and alkaline solutions. In case of acidic solutions, the value of ${H^ + }$ ion is always greater than the value of $O{H^ - }$ ion and in case of alkaline solutions, the value of $O{H^ - }$ ion is always greater than the value of ${H^ + }$ ion.