Question

At \[{90^o}C\] pure water has \[[{H_3}{O^ + }] = {10^{ - 6}}mol{L^{ - 1}}\]. What is the value of \[{K_W}\] at \[{90^o}C\]?
A. \[{10^{ - 6}}\]
B. \[{10^{ - 12}}\]
C. \[{10^{ - 7}}\]
D. \[{10^{ - 14}}\]

Answer 1

Hint: As we know that the hydronium ion is a type of oxonium ion having the formula, \[{H_3}{O^ + }\]. The hydronium ion is formed by the protonation reaction of water. When the Arrhenius acid is dissolved in the water, there is a formation of the positive ion in hydronium ion. Here, the hydrogen ion is joined to the water molecules. Because of the presence of positive charge bonded with the water molecules, the proton cannot exist in the aqueous solution. And the conjugate base of hydronium ions is water.

Complete answer:
The value of \[{K_W}\] at \[{90^o}C\] is not equal to \[{10^{ - 6}}\]. Hence, option (A) is incorrect.
According to the question, the concentration of water is equal to \[{10^{ - 6}}mol/L\]
Let’s see the ionization reaction of water;
\[{H_2}O \rightleftharpoons {H^ + } + O{H^ - }\]
The equilibrium constant, K for this reaction is,
\[K = \dfrac{{[{H^ + }][O{H^ - }]}}{{[{H_2}O]}}\]
By rearranging the above equation,
\[K \times [{H_2}O] = [{H^ + }][O{H^ - }]\]
Where, \[K \times [{H_2}O]\] is equal to \[{K_W}\]. Hence,
\[{K_W} = [{H^ + }][O{H^ - }]\]
The concentration of hydrogen ion and hydroxide ion of pure water is equal to\[{10^{ - 6}}mol/L\]. Substitute this value in the equation of \[{K_W}\];
\[{K_W} = [{H^ + }][O{H^ - }]\]
\[ = {10^{ - 6}} \times {10^{ - 6}}\]
\[ = {10^{ - 12}}\]
Thus, the value of \[{K_W}\] at \[{90^o}C\] is equal to \[{10^{ - 12}}\]. Hence, option (B) is correct.
The value of ion product constant for the liquid water is not equal to \[{10^{ - 7}}\]. Hence, option (C) is incorrect.
The value of \[{K_W}\] is not equal to \[{10^{ - 14}}\]. Hence, option (D) is incorrect.

So, the correct answer is “Option B”.

Note:
We need to know that the ion product constant for the liquid water is known as equilibrium constant and it can be denoted as, \[{K_W}\]. And it can be calculated by multiplying the concentration of hydronium ions and hydroxide ions. The water is an inorganic compound which does not have any taste and odor. The hydronium ion is formed from the water by attacking the hydrogen to water. And this water acts as a conjugate base for the hydronium ion.