Question

What is the product \[{H^ + }\] and \[O{H^ - }\] ions concentration at room temperature?
(A) \[{10^{ - 14}}\]
(B) \[{10^{ - 12}}\]
(C) \[2 \times {10^{ - 6}}\]
(D) \[2 \times {10^{ - 7}}\]

Answer 1

Hint: By using the formula of ionic product of water, we can easily find the product of \[{H^ + }\] and \[O{H^ - }\] ions concentration at room temperature.
\[{K_W} = [{H^ + }][O{H^ - }]\]

Complete Solution :
Due to the electrical conductivity of water, it undergoes dissociation. Water being a weak electrolyte undergoes only partial dissociation. Dissociation of pure water to a small extent into \[{H^ + }\] and \[O{H^ - }\] ions by itself is called self-dissociation.
Equilibrium reaction of the pure water is given below:
\[{H_2}O \rightleftharpoons {H^ + } + O{H^ - }\]
Dissociation constant of the acid is
\[K = \dfrac{{[{H^ + }][O{H^ - }]}}{{{H_2}O}}\]……. (1)
Concentration of the unionized ions is the same as the starting concentration.
\[{\text{[}}{{\text{H}}_{\text{2}}}{\text{O] = constant}}\]
Therefore, equation (1) becomes
\[{K_W} = [{H^ + }][O{H^ - }]\]…… (2)
Equation (2) gives ionic products of water.

Ionic product of pure water at \[{25^o}C\] is
\[{K_W} = [{H^ + }][O{H^ - }] = 1 \times {10^{ - 14}}\]……... (3)
In pure water, hydrogen ion concentration \[[{H^ + }]\] is equal to the hydroxide ion concentration \[[O{H^ - }]\].
i.e. \[[{H^ + }] = [O{H^ - }]\]

The concentration of each ion can be calculated from the equation for the ionic product of water.
We can take the concentration of \[[{H^ + }]\] and \[[O{H^ - }]\]as \[x\].
Substituting \[x\] into equation (3) gives
\[{K_W} = [{H^ + }][O{H^ - }] = 1 \times {10^{ - 14}}\]
\[{K_W} = {x^2} = 1 \times {10^{ - 14}}\]
\[x = 1 \times {10^{ - 7}}\]
Therefore, \[[{H^ + }] = [O{H^ - }] = 1 \times {10^{ - 7}}\]
Hence, product of \[{H^ + }\] and \[O{H^ - }\] ions concentration at room temperature is
\[[{H^ + }][O{H^ - }] = 1 \times {10^{ - 7}} \times 1 \times {10^{ - 7}} = 1 \times {10^{ - 14}} = {10^{ - 14}}\]
So, the correct answer is “Option A”.

Additional information-
Let us try to understand the pH value of acid, basis and neutral solution.
-Acidic solution will have pH value less than 7.
-Basic solution will have pH value more than 7.
-neutral solution will have pH value equal to 7.

Note: - In acidic solution, hydrogen ion concentration is greater than hydroxide ion concentration.
- In basic solution, hydroxide ion concentration is greater than hydrogen ion concentration.