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Question: What is the product \[{H^ + }\] and \[O{H^ - }\] ions concentration at room temperature? (A) \[{10...

What is the product H+{H^ + } and OH−O{H^ - } ions concentration at room temperature?
(A) 10−14{10^{ - 14}}
(B) 10−12{10^{ - 12}}
(C) 2×10−62 \times {10^{ - 6}}
(D) 2×10−72 \times {10^{ - 7}}

Explanation

Solution

By using the formula of ionic product of water, we can easily find the product of H+{H^ + } and OH−O{H^ - } ions concentration at room temperature.
KW=[H+][OH−]{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+{H^ + } and OH−O{H^ - } ions by itself is called self-dissociation.
Equilibrium reaction of the pure water is given below:
H2O⇌H++OH−{H_2}O \rightleftharpoons {H^ + } + O{H^ - }
Dissociation constant of the acid is
K=[H+][OH−]H2OK = \dfrac{{[{H^ + }][O{H^ - }]}}{{{H_2}O}}……. (1)
Concentration of the unionized ions is the same as the starting concentration.
[H2O] = constant{\text{[}}{{\text{H}}_{\text{2}}}{\text{O] = constant}}
Therefore, equation (1) becomes
KW=[H+][OH−]{K_W} = [{H^ + }][O{H^ - }]…… (2)
Equation (2) gives ionic products of water.

Ionic product of pure water at 25oC{25^o}C is
KW=[H+][OH−]=1×10−14{K_W} = [{H^ + }][O{H^ - }] = 1 \times {10^{ - 14}}……... (3)
In pure water, hydrogen ion concentration [H+][{H^ + }] is equal to the hydroxide ion concentration [OH−][O{H^ - }].
i.e. [H+]=[OH−][{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+][{H^ + }] and [OH−][O{H^ - }]as xx.
Substituting xx into equation (3) gives
KW=[H+][OH−]=1×10−14{K_W} = [{H^ + }][O{H^ - }] = 1 \times {10^{ - 14}}
KW=x2=1×10−14{K_W} = {x^2} = 1 \times {10^{ - 14}}
x=1×10−7x = 1 \times {10^{ - 7}}
Therefore, [H+]=[OH−]=1×10−7[{H^ + }] = [O{H^ - }] = 1 \times {10^{ - 7}}
Hence, product of H+{H^ + } and OH−O{H^ - } ions concentration at room temperature is
[H+][OH−]=1×10−7×1×10−7=1×10−14=10−14[{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.