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Question: The hydrogen ion concentration of a \({10^{ - 8}}{\text{ M HCl}}\) aqueous solution at \(298{\text{ ...

The hydrogen ion concentration of a 10−8 M HCl{10^{ - 8}}{\text{ M HCl}} aqueous solution at 298 K298{\text{ K}} (Kw=10−14)\left( {{{\text{K}}_{\text{w}}} = {{10}^{ - 14}}} \right) is:
1.0×10−6 M1.0 \times {10^{- 6}}{\text{ M}}
1.0525×10−7 M1.0525 \times {10^{-7}}{\text{ M}}
9.525×10−8 M9.525 \times {10^{-8}}{\text{ M}}
1.0×10−8 M1.0 \times {10^{-8}}{\text{ M}}

Explanation

Solution

To solve this we have to calculate the hydrogen ion concentration of aqueous solution of HCl{\text{HCl}} at the given temperature. The ionization constant of water i.e. Kw{{\text{K}}_{\text{w}}} is given to us. From the given values calculate the concentration of hydrogen ion due to HCl{\text{HCl}} and water. then find the total concentration.

Complete solution:
We are given that the concentration of HCl{\text{HCl}} is 10−8 M{10^{-8}}{\text{ M}}.
We know that HCl{\text{HCl}} is a strong acid and dissociates completely in water. The dissociation reaction of HCl{\text{HCl}} is as follows:
HCl⇌H++Cl−{\text{HCl}} \rightleftharpoons {{\text{H}}^ + } + {\text{C}}{{\text{l}}^-}
The concentration of H+{{\text{H}}^ + } is equal to the concentration of HCl{\text{HCl}}.
Thus, the concentration of H+{{\text{H}}^ + } due to HCl{\text{HCl}} is 10−8 M{10^{ - 8}}{\text{ M}}.
We are given that the ionization constant of water i.e. Kw{{\text{K}}_{\text{w}}} is 10−14{10^{ - 14}}.
We know that water is neutral in nature. The ionization constant of water is the product of hydrogen ion concentration and the hydroxide ion concentration. Thus,
Kw=[H+][OH−]{{\text{K}}_{\text{w}}} = [{{\text{H}}^ + }][{\text{O}}{{\text{H}}^-}]
But [H+]=[OH−][{{\text{H}}^ + }] = [{\text{O}}{{\text{H}}^-}].
Thus, the concentration of H+{{\text{H}}^ + } due to water is 10−7 M{10^{ - 7}}{\text{ M}}.
Now, the total hydrogen ion concentration will be equal to the sum of the concentration of H+{{\text{H}}^ + } due to HCl{\text{HCl}} and the concentration of H+{{\text{H}}^ + } due to water. thus,
[H+]=10−8+10−7[{{\text{H}}^ + }] = {10^{ - 8}} + {10^{-7}}
[H+]=0.1×10−7+1×10−7[{{\text{H}}^ + }] = 0.1 \times {10^{-7}} + 1 \times {10^{-7}}
[H+]=1.1×10−7 M≈1.0525×10−7 M[{{\text{H}}^ + }] = 1.1 \times {10^{-7}}{\text{ M}} \approx {\text{1}}{\text{.0525}} \times {10^{- 7}}{\text{ M}}
Thus, the hydrogen ion concentration of a 10−8 M HCl{10^{-8}}{\text{ M HCl}} aqueous solution at 298 K298{\text{ K}} (Kw=10−14)\left( {{{\text{K}}_{\text{w}}} = {{10}^{-14}}} \right) is 1.0525×10−7 M{\text{1}}{\text{.0525}} \times {10^{-7}}{\text{ M}}.

Thus, the correct option is (B) .

Note: The concentration of hydrogen ion is known as the pH. The pH is calculated as the negative logarithm of the hydrogen ion concentration. As water is neutral in nature the concentration of hydrogen and hydroxide ions in water is equal. As the calculated pH is less than 7, the solution is basic in nature.