Question

The hydrogen ion concentration of a ${10^{ - 8}}{\text{ M HCl}}$ aqueous solution at $298{\text{ K}}$ $\left( {{{\text{K}}_{\text{w}}} = {{10}^{ - 14}}} \right)$ is:
$1.0 \times {10^{- 6}}{\text{ M}}$
$1.0525 \times {10^{-7}}{\text{ M}}$
$9.525 \times {10^{-8}}{\text{ M}}$
$1.0 \times {10^{-8}}{\text{ M}}$

Answer 1

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


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

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.