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# What is the approximate $[{H^ + }]$ in a solution with pH = 2?A. $1 \times {10^{ - 12}}M$B. 12MC. $1 \times {10^{ - 7}}M$D. $1 \times {10^{ - 2}}M$

Last updated date: 10th Aug 2024
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Hint: pH is a scale used to measure acidity and alkalinity of a solution. The range goes from 0 to 14, where 7 is neutral, below 7 is acidic and above 7 is basic. It is the measure of concentration of hydrogen ions present in a substance.

Acids on dissociation produces hydrogen ions. Their concentration can be calculated if the pH of the solution is known. Thus, pH stands for potential of hydrogen. pH lower than 7 denotes that the solution is acidic. It becomes more acidic as we go from 7 to 0.
Due to an amphoteric nature of water, it reacts to form hydronium ions and hydroxide ions. This self-ionisation of water results in equal concentration of both the ions as $1:1$ ratio. The experimental molarity is the same for both, $1.0 \times {10^{ - 7}}M$ at room temperature. Their concentration product gives us a constant of water, ${K_w}$= $1.0 \times {10^{ - 14}}M$. This determines the range of the pH scale from 0 to 14 because $p{K_w}$ = 14.
The solution we are provided with has a pH = 2, this shows that the solution is a strong acid. Its hydrogen ion concentration can be calculated by using the pH formula given below.
$pH = - \log ({H^ + })$
$\therefore 2 = - \log ({H^ + })$
Or $\log ({H^ + })$= -2
$\therefore [{H^ + }] = 1.0 \times {10^{ - 2}}M$ or 0.01M.

Hence, the correct option is (D).

Note: The letter p is written small in pH because it is a word from its meaning ‘power or strength of hydrogen’. Also note that $p{K_w}$ = $pH + pOH = 14$ and from this we can also calculate the concentration of hydroxide ions. It is a unitless quantity as it involves logarithm value only.