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

What is the approximate [H+][{H^ + }] in a solution with pH = 2?
A. 1×10−12M1 \times {10^{ - 12}}M
B. 12M
C. 1×10−7M1 \times {10^{ - 7}}M
D. 1×10−2M1 \times {10^{ - 2}}M

Explanation

Solution

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.

Complete step-by-step answer:
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 1:11:1 ratio. The experimental molarity is the same for both, 1.0×10−7M1.0 \times {10^{ - 7}}M at room temperature. Their concentration product gives us a constant of water, Kw{K_w}= 1.0×10−14M1.0 \times {10^{ - 14}}M. This determines the range of the pH scale from 0 to 14 because pKwp{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+)pH = - \log ({H^ + })
∴2=−log⁡(H+)\therefore 2 = - \log ({H^ + })
Or log⁡(H+)\log ({H^ + })= -2
∴[H+]=1.0×10−2M\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 pKwp{K_w} = pH+pOH=14pH + 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.