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Question: At 298K the \[[{H_3}{O^ + }]\] of a solution is \(2 \times {10^{ - 9}}{\text{M}}\). The nature of th...

At 298K the [H3O+][{H_3}{O^ + }] of a solution is 2×10−9M2 \times {10^{ - 9}}{\text{M}}. The nature of the solution is:
A.Acidic
B.Basic
C.Neutral
D.Cannot be predicted

Explanation

Solution

To answer this question, you should recall the concept of pH scale. The pH scale is a logarithmic scale that is used to measure the acidity or the basicity of a substance. The possible values on the pH scale range from 0 to 14.
Formula used: pH=−log[H+]pH = - {\text{log}}\left[ {{H^ + }} \right]

Complete step by step answer:
The term pH is an abbreviation of potential for hydrogen. Acidic substances have pH values ranging from 1 to 7 and alkaline or basic substances have pH values ranging from 7 to 14. A perfectly neutral substance would have a pH of exactly 7.
The pH of a substance can be expressed as the negative logarithm of the hydrogen ion concentration in that substance.
Similarly, the pOH of a substance is the negative logarithm of the hydroxide ion concentration in the substance. These quantities can be expressed via the following formulae:
pH=−log[H+]pH = - {\text{log}}\left[ {{H^ + }} \right] and pOH=−log[OH−]pOH = - {\text{log}}\left[ {O{H^-}} \right]
The amphoteric nature of water is evident from its self-ionization reaction:
2H2O⇌H3O++OH−2{H_2}O \rightleftharpoons {H_3}{O^ + } + O{H^ - }.
This means that it can serve as a base, as well as an acid.
We can write the ionization constant of water as Kw=[H3O+][OH−]=10−14{K_w} = [{H_3}{O^ + }][O{H^ - }] = {10^{ - 14}}.
For neutral water: [H+]=[OH−]=10−7\left[ {{H^ + }} \right] = \left[ {O{H^-}} \right] = {10^{ - 7}}.
In the given the [H3O+][{H_3}{O^ + }] concentration i.e. 2×10−9M2 \times {10^{ - 9}}{\text{M}} is less than that of the concentration in neutral water.
It pH will be:
pH=−log[2×10−9]pH = - {\text{log}}\left[ {2 \times {{10}^{ - 9}}} \right]
⇒pH=8.69\Rightarrow pH = 8.69
Hence, the water is less acidic or more basic compared to neutral water.

Therefore, we can conclude that the correct answer to this question is option B.

Note:
You should know about the limitations of pH Scale
pH values do not reflect directly the relative strength of acid or bases: A solution of pH = 1 has a hydrogen ion concentration 100 times that of a solution of pH = 3 (not three times).
A solution of an acid having very low concentration, say 10 - 8N,{\text{1}}{{\text{0}}^{{\text{ - 8}}}}{\text{N,}} shows a pH = 8 and hence should be basic, but actual pH value is less than 7.