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Calculate the hydronium ion \[[{H_3}{O^ + }]\] and hydroxide ion \[[O{H^-}]\] concentration for a $0.0368\,{\text{M}}\,{\text{NaOH}}$

Last updated date: 13th Jun 2024
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Hint: 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.

The formula used: \[pOH{\text{ }} = {\text{ }} - {\text{log}}\left[ {O{H^-}} \right]\] and $pH + pOH = 14$

Complete Step by step solution:
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:
\[pH{\text{ }} = {\text{ }} - {\text{log}}\left[ {{H^ + }} \right]\] and \[pOH{\text{ }} = {\text{ }} - {\text{log}}\left[ {O{H^-}} \right]\].
The given $0.0368\,{\text{M}}\,{\text{NaOH}}$ will dissociate to give $0.0368\,$moles of hydroxide ions.

$\left[ {O{H^ - }} \right] = 0.0368{\text{M}}$
This concentration of hydroxide ions can be used to calculate the pOH of solution:
\[pOH{\text{ }} = {\text{ }} - {\text{log}}\left[ {0.0368} \right] = 1.4341\].
From this, we can calculate the pH using:
$pH + pOH = 14$.
The value of pH will be \[pH = 12.565\].
Now \[pH{\text{ }} = {\text{ }} - {\text{log}}\left[ {{H^ + }} \right]\] can be used to calculate the hydronium concentration:
\[[{H_3}{O^ + }] = 2.71 \times {10^{ - 13}}\].

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).
pH value is zero for \[{\text{1 N}}\] the solution of the strong acid. The concentration of \[{\text{2 N, 3 N, 10 N,}}\] etc. gives negative pH values.
A solution of an acid having very low concentration, say \[{\text{1}}{{\text{0}}^{{\text{ - 8}}}}{\text{N}}\] shows a pH = 8and hence should be basic, but actual pH value is less than 7.