Question

If the \[{{\text{H}}^ + }\] concentration as \[0.000001{\text{ M}}\], what is the \[{\text{pOH}}\] of the solution?

Answer 1

Hint: To calculate the \[{\text{pOH}}\] we will first calculate the \[{\text{pH}}\] using the formula. Using an ionic product of water we can convert \[{\text{pH}}\] into \[{\text{pOH}}\].
Formula used: \[{\text{pH}} = - \log \left[ {{{\text{H}}^ + }} \right]\]
\[{\text{p}}{{\text{K}}_{\text{W}}} = {\text{pH}} + {\text{pOH}}\]
Here \[{{\text{K}}_{\text{W}}}\] is the ionic product of water.

Complete step by step answer:
The concentration of hydrogen ion is given to us that is \[0.000001{\text{ M}}\]. We can remove the decimal and write in terms of power of 10. We know,
\[0.000001{\text{ M}} = \dfrac{1}{{1000000}} = \dfrac{1}{{{{10}^6}}}\]
We can take the power to the numerator from the denominator to write it like this\[{10^{ - 6}}\]. So the concentration of \[\left[ {{{\text{H}}^ + }} \right] = {10^{ - 6}}{\text{ M}}\]
Now using the formula we will first calculate the \[{\text{pH}}\]of the solution as:
\[{\text{pH}} = - \log \left[ {{{10}^{ - 6}}{\text{ }}} \right]\]
The use of log function brings cancels the 10 and bring power forward as:
\[{\text{pH}} = - \left( { - 6} \right) = 6\]
Hence the \[{\text{pH}}\] of the solution is 6.
Now the \[{\text{p}}{{\text{K}}_{\text{W}}} = {\text{pH}} + {\text{pOH}}\].
We can rewrite it as:
\[{\text{pOH}} = {\text{p}}{{\text{K}}_{\text{W}}} - {\text{pH}}\]
\[ \Rightarrow {\text{pOH}} = 14 - 6 = 8\]
Hence, the \[{\text{pOH}}\] of the solution is 8.

Additional information:
\[{{\text{K}}_{\text{W}}}\] is the ionic product of water. The ionic product of water as the name suggests is the product of the ions that the water gives after dissociation, which is hydrogen ion and the hydroxide ion. The concentration of both the ions is the same at room temperature that is \[{\text{1}}{{\text{0}}^{ - 7}}\]. Hence the ionic product becomes \[{\text{1}}{{\text{0}}^{ - 7}} \times {\text{1}}{{\text{0}}^{ - 7}} = {\text{1}}{{\text{0}}^{ - 14}}\]. It is a constant quantity at constant temperature. The \[{\text{pH}}\] scale is based on the ionic product of water

Note:
The \[{\text{pH}}\] is a scale to measure the concentration of hydrogen ions in a solution. The concentration in terms of molarity is very less to study and hence scientists devised the scale \[{\text{pH}}\] so that the study of concentration of hydrogen ions becomes easy. It ranges from 0 to 14. 7 is the neutral \[{\text{pH}}\], below 7 \[{\text{pH}}\] is acidic and above 7 \[{\text{pH}}\] is basic.