Question

The \[{\text{pH}}\] of \[{10^{ - 7}}\,{\text{M NaOH}}\] is:
A) \[7.01\]
B) Between 7 and 8
C) Between 8 and 9
D) Greater than 10

Answer 1

Hint: When the concentration of solution is less than \[{10^{ - 6}}\] M, then we have to consider the ions that we get by dissociation of water. Here we first need to calculate the \[{\text{pOH}}\] and then convert it into \[{\text{pH}}\] using the formula.

Formula used: \[{\text{pH}} + {\text{pOH}} = 14\]
\[{\text{pOH}} = - {\text{log}}[{\text{O}}{{\text{H}}^ - }]\]

Complete step-by-step answer: Since the given concentration of sodium hydroxide is very less, the \[{\text{pH}}\] of this solution will be neutral. This is not possible because this should be a basic solution due to the presence of sodium hydroxide. Water dissociate according to the following reaction:
\[{{\text{H}}_2}{\text{O}} \to {{\text{H}}^ + } + {\text{O}}{{\text{H}}^ - }\]
The ionic product of water can be written as follow and its value is \[{10^{ - 14}}\] at room temperature.
\[{{\text{K}}_w} = [{{\text{H}}^ + }][{\text{O}}{{\text{H}}^ - }]\]
At room temperature the concentration of both the ions are equal in dissociation of water.
\[{10^{ - 14}} = [{\text{O}}{{\text{H}}^ - }][{\text{O}}{{\text{H}}^ - }]\]
\[{10^{ - 14}} = {[{\text{O}}{{\text{H}}^ - }]^2}\]
We will get the concentration of hydroxide ion as:
\[{10^{ - 7}} = [{\text{O}}{{\text{H}}^ - }]\]
We are getting hydroxide ion from the dissociation of \[{10^{ - 7}}\,{\text{M NaOH}}\] also:
\[{\text{NaOH}} \to {\text{N}}{{\text{a}}^ + } + {\text{O}}{{\text{H}}^ - }\]
Hence total concentration of \[{\text{O}}{{\text{H}}^ - }\] ion is \[{10^{ - 7}} + {10^{ - 7}} = 2 \times {10^{ - 7}}\]
We will substitute the value into the formula:
\[{\text{pOH}} = - {\text{Log}}[2 \times {10^{ - 7}}]\]
\[{\text{pOH}} = 6.6989\]
To calculate the \[{\text{pH}}\] we need to use the formula for conversion and hence we will get:
\[{\text{pOH}} = 14 - 6.6989 = 7.30\]
Hence, the value of \[{\text{pH}}\] lies in the range of 7 to 8.
The correct option is B.

Note: Since the concentration of hydrogen ions are very less and hence are difficult to calculate. So the concept of \[{\text{pH}}\] was introduced to make the study easy. It is a scale with value ranging from 0 to 14. The \[{\text{pH}}\] 7 is considered as neutral which has an equal number of hydrogen and hydroxide ions. The \[{\text{pH}}\] 0 to 7 is acidic in nature and \[{\text{pH}}\] from 7 to 14 is basic nature.