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

The pH{\text{pH}} of 10−7 M NaOH{10^{ - 7}}\,{\text{M NaOH}} is:
A) 7.017.01
B) Between 7 and 8
C) Between 8 and 9
D) Greater than 10

Explanation

Solution

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

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

Complete step-by-step answer: Since the given concentration of sodium hydroxide is very less, the pH{\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:
H2O→H++OH−{{\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{10^{ - 14}} at room temperature.
Kw=[H+][OH−]{{\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=[OH−][OH−]{10^{ - 14}} = [{\text{O}}{{\text{H}}^ - }][{\text{O}}{{\text{H}}^ - }]
10−14=[OH−]2{10^{ - 14}} = {[{\text{O}}{{\text{H}}^ - }]^2}
We will get the concentration of hydroxide ion as:
10−7=[OH−]{10^{ - 7}} = [{\text{O}}{{\text{H}}^ - }]
We are getting hydroxide ion from the dissociation of 10−7 M NaOH{10^{ - 7}}\,{\text{M NaOH}} also:
NaOH→Na++OH−{\text{NaOH}} \to {\text{N}}{{\text{a}}^ + } + {\text{O}}{{\text{H}}^ - }
Hence total concentration of OH−{\text{O}}{{\text{H}}^ - } ion is 10−7+10−7=2×10−7{10^{ - 7}} + {10^{ - 7}} = 2 \times {10^{ - 7}}
We will substitute the value into the formula:
pOH=−Log[2×10−7]{\text{pOH}} = - {\text{Log}}[2 \times {10^{ - 7}}]
pOH=6.6989{\text{pOH}} = 6.6989
To calculate the pH{\text{pH}} we need to use the formula for conversion and hence we will get:
pOH=14−6.6989=7.30{\text{pOH}} = 14 - 6.6989 = 7.30
Hence, the value of pH{\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 pH{\text{pH}} was introduced to make the study easy. It is a scale with value ranging from 0 to 14. The pH{\text{pH}} 7 is considered as neutral which has an equal number of hydrogen and hydroxide ions. The pH{\text{pH}} 0 to 7 is acidic in nature and pH{\text{pH}} from 7 to 14 is basic nature.