Question

# The pH of a 0.001 M aqueous solution of sodium hydroxide will be:A.5.0B.7.5C.9.0D.11.0

Hint: Compounds or elements which tend to accept electrons, i.e. compounds with high electron affinity are known as acids. Contrary to acids, bases are compounds that are better electron donors. To put it in simpler terms, acids are electronegative compounds while bases are electropositive compounds.
The tendency for certain compounds to attract electrons is higher as compared to other compounds. Basically, there are certain substances that are stronger acids as compared to other substances
Formula Used:
$pOH{\text{ }} = {\text{ }} - {\text{ }}\log \left[ X \right]$,
$pH{\text{ }} + {\text{ }}pOH{\text{ }} = {\text{ }}14$

To mathematically quantify this property of acidity or basicity of any substance, a universal scale has been created. This scale is known as pH scale. A pH scale ranges from a value of 0 (which means most acidic) to 14 (which means most basic).
The mathematical representation to calculate the pH value can be given as follows:
$pOH{\text{ }} = {\text{ }} - {\text{ }}\log \left[ X \right]$,
where [X] is the concentration of the electron donating ion
hence, relating this to our given question,
when one mole of sodium hydroxide dissociates, it separates into one mole of sodium ion and one mole of hydroxide ion. Here, the hydroxide ion is the electronegative ion. Hence the concentration of the hydroxide ions present in the solution is equivalent to the concentration of sodium hydroxide, i.e. 0.001 M
hence, $pOH{\text{ }} = {\text{ }} - {\text{ }}log{\text{ }}\left[ {0.001} \right]$
$pOH{\text{ }} = {\text{ }}3.0$,
also, $pH{\text{ }} + {\text{ }}pOH{\text{ }} = {\text{ }}14$
hence, $pH{\text{ }} = {\text{ }}14{\text{ }}-{\text{ }}pOH$
$= {\text{ }}14{\text{ }}-{\text{ }}3$
$= 11.00$

Hence, Option D is the correct option.

Note:
If any substance can achieve a pH value of 7 on a pH scale, this implies that the value is exactly at the same distant form both the acidic and basic extremes, and hence is considered to be neutral in nature.