Question

Derive a relation between pH and pOH.

Answer 1

pH simply means power of hydrogen. Higher the power of hydrogen, stronger the acid is. Similarly, pOH means power of hydroxide ion, stronger the hydroxide ion power, higher will be the alkaline property in it. They are opposite to each other. And are linked by one equation.

Complete answer:
We know that a solution can be acidic, alkaline or neutral. pH is the measure of the acidity of solution while on the other hand pOH is measure of basicity of that solution, and when both have equal value, then that solution will be neutral.
As the hydrogen ion concentration can be expressed logarithmically by pH similarly the hydroxide ion concentration can be expressed logarithmically by pOH. The pOH is the negative logarithm of hydroxide – ion concentration. Or we can write in mathematical form as
$pOH = - \log {[OH]^ - }$
The pH of any solution can be related to pOH. These two are related to autoprotolysis reactions that occur in water at a particular temperature.
At ${25^ \circ }C$, the extent of this equilibrium has been measured as, ${K_w} = {[{H_3}O]^ + }{[OH]^ - } = {10^{ - 14}}$
This is called the ionic product of water.
Our equation will become, ${[{H_3}O]^ + }{[OH]^ - } = {10^{ - 14}}$
By taking log on both the side, we get the equation as
$\Rightarrow {\log _{10}}{[{H_3}O]^ + } + {\log _{10}}{[OH]^ - } = - 14$
This equation can also be written as
$\Rightarrow - {\log _{10}}{[{H_3}O]^ + } - {\log _{10}}{[OH]^ - } = + 14$
Since we know, $- {\log _{10}}{[{H_3}O]^ + } = pH$ and $- {\log _{10}}{[OH]^ - } = pOH$.
Putting those value in the above equation we get,
$\Rightarrow pH + pOH = 14$

Note:
The pOH scale and pH scale are similar. A basic solution has pOH value less than 7, the neutral solution has pOH value 7 while the acidic solution has pOH more than 7. pOH value is very convenient when we are dealing with hydroxide concentration.