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### Theory:

How to calculate the $$pH$$ of a solution?
The $$pH$$ is the negative logarithm of the hydrogen ion concentration.

i.e, $$pH= -log_{10}[H^+]$$
Example:

Calculate the $$pH$$ of $$0.01$$ $$M$$ $$HNO_3$$.

Solution:

$$[H^+] = 0.01$$
$$pH = -log_{10}$$ $$[H^+]$$
$$pH = -log_{10}$$ $$[0.01]$$
$$pH = -log_{10}$$ $$[1\times10^{-2}]$$
$$pH = -(log_{10}·1 - 2\, log_{10}10)$$
$$pH = 0 + 2\times\,log_{10}\,10$$
$$pH = 0 + 2\times1 = 2$$
$$pH = 2$$
pOH
The $$pH$$ is related to the $$pOH$$ of an aqueous solution.
The $$pOH$$ is the negative logarithm of the hydroxyl ion concentration.

$$pOH= -log_{10}[OH^-]$$
Example:

The hydroxyl ion concentration of a solution is $$1\times10^{-9}$$ $$M$$. What is the $$pOH$$ of the
solution?

Solution:

$$pOH = -log_{10}[OH^-]$$
$$pOH = -log_{10}[1\times10^{-9}]$$
$$pOH = -(log_{10}\times1.0 + log_{10}\times10^{-9})$$
$$pOH = -(0 - 9\,log_{10}\,10)$$
$$pOH = -(0 - 9)$$
$$pOH = 9$$

Relationship between $$pH$$ and $$pOH$$:

At $$25°C$$, the $$pH$$ and $$pOH$$ of a water solution are related by the following equation:

$$pH + pOH = 14$$

It is possible to calculate the other value if the $$pH$$ or $$pOH$$ of a solution is known.

Example:

$$pOH$$ of a solution is $$11.76$$. What is the $$pH$$ of this solution?
$$pH = 14 - pOH$$

$$pH = 14 – 11.76 = 2.24$$
$$pH$$ indicates acidity or hydrogen ion concentration, whereas $$pOH$$ indicates alkalinity or hydroxide ion concentration.