pH

The letters pH stand for "power of hydrogen".
pH of a solution is defined as the negative logarithm to base 10 of the hydrogen ion activity, a_H+.
pH is defined as the negative logarithm of hydrogen ion concentration.

$\mathrm{pH�}={\mathrm{-log}}_{10}{H}^{\mathrm{+}}$
$\mathrm{pH�}={\log }_{10}\frac{1}{H^{\mathrm{+}}}$
pOH can be defined as $\mathrm{pOH�}={\mathrm{-log}}_{10}{\mathrm{OH}}^{\mathrm{-}}$

pH Scale

The pH scale was introduced S.P.L. Sorenson.
pH scale is used to express the acidity of only dilute solutions.
The strength of an acid or base is measured on a scale called the pH scale, which goes from 0 to 14 in general usage.
A liquid with a pH of 7 is neutral.
A liquid with a pH lower than 7 is an acid.
A liquid with a pH higher than 7 is a base.
For a strong acid pH value is very low.
For a strong base pH value is very high.
Strong acids almost completely break apart in water to form H⁺ and A^- ions. This process is known as dissociation.
Because strong acids completely dissociate in water, the concentration of H⁺ solution is same as the concentration of the acid initially started with.
Weak acids are acids that only dissociate to a small degree in water.

If the aqueous solution of an acid is diluted with water, its pH value increases. $\mathrm{pH\; after\; dilution}=\mathrm{initial\; pH}+\log \frac{V_2}{V_1}$
where:
V₁ is the initial volume of the solution, V₂ is the volume of the solution after dilution.

If the aqueous solution of an base is diluted with water, its pH value decreases. $\mathrm{pH\; after\; dilution}=\mathrm{initial\; pH}-\log \frac{V_2}{V_1}$
where:
V₁ is the initial volume of the solution, V₂ is the volume of the solution after dilution.

If two strong acids or bases with different concentrations are mixed, $\mathrm{resultant\; normality\; of\; the\; mixture\; N}=\frac{N_1{V}_1+N_2{V}_2}{V_1+V_2}$

If two strong acids or bases with different concentrations are mixed, $\mathrm{resultant\; molarity\; of\; the\; mixture\; M}=\frac{M_1{V}_1+M_2{V}_2}{V_1+V_2}$

Neutralisation

If number of equivalents of acid is equal to the number of equivalents of base, the resulting solution will be neutral in nature $N_{\mathrm{A}}{V}_{\mathrm{A}}=N_{\mathrm{B}}{V}_{\mathrm{B}}$