Question

State the mathematical definitions of pH, pOH and pK are and give examples from your field of expertise (biology, health care, engineering etc.) where these are used and why they are useful.

Answer 1

pH = -log([H3O+])

where [H3O+] is the concnetration of Hydronium ions

i.e. the pH of sulfuric acid is pretty low, about 1, which is pretty corrosive.

pOH = -log([OH-])

where [OH-] is the concnetration of Hydroxide ions

The pOH of ammonium ions in solution (ammonia) is pretty low, making it pretty basic

pK = -log(K)

K is any equilibrium constant, will help to identify if the equilibrium is trong (low values of pK) or weak (high value of pK)

the pKa of acetic acid is 4.74, making it ideal for buffer solution in that range...

Why?

They are important so we can relate with "normal" numbers and avoid 10^-14, 10^-32, etc... notation is pretty useful when comparing stron/weak acids/bases