How to Calculate Hydronium Ion Concentration

I know that I must know the concentration of hydronium ions in an aqeous solution to be able to calculate the pH. How do I calculate the H30+ concentration?

If you have a strong acid (one that ionises completely) like HCl you write the equation. HCl(aq) + H2O(l)----> H3O+(aq) + Cl-(aq). Each mole of HCl makes 1 mole of H3O+, so if the starting [HCl] = 0.1M, [H3O+] will also be 0.1M and pH = -log[H3O+] = 1. If the acid is strong but diprotic like H2SO4, you will get 2 x H3O+ ions per unit of H2SO4 eg H2SO4 + 2H2O(l) ----> 2H3O+(aq) + SO42-(aq) ( some books show this ionising completely in two stages but you get the same overall reaction. If the starting [H2SO4] = 0.02M, then [H3O+] will be 0.04M and pH = 0.91.

With weak acids, like ethanoic acid, you will need an ICE table as the acid does not ionise completely. You will also need the Ka value. The ionisation is only partial and is an equilibrium (reversible arrows)

CH3COOH(aq) + H2O(l) <-----> CH3COO-(aq) + H3O+(aq). If you start with 0.1M acid you will have <0.1M H3O+ ions.

ICE TABLE  [CH3COOH(aq)] <--->[CH3COO-(aq)]  [H3O+]

Initial   0.1M  <---> 0 + 0

Change -w <---> +w   +w

Equilibrium [0.1-w] <---> w     w

If Ka for this acid is 1.5 x 10-3, the Ka = [w][w]/[0.1-w] = 1.5 x 10-3.

You then solve for w and this is the equilbrium [H3O+]. Plug this into pH expression