This protonated water ion is known as the hydronium ion (or hydroxonium ion, or hydrated proton). Another name for protonic acid is Bronsted acid.
pH SCALE
Chemists had devised a parameter pH to indicate the concentration of hydronium ion (and so the strength of the acid) in an aqueous solution. The the pH is defined as;
pH = - log10a({H3O}+)
where a, known as activity, is defined as the mole of hydronium ion per kilogram of solvent, per 1 mole of solvent per kilogram of solvent.
By dividing the molal concentration with 1 mole per kilogram of the solvent a is than a ratio, making the logarithm of a more rational. It is meaningless to log(concentration term).
The pH is taken as a measurement of the acidity of an aqueous solution. As a is a ratio, pH has no unit.
Example: For a solution of {H3O}+ with a molarity concentration of 0.01 mole per litre, the molality is taken to be the same the molarity since the density of water is 1 g ml‾� (assuming that the hydronium is not high enough to change the density). The activity will then be 0.01 M/(1 mole per litre) = 0.01. So;
pH = - log1010‾� = 2 Note: log1010x = x
Alternatively for a strong acids we can assume that it is fully dissociated.
WEAK ACIDS
Acids with Ka < 1, is considered a weak acid.
Let us repeated the above computation with a 0.100M of acetic acid (Ka = 1.8 x 10 ‾5). Accordingly a{H3O}+ = f x 0.100 M/M and a(acetic acid) = (1-f) x 0.100 M/M.
a({H3O}+) is computed to be 0.00133. So pH = - log10{0.00133} = 2.88
Alternatively since it is a weak acid we can assume that there is no dissociation. Then
a({H3O}+) x a({CH3COO}‾) = a({H3O}+)� = 1.8x10 -5 x 0.100 = 1.8x10 ‾6
Giving, a(H3O}+) = 1.34x10‾�, and pH = - log10{0.00134} = 2.87. This is close enough for industrial applications. Acetic acid is commonly known as vinegar.