The buffer equation, which is derived in the later link is:
#log_10K_a=log_10[H_3O^+] + log_10{[[A^-]]/[[HA]]}#
Upon rearrangement:
#-log_10[H_3O^+] = -log_10K_a+ log_10{[[A^-]]/[[HA]]}#
And upon simplification:
#pH=pK_a+log_10{[[A^-]]/[[HA]]}#.
The #pH# could be neutral, or ACIDIC, or BASIC, depending on #pK_a#, or the proportions of acid or base used.
A buffer then acts to keep the #pH# tolerably close to the #pK_a# of the starting acid. If the buffer is composed of equal concentrations of acid and conjugate base, #pH=pK_a#; why?
Depending on the capacity of the buffer, addition of small quantities of #H_3O^+# or #HO^-# protonate the conjugate base or deprotonate the acid, such that the #pH# remains fairly close to a predetermined value. Biological systems (including our digestion and respiration processes) are extensively buffered.
See here for the derivation of the formula.
