Solving equilibrium problems for the dissociation of a weak acid (or base)

HA   <-->   H   +   A -



H +

A -


[HA] o




- x

+ x

+ x


[HA] o - x



solving for x,

The above approximation is reasonable, when the % ionization   ≤  5 %, which occurs at

that is, the above approximation is valid, when  K  <  0.0025  [HA] o 

An alternative condition (% error 0.05)

Multiply the numerator and denominator by 2, then cross-multiply, and rearrange


Square both sides of the inequality and rearrange


Square both sides of the inequality, followed by rearrangement and factoring-out [HA]o

K < 0.00953 [HA]o.


above content based on link

also, see link about not needing Q to solve equilibrium problem, where given inital concentration of reactants and products