Solving equilibrium problems for the dissociation of a weak acid (or base)
HA <> H ^{+ } + A^{  }

HA 
H ^{+} 
A^{ } 
[initial] 
[HA] _{o } 
0 
0 
[change] 
 x 
+ x 
+ x 
[equilibrium] 
[HA]_{ o } x 
x 
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 crossmultiply, and rearrange
.
Square both sides of the inequality and rearrange
.
Square both sides of the inequality, followed by rearrangement and factoringout [HA]_{o}
K < 0.00953 [HA]_{o}.
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above content based on link
also, see link about not needing Q to solve equilibrium problem, where given inital concentration of reactants and products