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

HA   <-->   H ⁺   +   A ^-

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

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Square both sides of the inequality and rearrange

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

K < 0.00953 [HA]_o.

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