Final answer:
To simplify calculations for weak acids or bases, one can assume a small ionization percentage and a negligible change in initial concentration, unless the equilibrium constant is very large which would require using the quadratic equation.
Step-by-step explanation:
The two common assumptions that can simplify calculation of equilibrium concentrations in a weak acid or base are small ionization percentage and negligible change in initial concentration.
These assumptions are valid when the equilibrium constant (Ka for acids and Kb for bases) is sufficiently small, indicating that the acid or base ionizes only to a small extent. This means that the concentration of the weak acid or base remains essentially unchanged, and the concentration of ions formed is very small compared to the initial concentration of the weak acid or base.
However, for cases where the equilibrium constant is large (K ≥ 10³), indicating almost complete ionization, these assumptions are not valid. In such scenarios, you may need to use the quadratic equation to solve for equilibrium concentrations to account for significant changes in initial concentration.