Final answer:
To calculate Ka and Kb for weak acids and bases, use their equilibrium concentrations and the relationship Ka × Kb = Kw. For an acid, use Ka = [H+][A-] / [HA]; for a base, use Kb = [BH+][OH-] / [B]. Calculate one from the other by dividing Kw by the known constant.
Step-by-step explanation:
To calculate the equilibrium constant for weak acids (Ka) and weak bases (Kb), we need the equilibrium concentrations of the acid, its conjugate base, or the base and its conjugate acid. The relationship between Ka of an acid and Kb of its conjugate base is given by Ka × Kb = Kw, where Kw is the ion product of water which is 1.0 × 10-14 at 25 °C.
For a weak acid, the equilibrium expression is Ka = [H+][A-] / [HA], where [H+] is the concentration of hydrogen ions, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid. For a weak base, the equilibrium expression is Kb = [BH+][OH-] / [B], where [BH+] is the concentration of the conjugate acid, [OH-] is the concentration of hydroxide ions, and [B] is the concentration of the base.
If you have the value of Ka and need to find Kb (or vice versa), you can rearrange the equation to solve for the unknown: Kb = Kw / Ka or Ka = Kw / Kb. When given specific equilibrium concentrations, you simply plug those values into the appropriate expression to calculate the Ka or Kb.