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Introduction
Strong acids and bases dissociate completely in an aqueous solution and release H⁺ and OH⁻, respectively. Therefore, we can base their pH directly off of the concentration of the acid/base dissolved.
Weak acids and bases do not dissociate completely. Therefore, we cannot solve for the pH of an aqueous solution based solely off of the molarity of the acid/base dissolved. Instead, we can use equilibrium expressions to help the process.
Required data to solve Acid/Base Equilibria:
Equilibrium Constant (Ka or Kb)
Molarity of Acid/Base (M)
Weak Acids
Weak acids have a lower equilibrium constant, which mean that they dissociate less. To solve for the pH of a weak acid solution, we can use the equilibrium expression of Ka.
Acid Dissociation Constant:
H₂O (l) + HA (aq) ⇌ H₃O⁺ (aq) + A⁻ (aq)
Ka = [H₃O⁺][A⁻]/[HA]
The concentration of hydronium calculated can be placed into the formula -log[H₃O⁺] to calculate the pH.
Weak Bases
Weak bases generally react partially with water, accepting their protons while indirectly releasing OH⁻ as a byproduct.
Base Dissociation Constant:
H₂O (l) + B (aq) ⇌ HB⁺ (aq) + OH⁻ (aq)
Kb = [HB⁺][OH⁻]/[B]
The concentration of hydroxide calculated can be placed into the formula -log[OH⁻] to calculate the pOH.
Other Formulas to Help Find pH
pOH to pH Formula:
pH = 14 - pOH
Shortcut for Acid/Base Equilibria:
K = x²/I
K: Equilibrium Constant
x: Concentration of H₃O⁺ (acid) or OH⁻ (base).
I: Initial concentration of acid or base.
For weak acids and bases that dissociates into two entities.
Percent Dissociation Formula:
% = (x/I) × 100
%: Percent of acid or base dissociated.
x: Concentration of H₃O⁺ (acid) or OH⁻ (base).
I: Initial concentration of acid or base.
Kw Formula:
Kw = Ka × Kb
Also known as...
1.0×10⁻¹⁴ = Ka × Kb
pKa and pKb
The dissociation strength of an acid is logarithmically measured using pKa.
pKa = -log[Ka]
Ka: Acid Dissociation Constant
Lower pKa means that the acid dissociates more strongly.
The dissociation strength of a base is logarithmically measured using pKb.
pKb = -log[Kb]
Kb: Base Dissociation Constant
Lower pKb means that the base dissociates more strongly.
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