Calculating K_a from pH

The reaction quotient expression used to calculate the acidity constant K_a is defined by reaction of the acid with water.

acid + H₂O conjugate base + H₃O⁺
 

Ka =	[H3O+][conjugate base]
	[acid]
reaction quotient

For any acid-base conjugate pair, irrespective of the initial acid and conjugate base concentrations, [acid], [conjugate base] and [H₃O⁺] combine to give the same number.
 

reactant	product 1	product 2
initial (before reaction)
c(reactant)	c(product 1)	c(product 2)
change (due to reaction)
– change	+ change	+ change
equilibrium
c(reac) – change	c(pro1) + change	c(pro2) + change

 

• known initial concentrations.
• the pH (can calculate [H₃O⁺]).
• reaction to reach equilibrium.
  If pH < 7, reaction is:
  weak acid + H₂O conjugate base + H₃O⁺
  If pH > 7, reaction is:
  weak base + H₂O  conjugate acid + OH^–
   
  • The change in concentration of one component is calculated from the initial and equilibrium concentrations.
  • The magnitude of the change in other components is the same if all coefficients in the balanced equation for the reaction occurring to reach equilibrium are 1.
  • Changes are positive if the species is a product in the reaction to reach equilibrium.
  • Changes are negative if the species is a reactant in the reaction to reach equilibrium.
     
• Equilibrium concentrations = initial + change (change = equilibrium – initial).