Equilibria of Weak Acids, K_a

• What is a weak acid?
• Calculating K_a
• Calculating equilibrium concentraions in an aqueous solution of a weak acid

A weak acid is any acid that reacts with water (donates H⁺ ions) to a very small extent, usually less than 5 - 10%.  An aqueous solution of a weak acid in a state of equilibrium would consist mainly of the unionized form of the acid, and only a small amount of hydronium ions and of the anion (conjugate base) of the weak acid.  The equation representing the ionization of any weak acid, HA, and the equilibrium expression, K_a, are shown below.

Note: This expression, K_a, is based on the general form for K_c. The designation K_a is used to indicate that it is the equilibrium constant for the reaction of an acid with water.

Calculating K_a

To calculate the ionization constant, K_a, you need to know:

• the equation for the reaction of the acid with water
• the equilibrium expression, K_a, for the reaction
• the equilibrium concentration of each species (molarity or moles per liter) or have a means to obtain them

Example:  The pH of a 0.1000 M solution of acetylsalicylic acid (aspirin-"HAsp") was found to be 2.24.  Determine the value of K_a, the ionization constant for acetylsalicylic acid, K_a.  The formula for acetylsalicylic acid is CH₃CO₂C₆H₄COOH, but we use "HAsp" as an abbreviation.

• Write the equation for the equilibrium between aspirin and water.

  HAsp(aq) + H₂O(l)   H₃O⁺(aq) + Asp^-(aq)

• Write the equilibrium expression for the reaction.

  

• Convert the pH of the solution into the hydronium ion concentration.  This will be the equilibrium concentration of the hydronium ion.

  [H₃O⁺] = 10^-pH = 10^-2.24 = 0.0057 M

• Make an ICE chart to aid in identifying the variables.  The hydronium ion concentration in pure water is 1 x 10^-7 M which can be considred as being approximately zero.

  	HAsp(aq)	H3O+(aq)	Asp-(aq)
  Initial Concentration (M)	0.1000	~ 0	0
  Change in Concentration (M)	- 0.00575	+ 0.0057	+ 0.0057
  Equilibrium Concentration (M)	0.0943	0.0057	0.0057

  For explanation of the significance of the different colors click HERE.

• Substitute the equilibrium concentrations into the equilbrium expression and solve for K_a.

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Calculating the Equilibrium Concentrations in an Aqueous Solution of a Weak Acid

To calculate the equilibrium concentrations you need to know:

• The equation for the reaction of the acid with water.
• The equilibrium expression for the reaction and the value of the equilibrium constant, K_a.
• The initial concentration of the acid expressed in moles per liter.

• Make an ICE chart. Express the change in equilibrium concentrations for each species in terms of a variable "x".
• Substitute the expressions for the equilibrium concentration into the equilibrium expression and solve for "x".
• Calculate the equilibrium concentration for each species by substituting in value for "x" and solving.

• Write the equation for the reaction of the acid with water.

  HNO₂(aq) + H₂O(l)   H₃O⁺(aq) + NO₂^-(aq)

• Write the equilibrium expression for the reaction.

  

• Make an ICE chart to aid in the solution of the problem.  Let "x" represents the change in concentration of H₃O⁺ and NO₂^-.

  	HNO2(aq)	H3O+(aq)	NO2-(aq)
  Initial Concentraion (M)	0.1000	~ 0	0
  Change in Concentration (M)	- x	+ x	+ x
  Equilibrium Concentration (M)	0.1000 - x	0 + x	0 + x

  For explanation of the significance of the different colors click HERE.

• Substitute the expressions for the equilibrium concentration into the equilibrium expression and solve for "x".

  

  Solved using method of approximations or the quadratic equation.

• Calculate the equilibrium concentration for each species.

  [H₃O⁺] = x = 7.4 x 10^-3M

  [NO₂^-] = x = 7.4 x 10^-3M

  [HNO₂] = 0.1000 - x = 0.0926 M

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