Equilibria of Weak Bases, K_b

• What is a weak base?
• Calculating K_b
• Calculating equilibrium concentraions in an aqueous solution of a weak base

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

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

Calculating K_b

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

• the equation for the reaction of the base with water
• the equilibrium expression, K_b, 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 aniline solution was found to be 8.79.  Determine the value of  K_b, the ionization constant for aniline.  The formula for aniline is C₆H₅NH₂.

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

  C₆H₅NH₂(aq) + H₂O(l)   C₆H₅NH₃⁺(aq) + OH^-(aq)

• Write the equilibrium expression for the reaction.

  

• Convert the pH of the solution into pOH, and then into the hydroxide ion concentration.  This will be the equilibrium concentration of the hydroxide ion.

  pOH = 14 - pH = 14 - 8.79 = 5.21

  [OH^-] = 10^-pOH = 10^-5.21 = 6.17 x 10^-6 M

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

  	C6H5NH2(aq)	C6H5NH3+(aq)	OH-(aq)
  Initial Concentration (M)	0.1000	0	~ 0
  Change in Concentration (M)	- 6.17 x 10-6	+ 6.17 x 10-6	+ 6.17 x 10-6
  Equilibrium Concentration (M)	~ 0.1000	6.17 x 10-6	6.17 x 10-6

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

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

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

To calculate the equilibrium concentrations you need to know:

• The equation for the reaction of the base with water.
• The equilibrium expression for the reaction and the value of the equilibrium constant, K_b.
• The initial concentration of the base 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 the value for "x" and solving.

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

  NH₃(aq) + H₂O(l)   NH₄⁺(aq) + OH^-(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 the concentration of the NH₄⁺ and OH^-.

  	NH3(aq)	NH4+(aq)	OH-(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.

  [NH₄⁺] = x = 1.3 x 10^-3 M

  [OH^-] = x = 1.3 x 10^-3 M

  [NH₃] = 0.1000 - x = 0.0987 M

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