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Calculating Ka and Kb

Discusses methods of calculating ionization constants.

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Calculating Ka and Kb

Arnold Beckman created the first pH meter

Credit: User:Daderot/Wikimedia Commons
Source: http://commons.wikimedia.org/wiki/File:Beckman_Institute_-_UIUC_-_DSC09175.JPG
License: CC BY-NC 3.0

Who invented the pH meter?

The pH meter was invented because Florida orange growers needed a way to test the acidity of their fruit. The first meter was invented by Arnold Beckman, who went on to form Beckman Instruments. Beckman’s business was very successful and he used much of his fortune to fund science education and research. The Beckman family donated $40 million to build the Beckman Institute at the University of Illinois, shown above.

Calculating Ka and Kb

The numerical value of  Ka or  Kb can be determined from an experiment. A solution of known concentration is prepared and its pH is measured with an instrument called a pH meter .

A pH meter can be used for rapid, accurate determinations of pH

Credit: User:Datamax/Wikimedia Commons
Source: http://commons.wikimedia.org/wiki/File:PH_Meter.jpg
License: CC BY-NC 3.0

A pH meter is a laboratory device that provides quick, accurate measurements of the pH of solutions. [Figure2]

Sample Problem: Calculation of an Acid Ionization Constant

A 0.500 M solution of formic acid is prepared and its pH is measured to be 2.04. Determine the  Ka for formic acid.

Step 1: List the known values and plan the problem.

Known

  • initial [HCOOH] = 0.500 M
  • pH = 2.04

Unknown

  • Ka= ?

First, the pH is used to calculate the [H + ] at equilibrium. An ICE table is set up in order to determine the concentrations of HCOOH and HCOO - at equilibrium. All concentrations are then substituted into the  Ka expression and the  Ka value is calculated.

Step 2: Solve.

[H+]=10pH=102.04=9.12×103 M

Since each formic acid molecule that ionizes yields one H + ion and one formate ion (HCOO - ), the concentrations of H + and HCOO - are equal at equilibrium. We assume that the initial concentrations of each ion are zero, resulting in the following ICE table.

Concentrations [HCOOH] [H + ] [HCOO ]
Initial 0.500 0 0
Change -9.12 × 10 -3 +9.12 × 10 -3 +9.12 × 10 -3
Equilibrium 0.491 9.12 × 10 -3 9.12 × 10 -3

Now substituting into the  Ka expression gives:

Ka=[H+][HCOO][HCOOH]=(9.12×103)(9.12×103)0.491=1.7×104

Step 3: Think about your result .

The value of  Ka is consistent with that of a weak acid. Two significant figures are appropriate for the answer, since there are two digits after the decimal point in the reported pH.

Similar steps can be taken to determine the  Kb of a base. For example, a 0.750 M solution of the weak base ethylamine (C 2 H 5 NH 2 ) has a pH of 12.31.

C2H5NH2+H2OC2H5NH+3+OH

Since one of the products of the ionization reaction is the hydroxide ion, we need to first find the [OH ] at equilibrium. The pOH is 14 - 12.31 = 1.69. The [OH ] is then found from 10 -1.69  = 2.04 × 10 -2  M. The ICE table is then set up as shown below.

Concentrations [C 2 H 5 NH 2 ] [C 2 H 5 NH 3 + ] [OH ]
Initial 0.750 0 0
Change -2.04 × 10 -2 +2.04 × 10 -2 +2.04 × 10 -2
Equilibrium 0.730 2.04 × 10 -2 2.04 × 10 -2

Substituting into the  Kb expression yields the  Kb for ethylamine.

Kb=[C2H5NH+3][OH][C2H5NH2]=(2.04×102)(2.04×102)0.730=5.7×104

Summary

  • Calculations of  Ka and  Kb are described.

Practice

Questions

Read the material at the link below and answer the following questions:

http://www.ausetute.com.au/kb.html

  1. What does an Arrhenius base dissociate to?
  2. What does a Brønsted-Lowry base form in water?
  3. How is percent ionization determined?

Review

Questions

  1. What approach is used for calculation of ionization constants?
  2. What initial assumptions are made?
  3. What equilibrium assumptions are made?

Image Attributions

  1. [1]^ Credit: User:Daderot/Wikimedia Commons; Source: http://commons.wikimedia.org/wiki/File:Beckman_Institute_-_UIUC_-_DSC09175.JPG; License: CC BY-NC 3.0
  2. [2]^ Credit: User:Datamax/Wikimedia Commons; Source: http://commons.wikimedia.org/wiki/File:PH_Meter.jpg; License: CC BY-NC 3.0

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