The acid dissociation constant, or Ka, is a measure of the strength of an acid, i.e., how readily it donates a hydrogen ion or proton. The negative log of the Ka is the pKa. pKa values are often used because they are simpler to write than Ka values, which are typically so small they must be written using scientific notation. You can find the Ka using experimental data; if you're asked to calculate the pKa of acetic acid as part of a homework assignment for an entry-level chemistry class, however, you can follow the simple steps outlined below.
Write down the information you have to start with. A homework or quiz question in an entry-level chemistry class will typically give you the pH of the solution and the concentration of acetic acid in units of moles per liter.
Convert pH to hydrogen ion concentration using the following equation: [H+] or hydrogen ion concentration = 10 to the -pH. If the pH is 2, for example, the hydrogen ion concentration is 10 to the negative 2. Note that in chemistry, concentration of a substance in solution is often denoted by writing the formula of the substance in brackets.
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Write out the equilibrium constant equation for the dissociation constant. The equation is as follows: Ka = [acetate] [H+] / [acetic acid] , where [acetate] is the concentration of acetate anions, [acetic acid] is the concentration of acetic acid and [H+] is the concentration of hydrogen ions.
Make an assumption to solve the equation. Although the autoprotolysis of water contributes some small number of hydrogen ions, this amount is fairly negligible, so to make our calculation simpler we assume that all the hydrogen ions in the solution were donated by molecules of acetic acid. This implies that the concentration of acetate anions and the concentration of hydrogen ions are the same. Based on this logic we can also subtract the hydrogen ion concentration from the starting acetic acid concentration to find the acetic acid concentration at equilibrium.
Plug the acetate concentration, hydrogen ion concentration and acetic acid concentration into the equilibrium constant equation to find the Ka.
Take the negative log of the Ka to find the pKa and the answer for your homework problem.
Check your answer against the book. If your book doesn't list the pKa of acetic acid, the accepted value is 4.75.