How do you calculate pH from acid dissociation constant?

1 Answer
Chuck W. · mrpauller.weebly.com · Jackie Shlecter
Mar 19, 2014

For a weak acid, set up the equilibrium expression for dissociation to ions in solution, then solve this equation for the hydronium ion concentration. The pH can be calculated directly from #[H^+]#.

Example: The pH of 0.2 M acetic acid (HOAc)

#HOAC ↔ H^+ + OAc^-#
#K_a = 1.8x10^(-5) = ([H^+][OAc^-])/([HOAC])#
If the acid is weak, then only a small concentration, #x#, will dissociate. We can rewrite the equation as
#K_a = 1.8x10^(-5) = ([H^+][OAc^-])/([HOAC])# = #(x^2)/(0.2-x)# & approximately; #x^2/0.2#
where we have ignored #x# in the denominator because it is a small number compared with 0.2. Solving this equation gives * See note below about what to do if you do not want to ignore this...
#x = (0.2 · 1.8x10^(-5))^(1/2)# = #1.9x10^(-3)# = #[H^+]#
pH = #-log([H^+])# = 2.72

NOTE: If you don't simpify 0.2-x = 0.2, you need to use the quadratic equation to solve for the pH. Here is a video which discusses how to do this.

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