Autoionization of Water

The autoionization of water describes when water reacts with water in a solution of water. This forms the basis of understanding aqueous acid base chemistry.



Do not suspect a chemical process occurs only when chemicals dissolves in water.



Despite what most people believe when they look at an ordinary glass of water, it does not peacefully sit in a state of tranquility. It exists in a state of dynamic equilibrium where water reacts with water to produce hydronium and hydroxide ions, Equation (1).



\Large{H_2O + H_2O \rightleftarrows H_3O^{+1} + HO^{-1}}               (1)


As a result, we assign the mass action expression in terms of concentration, which conforms to the ratio of products over reactants, (2).



\Large{K_{eq} = \frac{[H_3O^{+1}][HO^{-1}]}{[H_2O][H_2O]}}               (2)

Figure 1: Autoionization of water supports ions in solution with molecular water

Ka Water



In particular, all acids have an equilibrium constant, Ka. This expresses the ratio of dissociated ionized acid compared to the neutral molecular acid species (3).





\Large{K_a = \frac{[H^{+1}][A^{-1}]}{[HA]}}                             (3)



It follows by substitution, the acid dissociation constant for water  (4).





\Large{K_a = \frac{[H_3O^{+1}][HO^{-1}]}{[H_2O]}}             (4)





The ionization concentration of H30+1 and OH-1 has a value of 1.00 x 10-7  M for each one. The concentration of pure water in the liquid state has a value 55.6 M, (5).



\Large{K_a = \frac{[1 x 10^{-7} M][1 x 10^{-7}] M}{[55.6 M]} = 1.8 x 10^{-16}}              (5)

pKa Water




The pKa of any acid expresses the equilibrium constant in terms of the negative -log10:



\Large{pK_a = -log[K_a]}              (6)

\Large{pK_a = -log[1.8 x 10^{-16}] = 15.7}              (7)





Similarly, we write the ion dissociation constant for water. From earlier, the actual ion concentration of H3O+1 and HO-1 has a small value compared to the concentration of water, a little less than 2 parts per billion,  Equation (8).



\Large{K_a[H_2O] = [H_3O^{+1}][HO^{-1}] = K_w}             (8)



Substituting numerical values for variables,,  and calculating Kw (9):




\Large{1.8 x 10^{-16}[55.6 M] = [H_3O^{+1}][HO^{-1}] = 1.0 x 10^{-14}}             (9)





Like pKa, you find the value of pH  by finding minus the log of the ionized acid concentration [H3O+1], (10).





Sometimes students get confused over the relationship between H3O+1 and H+1. The way we write H+1 creates something of a fiction. In our depiction of the autoionization of H2O, H3O+1 makes a more accurate description. For all intents and purposes, the two ways of writing acid concentration mean the same thing: [H3O+1] = [H+1].




\Large{pH = -log[H_30^{+1}]}              (10)



As a result, when you plug the H3O+1 concentration into the pH equation, the pH for the autoionization of water takes the value of 7, (11).




\Large{pH = -log(1 x 10^{-7} = 7)}              (11)



What Neutral Means




In conclusion, sometimes students believe a neutral solution does not contain any acid or base. You have seen that pure water contains a concentration of 1 x 10-7 M H+1.  On the other hand, it also contains 1 x 10-7 M HO-1




The correct way to understand this: a neutral solution has an equal concentration of acid and base.

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