# pH of Acids and Bases

Many properties of aqueous solutions depends on the concentration of H+ ions of the solutions and therefore there is a need to express these concentrations in simple terms. For this purpose we introduce the concept of pH.

pH = − log aH+ (Where aH+ is the activity of H+ ions).

Activity of H+ ions is the concentration of free H+ ions in a solution. By free, we mean those that are at a large distance from the other ion so as not to experience its pull. We can infer from this that in dilute solutions, the activity of an ion is same as its concentration since more number of solvent molecules would separate the two ions. For concentrated solutions the activity would be much less than the concentration itself.

Therefore, the earlier given expression of pH can be modified for dilute solutions as, pH = − log [H+]. This assumption can only be made when the solution is very much dilute, i.e, [H+] ≤ 1M. For higher concentration of H+ ions, one needs to calculate the activity experimentally and then calculate the pH.
Strong Acids Let us now see how to calculate the pH of a solution of a strong acid in water (it should be noted that pH calculations are only made for aqueous solutions). Let the strong acid be HCl. If we take 10−1M HCl, the [H+] would be 10−1 M, as HCl is a strong acid and would dissociate completely. Therefore the pH would be,

pH = −log 10−1 = 1

Concen. of HCl     pH
10−1M                1
10−2M                 2
10−3 M                3
10−4 M                4
10−5 M                5
10−6 M                6
10−7 M                7 (?)

We can see that for 10−7 M of HCl we have some hesitation in talking about the pH. This is because if we use our expression of pH, it works out to be 7 which is somehow associated with neutrality. We shall now explain how to calculate the pH of 10−7 M HCl. Before we do this we shall discuss the dissociation of water.

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