Why should we not add the H+ ion conc coming from water before calculating pH of acidic/basic solution?

For eg:
If we are calculating pH of the soln of a strong acid, we shall do this:
pH= - log [H+]


Where H+ is the concentration coming from that acid.


Why shall we not add to this concentration, the H+ ions coming from water itself (By the autoionization of water) before calculating the pH?


Does water not ionize in presence of the acid/base?


Thank you.




Pure water is very weakly dissociated, meaning that the amount of H+ and OH- is very small. If we look at the autoprotolysis equilibrium of water


$$\ce{H2O <=> H+ + OH-}$$


and its autoprotolysis constant at 25 °C


$$\ce{K\_w = [H+][OH-] = 1.01\times10^{-14}}$$


According to the equation above we know that the H+ and OH- are the same, so we can easily calculate that the concentration of H+ is around $\ce{1.005\times10^{-7}}$ mol/L


Now let's assume you add a small amount of a strong acid, such as HCl, so that the concentration of this acid solution is 0.001 mol/L. If we assume a complete dissociation of HCl according to the following equation


$$\ce{HCl -> H+ + Cl-}$$


we know that the concentrations of H+ and Cl- ions are the same, and equal to 0.001 or $\ce{1.0\times10^{-3}}$ mol/L. Thus, several orders of magnitude higher than the amount of H+ ions coming from water.


So when calculating the pH we can use only the concentration of H+ from HCl dissociation, where $\ce{pH = -log\_{10}(1.0\times10^{-3}) = 3}$. Or you can sum up the concentration of H+ coming from HCl and $\ce{H2O}$, where $\ce{pH = -log\_{10}(1.0\times10^{-3} + 1.005\times10^{-7}}) \approx 3$ or more specifically 2.99996. But of course, this amount of decimal numbers makes no sense.


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