Calculating pH of solutions?

When is self-ionisation of water taken into account when calculating pH?

• Sometimes, assuming the pH of the acid in water is simply the concentration of H+(aq) ions given out when the acid dissociates (into H+(aq) ions and its conjugate base) does not give accurate answers. Why? Also, why do we have to take the self-ionisation of water into account when very small amounts of strong acid are added to water? Is the same true of bases (alkalis, in this case)? Why/Why not? Also, the Wikipedia article on pH says that the ionisation equilibrium of water has to be taken into account when dealing with calculating the pH of highly concentrated basic (alkaline, in this case) solutions. Why? And lastly, why does self-ionisation of water have/not have to be taken into account when the acidic or basic (alkaline, in this case) solution is concentrated? (Above which molar concentration of H+(aq) ions does self-ionisation have/not have to be taken into account?)

• Answer:

  The law of logarithms comes into play here. We're dealing with equilibrium between all kinds of different moieties: dissociation constants of acids, base constants, and the self-dissociation of water. If you want to be 1% accurate in calculations, you can disregard anything that contributes less than 1% to the calculation.  Now, since we are working in logarithms, that means that anything that is more than 2 units away from where your calculations take place is "irrelevant". So if we're talking a solution of 1M acid, the self-dissociation of water which contributes [math]10^{-7}[/math]M can be disregarded. But for a 0,00001 M solution of a strong acid, you need to take it into account. The one "strange" exception you mention in your question is that the water constant is needed to calculate the pH of the solution of a strong base, but this is trickery.... Imagine a 1M solution of sodium hydroxide. This will have 1M hydroxide. So how much H+ is in equilibrium with that? To calculate this, we use the rule that pH+pOH = 14, which is a different way to write the water self dissociation constant.