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# Short Cut Method to Calculating pH of Polyprotic Acid?

I am doing the following question:

Calculate the pH of a $$4.00\ \mathrm{mol\ L^{-1}}$$ solution of citric acid. $$\mathrm{pK_{a1}} = 3.09~~~~~ \mathrm{pK_{a2}} = 4.75~~~~~ \mathrm{pK_{a3}} = 6.40$$

Usually for polyprotic acids, we can assume that the second, third and other dissociations of $$\ce{H+}$$ ions are negligible when compared to the first dissociation. However I believe that this is only valid when the pKa values are separated by around 4. So for citric acid, this would be an invalid assumption as the pKa values are pretty close to each other.

Now, I can find the pH of the solution by doing the long way by first finding the amount of $$\ce{H+}$$ ions formed by the first dissociation, then using that to find the amount of $$\ce{H+}$$ ions formed by the second dissociation and so on.

However the room that they have given for this question is pretty small and has only has enough room for a couple of lines of working out and I definitely wouldn't be able to fit all my working out in that box.

So am I missing some short cut method to finding the pH in cases like this, or is the above assumption that I have outline at the start still correct for citric acid?