[jwosley]

Hi everybody,

This is my first time on the forum - looks like a great place to be!

I'm having some difficulty with a weak acid/strong base question that I've spent about 10 hours on so far with no success. I would be very grateful if you could point me in the right direction.

The question is:

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A company has (accidentally) spilled 1078 kg of phosphoric acid into a lake, making it very acidic. How much NaOH would you have to add to get the pH to 8.0.
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We are given that the Mol. Wt. H3PO4 = 98; Mol. Wt. NaOH = 40; pKs of phosphate = 2, 7 and 11.

My current attempt started by trying to work out the moles of H3PO4, which I was able to do. However, I got stuck because there is no concentration (since I have no volume of the lake). Now I may not even need this information, but I am at a loss as to how to proceed.

I've also been attempting to use the Henderson-Hasselbalch equation, in a rearranged manner, by specifying that the pH of the lake needs to be 8, then using the pK of H3PO4 (given as 2, 7 and 11), but I'm unsure as to which one to use or how to combine them. Further, it always comes back to the fact that the concentration is not known.

Any help in this would be greatly appreciated!

Thanks for your help,

J.

[fledarmus]

I have to agree with you - without knowing the volume of the lake, it isn't possible to know the concentration of H⁺ and therefore the pH. If the lake is large enough (and this volume you could calculate), 1078 kg of H₃PO₄ may not be enough to raise the pH to 8.

[Borek]

It is about using HH equation, and you don't need volume. Note that ratio of concentrations of acid and conjugate base is identical to ratio of number of moles - as volume cancels out:







You need to neutralize first proton completely and second partially.

[jwosley]

Wow, thanks very much. I hadn't twigged that the volume would cancel out. I can see now that it will.

I am still left pondering over what to do with the multiple pKa's. In the lake all six species will be present in dynamic equilibrium so how should i account for that in terms of pKa. I have read several articles online that suggest because the first ionisation of H3PO4 is the easiest i can discount the other pKa values. There will be so few molecules of HPO4-2 and PO4-3 that the effect their addition dissociated protons will make to the overall concentration [H+] will be negligible. 

The question does say that the lake becomes very acidic, do you think I can take that to mean pKa of 2 is the only relevant value?