[fobbz]

In a lab, we used created buffer solutions using H2PO4^- and HCl.

Later we added a restoration solution that rose the pH back from 7.00 (modelling acidosis) to 7.45.

We have volumes on a graph for the amount of restoration volume added as well as the corresponding pH. Essentially I must create a chart, suggesting a real world scenario in which human blood volume is 100ml/kg. I am having a hard time understanding the math surrounding solving how much restoration volume must be added respective to the volumes we have captured.

Say, for example that to rise the pH from 7.00 to 7.10, 2.00mL of "restoration solution" was required. Note: we were not told what this solution was.

How much restoration solution would be required for a human of mass 50kg's pH to rise from 7.00 to 7.10? I believe that this is a simple calculation I however cannot work the math around it. They gave us a sample value of 7000mL at 50kg to raise from 7.00pH to 7.20pH.

[Babcock_Hall]

I am not sure of the answer to your question, but I see what looks like a mistake in your chemistry.  If you add HCl to H₂PO₄^-, you will create H₃PO₄.  That will buffer best near pH 2.  You may be thinking of HP0₄^2-.

[fobbz]

Well the HCl would react with the conjugate base of H₂PO₄^- which is HPO₄^2-. The solution was made using NaH₂PO₄^- and HCl.

I feel as if that is not pertaining to my question though as only maths is involved in calculating the volumes required, is it not?

[Babcock_Hall]

There are others here who are better with pH than I am, but I would like to make a few observations.  One, when adding a base to a buffer, the slope of pH versus volume of base is not constant.  Therefore, even if we know what volume of restoration solution changes the pH from 7.00 to 7.20, we cannot say that exactly half of that volume will produce a pH change from 7.00 to 7.10.  A linear approximation might be good enough for this problem, however.

Two, With respect to your last question, there is no HPO₄^2- in the solution as you described it.  That may not be relevant to the problem at hand, but I would urge you to think about it, anyway.

Three, by the rules of the forum you are required to show an attempt.  What was the result of your attempt at this calculation?  My suggestion is that you use units cancellation.  It sounds as if we are to assume that there is 100 mL of blood per kilogram of body mass.  Is that your understanding also?  Your first post is a bit ambiguous about which numbers refer to the number of milliters of blood versus milliliters of restoration solution.