How do I calculate ph using Ka1 Ka2 ka3 and, concentration in excel formula please?

Hello All

I am trying to create 2 formulas in excel
First formula, to use the concentration of Triprotic acid (H3PO4) to determine the pH (Using the ka1, ka2, ka3 and the concentration)

Example for H3PO4 with a concentration 0.0010035, Wolfram Alpha, says it has a pH of 3.05 but it is missing the 3rd decimal point. https://www.wolframalpha.com/widget/...=pH+Calculator
While Sensorex says it has a pH of 3.03 again missing the third decimal point. https://sensorex.com/ph-calculator/
I need it accurate it to a pH of +/- .005 for the calculations that I am doing

Second formula to do the reverse, to be able to use the pH of Triprotic acid (H3PO4) to determine the concentration (Using the ka1, ka2, ka3 and the pH.)

I know that for H3PO4, it has a
ka1 of =7.1*10^-3 Equates to a pH of =-LOG(7.1*10^-3) 2.148741651
ka2 of =6.3*10^-8 Equates to a pH of =-LOG(6.3*10^-8) 7.200659451
ka3 of =4.5*10^-13 Equates to a pH of =-LOG(4.5*10^-13) 12.34678749

Lets say that the pH of the solution is 3.05

I have tried to do this without using the pka values and got a variation of up to .12 which is way to great. I have NO Clue how to do with the pka values.

Please help Thank you

Brad

The infamous triprotic phosphoric acid problem. I recall trying to do this at least 4 times as an undergrad (in class lecture, on the homework assignment, on the unit test, and on the final exam), and not once getting it exactly right. That was 20+ years ago, and it still haunts me.

The problem should boil down to finding the three equations that describe the three equilibria (plus any material balance equations that might enter into the problem) and simultaneously solve those three equations. I see three broad parts to solving this problem:
1) The Chemistry part -- where we use what we know about chemistry to help us understand and formulate the equations that describe the various equilibria present in the solution. We have a couple of chemists on the forum who may be able to help with this part of the problem.
1a) The values you list as pKa values look more like Ka values to me. You might review the difference between Ka and pKa and make sure you are using them correctly.
1b) If I were to seriously tackle this problem, I would need to start with something like this: http://barbara.cm.utexas.edu/courses...roticacids.pdf to refresh my memory around the equilibria involved and the equations used to describe those equilibria.
2) The Math part -- where we analyze the equations from part 1 and come up with available strategies for solving those equations. We have a few good mathematicians who can help with this part.
3) The Programming (in Excel) part -- where we take the algorithms identified in part 2 and program them into Excel. As an Excel forum, naturally this is our strength. As this part depends a lot on what comes out of parts 1 and 2, I find that it is difficult to tackle the programming part until the chemistry and math parts are well understood.
3a) You mention the need to be able to identify knowns and unkowns and have the spreadsheet be able to "branch out" according to what is given in the problem statement. Are you required to automate this step in a single spreadsheet, or can you have different spreadsheets for the different possible scenarios and leave it up to you (or the user) to decide which spreadsheet to use?

As this looks like a common student's homework problem, you will forgive me if I don't do the work for you. However, if you will help us understand the parts you understand and ask narrow, specific questions about the specific parts/steps that you are having trouble with, we will help as best we can.