[Vinegarman]

The pKa of vinegar is 4.76. If I know the ph of the vinegar, what would be the formula for determining the percentage acid base on the relationship between ph, pKa and concentration? Can you show the formula so that I only need to plug in the ph?

I am not a chemistry student and I have not done these kinds of calculations. I am searching for a convenient way for farmers in developing countries to quickly approximate the strength of vinegar. The final test would be done in a lab but I need a way for them to test vinegar other than titration because titration can seem more like witchcraft than science to the uninitiated :-).

[Paul Martin]

If pKa=4.76, then Ka=1.74×10−5
Then approximating that Ka can be written in terms of concentration rather than the true definition which is in terms of activities:
Ka=1.74×10−5M=[A−][H+][HA]=[H+]2c−[H+]
1.74×10−5M=[H+]2c−[H+]
where c is the molar concentration of the vinegar
If you want pH explicitly in the equation, then approximating pH = -log[H+], then:
1.74×10−5M=(10−pHM)2c−(10−pHM)
So, for example if pH is 3, 10−3 is 0.001, so
1.74×10−5=10−6Mc−(10−3M)
1.74×10−5c−1.74×10−8M=10−6M
1.74×10−5c=1.02×10−6M
c=0.059M