I'm trying to take your description literally, and this is what I come up with:

ListPlot[{Reverse[dataPairs1, 2], Reverse[dataPairs2, 2]}, PlotRange -> {{0, 20}, {0, 14}}]

Based on how that looks, I'm guessing that I misinterpreted something. But maybe there is enough there for you to fiddle with until you get what you want.

As far as I know, Plot will always be arranged with the independent variable on the horizontal axis (but I honestly wouldn't be surprised if I were wrong and there is some option that affected this). So, you either need to find the inverse function or use your function to generate a list of points that you can deal with like we already did with your dataPairs1 example.

For completeness, I'll mention that you might be able to extract the data from the underlying Graphics expression that Plot produces. You could manipuate that raw data and create a new plot. But this would be a desperate last resort.

I have checked the documentation but I am still not clear why ",2" is needed in Reverse[dataPairs1,2] I know it means reverse the elements at level 2 but what is level 2 ?

Also, in the same document I have

Plot[Vb[pH, Ca, Cb, pKa, pKb, Kw, Va], {pH, 2.9, 12.5}]

but again the axes are the "wrong" way round. Vb comes from

  Vb[pH_, Ca_, Cb_, pKa_, pKb_, Kw_, Va_] := 
   Va*((Ca/(1 + H[pH]/Ka[pKa])) - H[pH] + 
       Kw/H[pH])/((Cb/(1 + Kw/(H[pH]*Kb[pKb]))) + H[pH] - Kw/H[pH])

Is this enough or should I attach my document? Thank you.

Plot will always be arranged with the independent variable on the horizontal axis Blockquote

I suspected as much. Finding the inverse function is what I am effectively doing in a second document. The first and simpler document derives Vb from pH (i.e. input pH values, output Vb values). The second document does the opposite. I'll stick with generating a list of points ...

Life is too short for me even to consider your last suggestion - that would indeed be a desperate last resort.

Thanks again!