# Titration curve equation/function

How can I create a graph of a titration curve (acid-base, strong or weak, not something specific), with an equation or a function. In other words, what is the equation that describes such a curve that could be used in graphing software to recreate the curve without actually needing any experimental values? Also, if they exist, what are the parameters of the function (Molarity? Volume? Etc.)

• doi.org/10.1007/s00897000426a Mar 16, 2021 at 13:01
• This has essentially been done in a number of good answers at this site. Among other ways I do this, I use the equations in the spreadsheet screenshots in this answer: chemistry.stackexchange.com/a/136203/79678.
– Ed V
Mar 16, 2021 at 13:13
• Or try Tom O’Haver’s free Excel or OpenOffice titration curve software: terpconnect.umd.edu/~toh/models/TitrationDemo.html. There is a lot of stuff at his website, so maybe look around there. And, of course, there are books, other free pH calculation software, etc.
– Ed V
Mar 16, 2021 at 14:06
• @EdV This is for excel, I'll try it out but I prefer a mathematical function rather than a spreadseet, so that I can use it anywhere. Except if there's a way to extract the function from excel? Mar 16, 2021 at 15:46
• citeseerx.ist.psu.edu/viewdoc/… Mar 17, 2021 at 9:03

If $$\pu{1 l}$$ of $$\pu{1 M}$$ $$\ce{HCl}$$ is gradually neutralized by adding $$x\,\pu{mol}$$ $$\ce{NaOH}$$ without change in volume, the $$\mathrm{pH}$$ of the obtained solution is given by
$$\mathrm{pH} = -\log\left(\frac{1-x}{2} + \frac{1}{2}\sqrt{(1 - x)^2 + 4\times10^{-14}}\right).$$