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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.)

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    $\begingroup$ doi.org/10.1007/s00897000426a $\endgroup$
    – andselisk
    Mar 16, 2021 at 13:01
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    $\begingroup$ 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. $\endgroup$
    – Ed V
    Mar 16, 2021 at 13:13
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    $\begingroup$ 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. $\endgroup$
    – Ed V
    Mar 16, 2021 at 14:06
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    $\begingroup$ @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? $\endgroup$
    – MariosA
    Mar 16, 2021 at 15:46
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    $\begingroup$ citeseerx.ist.psu.edu/viewdoc/… $\endgroup$
    – Buck Thorn
    Mar 17, 2021 at 9:03

1 Answer 1

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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

$$\mathrm{pH} = -\log\left(\frac{1-x}{2} + \frac{1}{2}\sqrt{(1 - x)^2 + 4\times10^{-14}}\right).$$

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    $\begingroup$ I want the volume to be a variable here. Suppose we have an unkown molarity weak acid we want to titrate with a strong base of known molarity. We gradually add the base solution to the acid solution. The volume is variable. $\endgroup$
    – MariosA
    Mar 16, 2021 at 21:04
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    $\begingroup$ @MariosA And that is already done in the equation I referenced in other comments: just zero out the second and third acid dissociation constants and the equation simplifies greatly. Then either use pH as the independent variable, computing base volumes as a function of pH (this is the very easy trick) or use base volume as the independent variable and compute pH as a function of base volume (a little harder, but we have computers now). $\endgroup$
    – Ed V
    Mar 16, 2021 at 21:11

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