T-Builder
Allows the user to plot any polyprotic or polyfunctional titration curve.
Run the executable to open the GUI.
Enter the data as indicated into the data entry area of the GUI. Click "Save Titration Data" or "Save Bjerrum Data" to save the data plotted above to a CSV file.
Features
- Plot Titration curves and Relative Species Plots
- Arbitrarily functional analyte
- Arbitrarily functional titrant
- Calculate Equivalence Points
- Calculate Buffer points. Where pH = pKa or pKb
- View Derivatives of plots
- Save all generated data to a csv
Citric acid titrated with KOH:
Species of Citric acid as pH increases:
TODO:
- Optional activity coefficients.
- Allow for preset compounds
- Saving and loading compounds
- Fitting and predicting titration curve composition
Math
Variables with the subscript 't' refer to the titrant. Variables with the subscript 'a' refer to the analyte.
Equations are a generalized form of the equations found in Quantitative Chemical Analysis 9th Ed. by Daniel C. Harris. (Ch. 11.10)
The alpha value for a species tells the relative predominance of the species at a given pH. The values range between 0 and 1. The larger the alpha value for the species, the higher concentration the species is in at that pH. The alpha value for a given species at a certain concentration of hydronium can be given by the equation:
$$\alphas = \frac{[H^+]^{i-s} * \Pi^s{j=0}{Kj}}{\Sigma{n=0}^i({[H^+]^{i-n} * \Pi_{j=0}^n{K_j}})}$$
where 's' is equal to the speciation index of the given species, ex. HCl -> Cl- have 's' of 1 and 2. The value of i is the degree of functionality for the analyte. $K_j$ represents the indexed dissociation constant for the analyte (For this notation, assume $K_0$ = 1). These values can be directly ported into a bjerrum plot or predominance zone diagram.
With the alpha values now calculated, another relationship can be utilized. The following equation can be obtained:
$$\phi = \frac{C_tV_t}{C_aVa} = \frac{\Sigma {n=0}^i (n\alpha_{an}) \pm (\frac{[H^+] - [OH^-]}{Ca})} {\Sigma{m=0}^j( n\alpha_{tm}) \mp (\frac{[H^+] - [OH^-]}{C_t})}$$
where $\phi$ is defined as the "Fraction of the way to the equivalence point", and i and j are the functionality of the analyte and titrant, respectively, $\alpha{an}$ represents the indexed alpha values of the analyte, and the similarly, $alpha{tm}$ represents the indexed alpha values of the titrant. The $\pm$ in the numerator is positive if the analyte is a base, and negative if the analyte is an acid. The opposite is true for the denominator, as indicated. $C_a$ and $V_a$ are the concentration and volume of the analyte. $C_t$ and $V_t$ are the concentration and volume for the titrant.
$\phi$ can be used to determine the volume of titrant required to reach a certain pH. Since all the values in the definition of $\phi$ are known, they can be solved to find $\phi$. Using $\phi$ and known values for the volume of analyte, and the concentration of both analyte and titrant, the volume of titrant can be calculated through re-aranging the previous equation to find:
$$V_t = \frac{\phi C_a V_a}{C_t}$$
This equation is then solved thousands of times to produce a plot of volumes to pH values. The volume of titrant is set as the x-axis, and the pH the y-axis, and a titration curve is born.