Buffer

Calculates the pH of mixtures of buffers.

Description

This program calculates the final pH of an aqueous solution containing any number of buffers or other chemicals. For each buffer or chemical, the required input data is:

• name of chemicals
• pKa
• concentration (in molar, M)
• volume (in litres, L)

Executing program

• In main.py, create a dictionary for each chemical solution you wish to mix together. (See below for how to format the data in the dictionary.)
• Add each chemical dictionary to a chemical list.
• Put chemical list into search function to calculate the pH of the mixture. Set printer=1 to print the result.
• Run main.py

Run example1.py to see a demonstration of the pH calculation for a phosphate buffer being mixed with hydrochloric acid.

Run example2.py to see a demonstration of plotting the pH of the titration of 1M H₃PO₄ with 1M NaOH.

Formatting chemical dictionary

• "species_names" (list[str]) contains names for the conjugate acids and bases in a series of deprotonations.
• "pKa" (list[float]) contains literature pKa values for each deprotonation step.
• "initial_conc" (list[float]) contains concentrations (in molar, M) for each chemical in "species_names".
• "volume" (float) contains the total volume of solution (in litres, L).
• "volume_list" (list[float]) contains the volume (in litres, L) of each chemical in "species_names".
• use "volume" or "volume_list" but not both. Leave the unused one as None.

For example, to create 1.5L of phosphate buffer containing 0.1M H₂PO₄^- and 0.4M HPO₄^2-, the required dictionary is:

phosphoric_dict1 =
{"species_names": ["H3PO4", "H2PO4 -", "HPO4 2-", "PO4 3-"],
"pKa": [2.15, 6.86, 12.32], # literature values
"initial_conc": [0, 0.1, 0.4, 0],
"volume": 1.5,
"volume_list": None}

Note that even though only H₂PO₄^- and HPO₄^2- are present in the initial solution, all 4 protonation states of phosphoric acid must be listed since they are connected by the following equilibrium equations:
H₃PO₄ <---> H₂PO₄^- + H⁺, pK_a = 2.15
H₂PO₄^- <---> HPO₄^2- + H⁺, pK_a = 6.86
HPO₄^2- <---> PO₄^3- + H⁺, pK_a = 12.32

"species_names" must contain all protonation states of the chemical, ordered from most protonated on the left (acidic) to least protonated on the right (basic). If there are n protonation states, "species_names" will be a list of length n.

"pKa" must contain the literature pKa values of each successive deprotonation equation, with the lowest value on the left and highest value on the right. "pKa" will contain a list of length n - 1.

"initial_conc" contains a list of the concentrations (in molar, M) of each chemical specified in "species_names" in order.

"volume" is the total volume of solution (in litres, L).
Alternatively, you can specify "volume_list" which is a list (of length n) of the volumes (in litres, L) of each chemical in "species_names" at the concentration specified in "initial_conc".
If specifying "volume", leave "volume_list" as None.
If specifying "volume_list", leave "volume" as None.

For example, mixing 0.5L of 0.3M H₂PO₄^- with 1.0L of 0.6M HPO₄^2- would be represented by the following dictionary.
phosphoric_dict2 =
{"species_names": ["H3PO4", "H2PO4 -", "HPO4 2-", "PO4 3-"],
"pKa": [2.15, 6.86, 12.32], # literature values
"initial_conc": [0, 0.3, 0.6, 0],
"volume": None,
"volume_list": [0, 0.5, 1.0, 0]}

phosphoric_dict2 is equivalent to phosphoric_dict1, since:

• the total volume is the same: 0.5L + 1.0L = 1.5L
• the concentration of H₂PO₄^- is 0.3M * 0.5L / 1.5L = 0.1M
• the concentration of HPO₄^2- is 0.6M * 1.0L / 1.5L = 0.4M

Further notes

Calculations of pH by this program do not take into account the effects of ionic strength, nor does it account for differences between activity and concentration.

Authors

Ethan Watkins

License

This project is licensed under the MIT License - see the LICENSE.txt file for details

Acknowledgements

"Quest Calculate™ Phosphate Buffer (pH 5.8 to 7.4) Preparation and Recipe." AAT Bioquest, Inc., 29 Mar. 2022, https://www.aatbio.com/resources/buffer-preparations-and-recipes/phosphate-buffer-ph-5-8-to-7-4.