Systemtic pH calculation package for Python.
Project description
pHcalc
pHcalc is a Python library for systematically calculating solution pH, distribution diagrams, and titration curves.
This package is Python 3.5 compatible with dependencies only on Numpy and Scipy. If you will be plotting the data, then there is an optional dependency as well.
Bug fixes, questions, and update requests are encouraged and can be filed at the GitHub repo.
Dependencies
Numpy >= 1.10
Scipy >= 0.17
Optional Packages
Matplotlib >= 1.5
Installation
pHcalc is only a single Python file, so installation is quite simple. After installation of the dependencies, the most recent version of pHcalc is available via pip, either from PyPI (stable) or the GitHub repo (most recent).
From PyPI:
$ pip install pHcalc
From the GitHub repo:
$ pip install git+https://github.com/rnelsonchem/pHcalc.git
Of course, the GitHub installation requires that you have installed Git on your computer.
Background
pHcalc calculates the pH of a complex system of potentially strong and weak acids and bases using a systematic equilibrium solution method. This method is described in detail in the Journal of Chemical Education and in this ChemWiki article, for example. (There is also another, older Pascal program called PHCALC, which uses matrix algebra to accomplish the same task. To the best of my knowledge, the source code for this program is no longer available.)
Basically, this method calculates the fractional distribution of a potentially polyprotic weak acid species at a given pH value. Multiplying this by the concentration of acid in solution provides the concentration of each acidic species in the system. The optimium pH for this system is found when charge balance is achieved, i.e. the concentrations of positively charged ions equals the charge for the negatively charged ions.
Using this methodology bases and strong acids can be described using neutral, charged species. These are ions that do not react with water, such as Na+ and Cl-. In this context, any Cl- in solution must be charged balanced with an appropriate amount of H3O+, which would define HCl in solution. Na+ must be offset by an equivalent amount of OH-, which defines a solution of NaOH. A 1:1 combination of Na+ and H2CO3 would describe a solution of NaHCO3.
Example Usage
pHcalc defines three classes - Acid, Neutral, and System - which are used in calculating the pH of the system. H3O+ and OH- are never input. The H3O+ concentration is adjusted internally, and OH- is calculated using KW.
>>> from pHcalc.pHcalc import Acid, Neutral, System
>>> import numpy as np
>>> import matplotlib.pyplot as plt # Optional for plotting belowpH of 0.01 M HCl
First of all, HCl completely dissociates in water to give equal amounts of H3O+ and Cl-, so all you need to define is Cl-.
>>> cl = Neutral(charge=-1, conc=0.01)
>>> system = System(cl)
>>> system.pHsolve()
>>> print(system.pH) # Should print 1.9999pH of 1e-8 M HCl
This is a notoriously tricky example for introductory chemistry students; however, pHcalc handles it nicely.
>>> cl = Neutral(charge=-1, conc=1e-8)
>>> system = System(cl)
>>> system.pHsolve()
>>> print(system.pH) # Should print 6.978295898 (NOT 8!)pH of 0.01 M NaOH
This example is very similar to our HCl example, except that our Neutral species must have a positive charge.
>>> na = Neutral(charge=1, conc=0.01)
>>> system = System(na)
>>> system.pHsolve()
>>> print(system.pH) # Should print 12.00000pH of 0.01 M HF
Here we will use an Acid object instance to define the weak acid HF, which has a Ka of 6.76e-4 and a pKa of 3.17. You can use either value when you create the Acid instance. When defining an Acid species, you must always define a charge keyword argument, which is the charge of the fully protonated species.
>>> hf = Acid(Ka=6.76e-4, charge=0, conc=0.01)
>>> # hf = Acid(pKa=3.17, charge=0, conc=0.01) will also work
>>> system = System(hf)
>>> system.pHsolve()
>>> print(system.pH) # Should print 2.6413261pH of 0.01 M NaF
This system consist of a 1:1 mixture of an HF Acid instance and a Na+ Neutral instance. The System can be instantiated with an arbitrary number of Acids and Neutral objects.
>>> hf = Acid(Ka=6.76e-4, charge=0, conc=0.01)
>>> na = Neutral(charge=1, conc=0.01)
>>> system = System(hf, na)
>>> system.pHsolve()
>>> print(system.pH) # Should print 7.5992233pH of 0.01 M H2CO3
The Ka and pKa attributes can also accept lists of values for polyprotic species.
>>> carbonic = Acid(pKa=[3.6, 10.32], charge=0, conc=0.01)
>>> system = System(carbonic)
>>> system.pHsolve()
>>> print(system.pH) # Should print 2.8343772pH of 0.01 M Alanine Zwitterion Form
Alanine has two pKa values, 2.35 and 9.69, but the fully protonated form is positively charged. In order to define the neutral zwitterion, the Acid object needs to be combined with a positively-charged Neutral species as well, which would represent one equivalent of NaOH.
>>> ala = Acid(pKa=[2.35, 9.69], charge=1, conc=0.01)
>>> na = Neutral(charge=1, conc=0.01)
>>> system = System(ala, na)
>>> system.pHsolve()
>>> print(system.pH) # Should print 6.0991569pH of 0.01 M (NH4)3PO4
This is equivalent to a 1:3 mixture of H3PO4 and NH4+, both of which are defined by Acid objects.
>>> phos = Acid(pKa=[2.148, 7.198, 12.319], charge=0, conc=0.01)
>>> nh4 = Acid(pKa=9.25, charge=1, conc=0.01*3)
>>> system = System(phos, nh4)
>>> system.pHsolve()
>>> print(system.pH) # Should print 8.95915298Distribution Diagrams
Acid objects also define a function called alpha, which calculates the fractional distribution of species at a given pH. This function can be used to create distribution diagrams for weak acid species. alpha takes a single argument, which is a single pH value or a Numpy array of values. For a single pH value, the function returns a Numpy array of fractional distributions ordered from most acid to least acidic species.
>>> phos = Acid(pKa=[2.148, 7.198, 12.319], charge=0, conc=0.01)
>>> phos.alpha(7.0)
array([ 8.6055e-06, 6.1204e-01, 3.8795e-01, 1.8611e-06])
>>> # This is H3PO4, H2PO4-, HPO4_2-, and HPO4_3-For a Numpy array, a 2D array of fractional distribution values is returned, where each row is a series of distributions for each given pH. The 2D returned array can be used to plot a distribution diagram.
>>> phos = Acid(pKa=[2.148, 7.198, 12.319], charge=0, conc=0.01)
>>> phs = np.linspace(0, 14, 1000)
>>> fracs = phos.alpha(phs)
>>> plt.plot(phs, fracs)
>>> plt.show()Titration Curves
Using a simple loop, we can also construct arbitrary titration curves as well. In this example, we will titrate H3PO4 with NaOH. The guess_est keyword argument for the System.pHsolve method forces the calculation of a best guess for starting the pH optimization algorithm. This may speed up the evaluation of the pH and can also be used if the minimizer throws an error during the pH calculation.
>>> na_concs = np.linspace(1e-8, 5.e-3, 500)
>>> phos = Acid(pKa=[2.148, 7.198, 12.375], charge=0, conc=1.e-3)
>>> phs = []
>>> for conc in Na_concs:
>>> na = Neutral(charge=1, conc=conc)
>>> system = System(phos, na)
>>> system.pHsolve(guess_est=True)
>>> phs.append(system.pH)
>>> plt.plot(na_concs, phs)
>>> plt.show()
