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## Module to simulate titration of a weak acid or a weak base |
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## with a strong base or strong acid, respectively |
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## to prepare a buffer solution |
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## with widgets to allow interactive control in a Jupyter notebook |
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## Computations of pH during titration as described at: |
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## https://chem.libretexts.org/Bookshelves/Ancillary_Materials/Demos_Techniques_and_Experiments/General_Lab_Techniques/Titration/Titration_of_a_Weak_Base_with_a_Strong_Acid |
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## David P. Goldenberg, January 2021 |
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## goldenberg@biology.utah.edu |
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import numpy as np |
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from scipy.optimize import fsolve |
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import ipywidgets as widgets |
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from IPython.display import display, HTML |
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from IPython.display import display, clear_output, HTML, FileLink |
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from time import sleep |
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import threading |
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import random as rand |
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display(HTML("<style>div.output_scroll { height: 300ex; }</style>")) |
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#----------Functions for calculating pH under different circumstances--------------# |
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def OHfunc(OH,base_conc,pKa): |
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'''Function to be solved to calculate OH concentration |
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for untitrated base''' |
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Ka = 10.0**(-pKa) |
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K = 1e-14/Ka |
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return OH**2 + OH*K - base_conc*K |
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def pH_base(pKa,base_conc): |
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'''Calculates pH for untitrated base''' |
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OHconc =fsolve(OHfunc,1e-7,(base_conc,pKa)) |
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pH = float(-np.log10(1e-14/OHconc)) |
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return pH |
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def Hfunc(H,acid_conc,pKa): |
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'''Function to solve to calculate H concentration |
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from dissociation of conjugate acid''' |
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Ka = 10.0**(-pKa) |
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return H**2 + Ka*H - Ka*acid_conc |
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def pH_acid(pKa,acid_conc): |
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'''Calculates pH for untitrated acid''' |
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Hconc = fsolve(Hfunc,1e-7,(acid_conc,pKa)) |
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pH = -np.log10(Hconc) |
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return float(pH) |
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def pH_base_titr(pKa,base_moles,titr_moles): |
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'''Calculates pH when moles of added strong acid |
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are less than moles weak base''' |
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ba_ratio = (base_moles-titr_moles)/titr_moles |
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pH = pKa + np.log10(ba_ratio) |
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return pH |
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def pH_acid_titr(pKa,acid_moles,titr_moles): |
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'''Calculates pH when moles of added strong base |
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are less than moles weak acid''' |
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ba_ratio = titr_moles/(acid_moles-titr_moles) |
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pH = pKa + np.log10(ba_ratio) |
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return pH |
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def pH_post_eq_b(base_moles,titr_moles,volume): |
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'''Calculates pH when moles of added strong acid |
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are greater than moles weak base''' |
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Hconc = (titr_moles - base_moles)/volume |
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pH = -np.log10(Hconc) |
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return(pH) |
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def pH_post_eq_a(acid_moles,titr_moles,volume): |
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'''Calculates pH when moles of added strong base |
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are greater than moles weak acid''' |
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OHconc = (titr_moles - acid_moles)/volume |
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pH = np.log10(OHconc) + 14.0 |
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return(pH) |
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def pH_full_titr_b(pKa,base_moles,v_init,titr_moles,titr_vol): |
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'''Calculates pH over full titration of a weak base |
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with a strong acid''' |
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vol_tot = v_init + titr_vol |
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if titr_moles == 0: |
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base_conc = base_moles/v_init |
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return pH_base(pKa,base_conc) |
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elif 0 < titr_moles < base_moles: |
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return pH_base_titr(pKa,base_moles,titr_moles) |
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elif titr_moles == base_moles: |
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conc = base_moles/vol_tot |
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return pH_acid(pKa,conc) |
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else: |
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return pH_post_eq_b(base_moles,titr_moles,vol_tot) |
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def pH_full_titr_a(pKa,acid_moles,v_init,titr_moles,titr_vol): |
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'''Calculates pH over full titration of a weak acid |
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with a strong base''' |
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vol_tot = v_init + titr_vol |
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if titr_moles == 0: |
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acid_conc = acid_moles/v_init |
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return pH_acid(pKa,acid_conc) |
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elif 0 < titr_moles < acid_moles: |
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return pH_acid_titr(pKa,acid_moles,titr_moles) |
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elif titr_moles == acid_moles: |
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conc = acid_moles/vol_tot |
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return pH_base(pKa,conc) |
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else: |
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return pH_post_eq_a(acid_moles,titr_moles,vol_tot) |
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def pH_calc(buffer,pKa,buff_moles,v_init,titr_moles,titr_vol): |
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'''Calculates pH over full titration of either a weak acid |
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or a weak base''' |
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if buffer == 'Weak acid': |
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ph = pH_full_titr_a(pKa,buff_moles, |
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v_init,titr_moles,titr_vol) |
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elif buffer == 'Weak base': |
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ph = pH_full_titr_b(pKa,buff_moles, |
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v_init,titr_moles,titr_vol) |
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else: |
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ph = float('nan') |
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return ph |
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#------------Widgets-------------# |
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header_html = """ |
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<h2> Biology 3515/Chemistry 3515 |
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<br> |
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Biological Chemistry Laboratory |
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<br> |
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University of Utah </h2> |
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<h3> Spring 2021 </h3> |
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<h3> Experiment 1, Part B: Buffer Preparation</h3> |
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<p style="font-size:16px"> |
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This web page simulates a common laboratory protocol for preparing buffer solutions, in which a weak acid or base is titrated with a strong base or acid, respectively. |
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<br> |
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The top two rows of controls specify the starting parameters for the |
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titration: The buffer type (weak acid or weak base),the buffer |
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pK<sub>a</sub>, the number of moles of buffer and the initial solution |
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volume. The next row contains controls for specifying concentration |
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and volumes of individual titrant additions. |
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Titrant is added by clicking the green button. After each addition |
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the new pH is displayed, but it takes a little while to settle down! |
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The volumes of titrant are also updated. Click the orange button to |
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reset the titration. |
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<hr border-width:6px, color:black> |
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""" |
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style = {'description_width': 'initial'} |
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header = widgets.HTML( |
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value=header_html |
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) |
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footer = widgets.HTML( |
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value=''' |
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<hr border-width:6px, color:black> |
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David P. Goldenberg, January 2021<br> |
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<a href="mailto:goldenberg@biology.utah.edu" target="new">goldenberg@biology.utah.edu</a><br> |
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School of Biological Sciences, University of Utah<br> |
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Salt Lake City, Utah 84112<br> |
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<a href="https://goldenberg.biology.utah.edu/courses/biol3515/index.shtml" |
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target="new">https://goldenberg.biology.utah.edu/courses/biol3550.</a> |
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''') |
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buffer = widgets.Dropdown( |
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options=['Weak acid','Weak base'], |
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value='Weak acid', |
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description='Buffer type:', |
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style=style, |
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layout=widgets.Layout(width='200px',margin='0px 100px 15px 0px') |
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) |
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pK = widgets.FloatSlider( |
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value = 7.0, |
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min = 3.0, |
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max = 11.0, |
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step = 0.1, |
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description = 'Buffer pKa:', |
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orientation = 'horizontal', |
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readout=True, |
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readout_format='.1f', |
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style=style, |
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layout=widgets.Layout(width='300px',margin='0px 0px 15px 0px') |
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) |
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moles = widgets.FloatText( |
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value = 0.5, |
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min = 0.01, |
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max = 5.0, |
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step = 0.01, |
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description = 'Moles buffer:', |
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style=style, |
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layout=widgets.Layout(width='200px',margin='0px 100px 15px 0px') |
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) |
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init_vol = widgets.FloatText( |
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value = 0.5, |
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min = 0.01, |
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max = 5.0, |
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step = 0.01, |
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description = 'Initial vol. (L):', |
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style=style, |
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layout=widgets.Layout(width='200px',margin='0px 0px 15px 0px') |
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) |
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hrule = widgets.HTML( |
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value = '<hr border-width:6px, color:black>' |
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) |
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titr_conc = widgets.Dropdown( |
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options=[('6 M',6.0),('1 M',1.0),('0.1 M',0.1)], |
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value = 6.0, |
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description = 'NaOH conc:', |
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style=style, |
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layout=widgets.Layout(width='200px',margin='10px 100px 15px 0px') |
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) |
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aliq_vol = widgets.Dropdown( |
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options = [('10 mL',10.0),('1.0 mL',1.0),('0.1 mL',0.1)], |
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value = 1.0, |
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description = 'NaOH vol:', |
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style=style, |
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layout=widgets.Layout(width='200px',margin='10px 100px 15px 0px') |
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) |
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add_titr_butt = widgets.Button( |
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description='Add NaOH', |
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button_style = 'success', |
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style=style, |
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layout=widgets.Layout(width='150px',margin='25px 150px 15px 70px') |
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) |
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reset_butt = widgets.Button( |
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description = 'Reset titration', |
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button_style ='warning', |
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style=style, |
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layout=widgets.Layout(width='150px',margin='25px 0px 15px 0px') |
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) |
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pH = widgets.HTML( |
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layout=widgets.Layout(width='150px',margin='25px 0px 15px 250px') |
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) |
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vol_header = widgets.HTML( |
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value = '<h3> NaOH volumes added: </h3>', |
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layout=widgets.Layout(width='80%',margin='10px 0% 0px 0%') |
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) |
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vol_add_6M = widgets.HTML( |
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value = '<h4> 6M: 0 </h4>', |
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layout=widgets.Layout(width='200px',margin='0px 25px 15px 0px') |
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) |
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vol_add_1M = widgets.HTML( |
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value = '<h4> 1M: 0 </h4>', |
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layout=widgets.Layout(width='200px',margin='0px 25px 15px 0px') |
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) |
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vol_add_0p1M = widgets.HTML( |
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value = '<h4> 1M: 0 </h4>', |
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layout=widgets.Layout(width='200px',margin='0px 25px 15px 0px') |
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) |
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#------------Widget Control Functions---------------------# |
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# some global variables. The shame! |
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global vol_6M, vol_1M, vol_0p1M, ph, titr_moles,titr_vol |
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titr_moles = 0.0 |
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titr_vol =0.0 |
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vol_6M = 0.0 |
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vol_1M = 0.0 |
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vol_0p1M = 0.0 |
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def adjust_pH(start,end,t_tot,steps,sigma): |
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tau = 0.2*t_tot |
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for i in range(steps+1): |
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t = t_tot*i/steps |
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noise = rand.normalvariate(1,sigma) |
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pH = (start-end)*np.exp(-t/tau)*noise + end |
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sleep(t_tot/steps) |
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update_pH(pH) |
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def update_titr(b): |
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global vol_6M, vol_1M, vol_0p1M,ph, titr_moles |
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old_ph = ph |
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if titr_conc.value == 6.0: |
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vol_6M += aliq_vol.value |
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if titr_conc.value == 1.0: |
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vol_1M += aliq_vol.value |
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if titr_conc.value == 0.1: |
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vol_0p1M += aliq_vol.value |
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titr_moles = (6.0*vol_6M + |
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1.0*vol_1M + |
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0.1*vol_0p1M)/1000.0 |
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titr_vol = vol_6M + vol_1M + vol_0p1M |
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ph = pH_calc(buffer.value,pK.value,moles.value, |
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init_vol.value,titr_moles,titr_vol) |
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update_vols(vol_6M,vol_1M,vol_0p1M) |
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adjust = threading.Thread(target=adjust_pH, args=(old_ph,ph,10,50,0.2)) |
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adjust.start() |
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def update_pH(ph): |
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pH.value='<h1> pH: <span style="color:red;"> {:.2f}'.format(ph) + '</span></h1>' |
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def update_vols(vol_6M,vol_1M,vol_0p1M): |
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vol_add_6M.value = '<h4> 6M: ' + str(round(vol_6M,2)) + ' mL </h4>' |
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vol_add_1M.value = '<h4> 1M: ' + str(round(vol_1M,2)) + ' mL </h4>' |
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vol_add_0p1M.value = '<h4> 0.1M: ' + str(round(vol_0p1M,2)) + ' mL </h4>' |
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def on_reset(change): |
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global titr_moles,vol_6M,vol_1M, vol_0p1M,ph |
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titr_moles = 0 |
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vol_6M = 0 |
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vol_1M = 0 |
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vol_0p1M = 0 |
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ph = pH_calc(buffer.value,pK.value,moles.value, |
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init_vol.value,titr_moles,titr_vol) |
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if buffer.value=='Weak acid': |
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titr_conc.description = 'NaOH conc:' |
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aliq_vol.description = 'NaOH vol:' |
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add_titr_butt.description='Add NaOH' |
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vol_header.value = '<h3> NaOH volumes added: </h3>' |
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else: |
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titr_conc.description = 'HCl conc:' |
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aliq_vol.description = 'HCl vol:' |
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add_titr_butt.description='Add HCl' |
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vol_header.value = '<h3> HCl volumes added: </h3>' |
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update_vols(vol_6M,vol_1M,vol_0p1M) |
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update_pH(ph) |
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add_titr_butt.on_click(update_titr) |
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reset_butt.on_click(on_reset) |
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buffer.observe(on_reset,names='value') |
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pK.observe(on_reset,names='value') |
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moles.observe(on_reset,names='value') |
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init_vol.observe(on_reset,names='value') |
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#------------Display all of the widgets-----------------# |
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row1 = widgets.HBox([buffer,pK]) |
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row2 = widgets.HBox([moles,init_vol]) |
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row3 = widgets.HBox([titr_conc,aliq_vol]) |
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row4 = widgets.HBox([add_titr_butt,reset_butt]) |
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row5 = pH |
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row6 = vol_header |
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row7 = widgets.HBox([vol_add_6M,vol_add_1M,vol_add_0p1M]) |
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display(widgets.VBox([header,row1,row2,hrule,row3,row4,row5,hrule,row6,row7,footer])) |
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on_reset(0) |
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