Bufffer titration simulation

Biol 3515-Chem 3515 Buffer Titration Simulation

Gist title

buffer_simulation.ipynb

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buffer_titr.py

## Module to simulate titration of a weak acid or a weak base
## with a strong base or strong acid, respectively
## to prepare a buffer solution
## with widgets to allow interactive control in a Jupyter notebook

## Computations of pH during titration as described at:
## https://chem.libretexts.org/Bookshelves/Ancillary_Materials/Demos_Techniques_and_Experiments/General_Lab_Techniques/Titration/Titration_of_a_Weak_Base_with_a_Strong_Acid
## David P. Goldenberg, January 2021
## goldenberg@biology.utah.edu

import numpy as np 
from scipy.optimize import fsolve
import ipywidgets as widgets
from IPython.display import display, HTML
from IPython.display import display, clear_output, HTML, FileLink
from time import sleep
import threading
import random as rand
display(HTML("<style>div.output_scroll { height: 300ex; }</style>"))

#----------Functions for calculating pH under different circumstances--------------#

def OHfunc(OH,base_conc,pKa):
    '''Function to be solved to calculate OH concentration
    for untitrated base'''
    Ka = 10.0**(-pKa)
    K = 1e-14/Ka
    return OH**2 + OH*K - base_conc*K

def pH_base(pKa,base_conc):
    '''Calculates pH for untitrated base'''
    OHconc =fsolve(OHfunc,1e-7,(base_conc,pKa))
    pH = float(-np.log10(1e-14/OHconc))
    return pH
    
def Hfunc(H,acid_conc,pKa):
    '''Function to solve to calculate H concentration 
    from dissociation of conjugate acid'''
    Ka = 10.0**(-pKa)
    return H**2 + Ka*H - Ka*acid_conc
    
def pH_acid(pKa,acid_conc):
    '''Calculates pH for untitrated acid'''
    Hconc = fsolve(Hfunc,1e-7,(acid_conc,pKa))
    pH = -np.log10(Hconc)
    return float(pH)
    
def pH_base_titr(pKa,base_moles,titr_moles):
    '''Calculates pH when moles of added strong acid
    are less than moles weak base'''
    ba_ratio = (base_moles-titr_moles)/titr_moles
    pH = pKa + np.log10(ba_ratio)
    return pH
    
def pH_acid_titr(pKa,acid_moles,titr_moles):
    '''Calculates pH when moles of added strong base
    are less than moles weak acid'''
    ba_ratio = titr_moles/(acid_moles-titr_moles)
    pH = pKa + np.log10(ba_ratio)
    return pH
    
def pH_post_eq_b(base_moles,titr_moles,volume):
    '''Calculates pH when moles of added strong acid
    are greater than moles weak base'''
    Hconc = (titr_moles - base_moles)/volume
    pH = -np.log10(Hconc)
    return(pH)
    
def pH_post_eq_a(acid_moles,titr_moles,volume):
    '''Calculates pH when moles of added strong base
    are greater than moles weak acid'''
    OHconc = (titr_moles - acid_moles)/volume
    pH = np.log10(OHconc) + 14.0
    return(pH)
    
def pH_full_titr_b(pKa,base_moles,v_init,titr_moles,titr_vol):
    '''Calculates pH over full titration of a weak base 
    with a strong acid'''
    vol_tot = v_init + titr_vol
    if titr_moles == 0:
        base_conc = base_moles/v_init
        return pH_base(pKa,base_conc)        
    elif 0 < titr_moles < base_moles:
        return pH_base_titr(pKa,base_moles,titr_moles)      
    elif titr_moles == base_moles:
        conc = base_moles/vol_tot
        return pH_acid(pKa,conc)      
    else:       
        return pH_post_eq_b(base_moles,titr_moles,vol_tot)
        
def pH_full_titr_a(pKa,acid_moles,v_init,titr_moles,titr_vol):
    '''Calculates pH over full titration of a weak acid
    with a strong base'''
    vol_tot = v_init + titr_vol
    if titr_moles == 0:
        acid_conc = acid_moles/v_init
        return pH_acid(pKa,acid_conc)      
    elif 0 < titr_moles < acid_moles:
        return pH_acid_titr(pKa,acid_moles,titr_moles)      
    elif titr_moles == acid_moles:
        conc = acid_moles/vol_tot
        return pH_base(pKa,conc)        
    else:
        return pH_post_eq_a(acid_moles,titr_moles,vol_tot)

def pH_calc(buffer,pKa,buff_moles,v_init,titr_moles,titr_vol):
    '''Calculates pH over full titration of either a weak acid
    or a weak base'''

    if buffer == 'Weak acid':
        ph = pH_full_titr_a(pKa,buff_moles,
                    v_init,titr_moles,titr_vol)
    elif buffer == 'Weak base':
        ph = pH_full_titr_b(pKa,buff_moles,
                    v_init,titr_moles,titr_vol)
    else:
        ph = float('nan')
    return ph     
        
#------------Widgets-------------#

header_html = """
<h2> Biology 3515/Chemistry 3515
<br>
Biological Chemistry Laboratory 
<br>
University of Utah </h2>
<h3> Spring 2021 </h3>
<h3> Experiment 1, Part B: Buffer Preparation</h3>
<p style="font-size:16px">

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. 
<br>

The top two rows of controls specify the starting parameters for the
titration: The buffer type (weak acid or weak base),the buffer 
pK<sub>a</sub>, the number of moles of buffer and the initial solution 
volume. The next row contains controls for specifying concentration
and volumes of individual titrant additions. 

Titrant is added by clicking the green button. After each addition
the new pH is displayed, but it takes a little while to settle down!
The volumes of titrant are also updated. Click the orange button to
reset the titration.

<hr border-width:6px, color:black>
"""
style = {'description_width': 'initial'}
header = widgets.HTML(
    value=header_html
    )
    
footer = widgets.HTML(
    value='''
    <hr border-width:6px, color:black>
    David P. Goldenberg, January 2021<br>
    <a href="mailto:goldenberg@biology.utah.edu" target="new">goldenberg@biology.utah.edu</a><br>
    School of Biological Sciences, University of Utah<br>
    Salt Lake City, Utah 84112<br>
     <a href="https://goldenberg.biology.utah.edu/courses/biol3515/index.shtml" 
     target="new">https://goldenberg.biology.utah.edu/courses/biol3550.</a>
''')



buffer = widgets.Dropdown(
    options=['Weak acid','Weak base'],
    value='Weak acid',
    description='Buffer type:',
    style=style,
    layout=widgets.Layout(width='200px',margin='0px 100px 15px 0px')
    )
pK = widgets.FloatSlider(
    value = 7.0,
    min = 3.0,
    max = 11.0,
    step = 0.1,
    description = 'Buffer pKa:',
    orientation = 'horizontal',
    readout=True,
    readout_format='.1f',
    style=style,
    layout=widgets.Layout(width='300px',margin='0px 0px 15px 0px')
    )
moles = widgets.FloatText(
    value = 0.5,
    min = 0.01,
    max = 5.0,
    step = 0.01,
    description = 'Moles buffer:',
    style=style,
    layout=widgets.Layout(width='200px',margin='0px 100px 15px 0px')
    )

init_vol = widgets.FloatText(
    value = 0.5,
    min = 0.01,
    max = 5.0,
    step = 0.01,
    description = 'Initial vol. (L):',
    style=style,
    layout=widgets.Layout(width='200px',margin='0px 0px 15px 0px')
    )

hrule = widgets.HTML(
    value = '<hr border-width:6px, color:black>'
    )

titr_conc = widgets.Dropdown(
    options=[('6 M',6.0),('1 M',1.0),('0.1 M',0.1)],
    value = 6.0,
    description = 'NaOH conc:',
    style=style,
    layout=widgets.Layout(width='200px',margin='10px 100px 15px 0px')
    )
aliq_vol = widgets.Dropdown(
    options = [('10 mL',10.0),('1.0 mL',1.0),('0.1 mL',0.1)],
    value = 1.0,
    description = 'NaOH vol:',
    style=style,
    layout=widgets.Layout(width='200px',margin='10px 100px 15px 0px')   
    )
add_titr_butt = widgets.Button(
    description='Add NaOH',
    button_style = 'success',
    style=style,
    layout=widgets.Layout(width='150px',margin='25px 150px 15px 70px')
    )

reset_butt = widgets.Button(
    description = 'Reset titration',
    button_style ='warning',
    style=style,
    layout=widgets.Layout(width='150px',margin='25px 0px 15px 0px')
    )


pH = widgets.HTML(
    layout=widgets.Layout(width='150px',margin='25px 0px 15px 250px')
    )


vol_header = widgets.HTML(
    value = '<h3> NaOH volumes added: </h3>',
    layout=widgets.Layout(width='80%',margin='10px 0% 0px 0%')
    )

vol_add_6M = widgets.HTML(
    value = '<h4> 6M: 0 </h4>',
    layout=widgets.Layout(width='200px',margin='0px 25px 15px 0px') 
    )

vol_add_1M = widgets.HTML(
    value = '<h4> 1M: 0 </h4>',
    layout=widgets.Layout(width='200px',margin='0px 25px 15px 0px') 
    )

vol_add_0p1M = widgets.HTML(
    value = '<h4> 1M: 0 </h4>',
    layout=widgets.Layout(width='200px',margin='0px 25px 15px 0px') 
    )


#------------Widget Control Functions---------------------#
# some global variables. The shame!
global vol_6M, vol_1M, vol_0p1M, ph, titr_moles,titr_vol
titr_moles = 0.0
titr_vol =0.0
vol_6M = 0.0
vol_1M = 0.0
vol_0p1M = 0.0


def adjust_pH(start,end,t_tot,steps,sigma):
    tau = 0.2*t_tot
    for i in range(steps+1):
        t = t_tot*i/steps
        noise = rand.normalvariate(1,sigma)
        pH = (start-end)*np.exp(-t/tau)*noise + end  
        sleep(t_tot/steps)
        update_pH(pH)
    

def update_titr(b):
    global vol_6M, vol_1M, vol_0p1M,ph, titr_moles
    old_ph = ph
    if titr_conc.value == 6.0:
        vol_6M += aliq_vol.value
        
    if titr_conc.value == 1.0:
        vol_1M += aliq_vol.value

    if titr_conc.value == 0.1:
        vol_0p1M += aliq_vol.value
        
    titr_moles = (6.0*vol_6M +
                  1.0*vol_1M +
                  0.1*vol_0p1M)/1000.0
    titr_vol = vol_6M + vol_1M + vol_0p1M
    
    ph = pH_calc(buffer.value,pK.value,moles.value,
                init_vol.value,titr_moles,titr_vol)
    update_vols(vol_6M,vol_1M,vol_0p1M)
    
    adjust = threading.Thread(target=adjust_pH, args=(old_ph,ph,10,50,0.2))
    adjust.start()
    
def update_pH(ph):
    pH.value='<h1> pH: <span style="color:red;"> {:.2f}'.format(ph) + '</span></h1>'
    

def update_vols(vol_6M,vol_1M,vol_0p1M):    
    vol_add_6M.value = '<h4> 6M: ' + str(round(vol_6M,2)) + ' mL </h4>'
    vol_add_1M.value = '<h4> 1M: ' + str(round(vol_1M,2)) + ' mL </h4>'
    vol_add_0p1M.value = '<h4> 0.1M: ' + str(round(vol_0p1M,2)) + ' mL </h4>'
 

   
def on_reset(change):
    global titr_moles,vol_6M,vol_1M, vol_0p1M,ph
    titr_moles = 0
    vol_6M = 0
    vol_1M = 0
    vol_0p1M = 0
     
    ph = pH_calc(buffer.value,pK.value,moles.value,
                init_vol.value,titr_moles,titr_vol)
                
                
    if buffer.value=='Weak acid':
        titr_conc.description = 'NaOH conc:'
        aliq_vol.description = 'NaOH vol:'
        add_titr_butt.description='Add NaOH'
        vol_header.value = '<h3> NaOH volumes added: </h3>'
    else:
        titr_conc.description = 'HCl conc:'
        aliq_vol.description = 'HCl vol:'
        add_titr_butt.description='Add HCl'
        vol_header.value = '<h3> HCl volumes added: </h3>'
             
    
    update_vols(vol_6M,vol_1M,vol_0p1M)
    update_pH(ph)

    

add_titr_butt.on_click(update_titr)
reset_butt.on_click(on_reset)

buffer.observe(on_reset,names='value')
pK.observe(on_reset,names='value')   
moles.observe(on_reset,names='value') 
init_vol.observe(on_reset,names='value') 


#------------Display all of the widgets-----------------#

row1 = widgets.HBox([buffer,pK])
row2 = widgets.HBox([moles,init_vol])
row3 = widgets.HBox([titr_conc,aliq_vol])
row4 = widgets.HBox([add_titr_butt,reset_butt])
row5 = pH
row6 = vol_header
row7 = widgets.HBox([vol_add_6M,vol_add_1M,vol_add_0p1M])
display(widgets.VBox([header,row1,row2,hrule,row3,row4,row5,hrule,row6,row7,footer]))


on_reset(0)
        

environment.yml

name: buffer_sim
channels:
  - conda-forge
  - defaults
  - conda-forge/label/broken
dependencies:
  - numpy
  - scipy
  - ipywidgets
  - voila