SSAC2007.QD561.AH1.1 – QD561
Buffer Capacity in Chemical Equilibrium
How long can you hyperventilate before
severe alkalosis sets in?
Core Quantitative Issue
Your blood pH is controlled (buffered) within a
narrow range. In this module we will
investigate the chemical characteristics of this
buffer and estimate its physiologic limitations.
This module will improve your understanding
of buffer capacity through graphical analysis of
the Henderson-Hasselbalch equation.
Algebra: Manipulating logarithmic equations
Supporting Quantitative Issues
Algebra: Manipulating equations, Solving
simultaneous equations
Modeling: What-if analysis
Number sense: Dimensional analysis,
Logarithms, Scientific notation
Visual display of data: Rate of change, Slope,
XY scatter plots
Prepared for SSAC by
Dr. Armando Herbelin – Lower Columbia College
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2007
1
Overview of Module
A chemical buffer’s ability to resist pH change, the Buffer Capacity, is
important to the buffer’s practical performance. Calculation of buffer
capacity is conceptually straightforward but involves repeated calculations.
Application of a spreadsheet to repeat these calculations automatically
simplifies the process and facilitates deeper understanding of its
implications.
After briefly reviewing several buffer calculations you will implement a
spreadsheet to graphically investigate buffer capacity and characterize a
physiological buffer – blood.
Slide 3
Slides 4-7
Slide 8
Slides 9-10
Slides 11
Problem Specification
Buffer Review (Includes three worked examples)
Chemistry of the Blood Buffer System
Graphing the Blood Buffer System
Updated spreadsheet for disturbing the buffer system.
Slide 12
Slides 13-14
Slide 15
Definition and Meaning of Buffer Capacity
How much CO2 do you lose per breath?
End of Module Questions
2
Problem
When someone hyperventilates, why do you have them breathe into a paper bag? Should you
really be worried?
Your blood pH is controlled between a pH of 7.35 and 7.45 by the bicarbonate/carbon dioxide
(HCO3 / CO2) buffer system. When CO2 dissolves in your blood, it combines with a water
molecule to form carbonic acid, H2CO3:
CO2 (aq)  H2O (l) ⇌ H2CO3 (aq)
pK  1.46
Carbonic acid is a weak acid that forms HCO3:
H2CO3 (aq) ⇌ HCO-3 (aq)  H (aq)
pKa  6.36
Biologically, we focus on CO2 and HCO3-. The equilibrium expression for a combined reaction is:
CO2 (aq)  H2O (l) ⇌ HCO-3 (aq)  H (aq)
When you hyperventilate, the CO2 concentration
in your blood drops. According to the HendersonHasselbalch equation, the pH will increase.
pKa  7.81


 HCO3 

pH  pKa  log


CO
2


Death occurs when blood pH reaches about 7.8. By quantifying the pH
change, we can gauge how serious hyperventilation might be.
Question:
How long can you hyperventilate before your blood pH reaches
a dangerous level?
Picture: www.uah.edu/ASEF/teachers.htm
3
Buffer Review: Terminology
•
Square brackets are used as a
shorthand for concentration in molarity.
– [H+] = molarity of the hydrogen ion.
•
pKa is the “p” of the acidity constant Ka.
“p” means negative log:
Exam ple:
[ H  ]  1.23 108 M
pH
 0.012 
pH  4.74  log


  log[H ] 0.025 
pH   log[1.23 108 ]  7.910
pH = log[H+]
pKa = log(Ka)
•
Use the following shorthand when you
have to do algebra with chemical
symbols:
– HA = protonated (acid) form of the
buffer molecule.
– A = conjugate base form of the buffer
molecule.
– For example, acetic acid would be
HA=CH3COOH, A = CH3COO


 CH 3COO 

pH  pK a  log
 CH 3COOH 
vs
 
 A 

pH  pK a  log
 HA 
Click here for an optional
derivation of the HendersonHasselbalch equation.
4
Buffer Review: pH from [HA] & [A-].
• Determine the pH of an acetic acid
buffer formed from 0.025M acetic acid
and 0.012M sodium acetate
(Ka=1.8105)
• Givens:
[HA] = 0.025M
[A-] = 0.012M
pKa = log(1.8105)=4.74
• To solve, plug into the HendersonHasselbalch equation.
 
 A 


pH  pK a  0log
.012 
pH  4.74  log
 HA  

 0.025 
 0.012 
pH  4.74  log

 0.025 
pH  4.74  log0.48
pH  4.74  0.32
pH  4.42
5
Buffer Review: [HA] and [A-] for a given pH.
 
 
 A 

pH  pK a  log


HA


•
What is the concentration of acetic
 A  
 A  
acid and sodium acetate in a
 log
  5.00  4.74  0.26
5.00  4.74  log




HA
HA




solution at pH=5.00? The total
amount of buffer molecules is
A   100.26 A   1.819
0.037M.
HA
HA
Given:


•
– pH=5.0
– pKa = 4.74 (previous page)
•
“Total amount of buffer
molecules is 0.037M” means:
– [HA]+[A]=0.037M
•
 A 

pH  pKa  log


HA


Solution:
– Plug in pH and pKa, Solve the
Henderson-Hasselbalch equation
for the ratio of [A]/[HA]
– Solve two equations in 2
unknowns (A hassle) for [HA]
and [A]


2 Equations in 2 Unknowns
A   1.819

HA
HA  A

  0.037
A   1.819HA HA  1.819HA  0.037

1  1.819HA  0.037
HA 
0.037
 0.013M
1  1.819
A   1.819 0.013  0.024M

Steps with red borders will be used
in the spreadsheet calculations.
6
Buffer Review: pH of a Disturbed Buffer.
• What is the pH of the previous
buffer if 0.007M of acid is
added.
• These problems are easier
than they seem.
• Solution:
– If acid has been added, if will
convert conjugate base (A)
into the acid (HA).
– [HA] goes up by 0.007M
– [A] goes down by 0.007M
– Plug into the HendersonHasselbalch equation.
[ HA]  0.013 0.007  0.020M
[ A - ]  0.024  0.007  0.017M
 0.017 
pH  4.74  log



0
.
020


pH  4.67
Note: If these examples cause you to breathe into a paper bag, go
back and review material on buffers in your chemistry textbook.
7
The Blood Buffer System
Death
6.0
Acidosis
6.5
Normal
7.0
Alkalosis
Death
8.0
7.5
• pH of Blood
– Normal pH is approximately 7.35-7.45.
– pH values compatible with life in mammals are limited to a pH range
between 6.8 and 7.8.
• The blood is buffered by a carbonate buffer system with a total blood
carbonate level of approximately 0.0048 M.
CO2 (aq)  H2O (l)
⇌
HCO-3 (aq)  H (aq)
pKa  7.81
– To make the numbers easier to work with, physiologists typically
use millimolar as a unit (1mM = 0.001M)
• To work with buffers, we use the
Henderson-Hasselbalch equation:


 HCO3 

pH  pKa  log
 CO2  
• The total blood carbonate is the sum of [HCO3] and [CO2]
Click here for extra help with Excel before you start the buffers.
8
Graphing the Carbonate Buffer System
To help understand the blood buffer system, we will generate a
spreadsheet to repeat the buffer calculations from Slide 6.
Yellow cells contain a number.
Orange cells contain a formula.
Take a minute to read the spreadsheet then click to continue.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
B
C
D
E
F
G
To create your spreadsheet, start with your name
Name:
Armando Herbelin
Date:
7/20/07
and the date in Rows 2 & 3. Be sure to label it.
Total Buffer Concentration:
4.8
Buffer pKa:
7.81
#
pH
pH-pKa [A-]/[HA]
[HA]
[A-]
Rows 4 & 5 have the constants for this problem –
1
4.00
-3.81
0.00
4.799
0.001
2
4.30
-3.51
0.00
4.799
0.001 total buffer concentration and pKa.
3
4.60
-3.21
0.00
4.797
0.003
4
4.90
-2.91
0.00
4.794
0.006
Column C has the pH values from 4.00 to 10.00
5
5.20
-2.61
0.00
4.788
0.012
6
5.50
-2.31
0.00
4.777
0.023 in increments of 0.3.
7
5.80
-2.01
0.01
4.754
0.046
8
6.10
-1.71
0.02
4.708
0.092 the process of entering these numbers:
Excel can automate
9
6.40
-1.41
0.04
4.620
0.180 Columns D-G are single steps through the
10
6.70
-1.11
0.08
4.454
0.346
1.0.15Enter
4.00 in
Cellcalculation
C7. Format
theSlide
cell with
from
6. 3 decimal
11
7.00
-0.81
4.156
0.644
12
7.30
-0.51
0.31
3.667using
1.133
places
the Enter formulas
buttons.for the calculations in Row 7 then
13
7.60
-0.21
0.62
2.969
1.831
14
7.90
0.09
1.23
2.152
2.648 copy and paste the cells for the whole column.
2.
Re-select
Cell
C7.
15
8.20
0.39
2.45
1.389
3.411
Hint: Columns D and F should have a fixed
16
8.50
0.69
4.90
0.814
3.986
3.9.77Open
the Edit
17
8.80
0.99
0.446
4.354 menu,
references (pKa is in cell $E$5)
18
9.10
1.29
19.50
0.234
4.566
Select Fill, and then Series.
19
9.40
1.59
38.90
0.120
4.680
20
9.70
1.89
77.62
0.061
4.739
4.
Fill in0.031
the form
21
10.00
2.19
154.88
4.769 as shown.
Click Ok.
5. Now try this technique to fill in the numbers in Column B.
9
Graphing the Carbonate Buffer System
We will now generate a graph of the buffer system.
Open the Insert menu and select
Chart.
Chart Wizard Step 1: Select XY Scatter, do not
connect
the dots.
Next.
Chart Wizard
StepClick
2 (a):
Select all text in the
Data
and2 delete
it. the Series Tab.
ChartRange
Wizardbox
Step
(b): Click
Chart Wizard Step 2 (c): Click Add.
Name:
Click inStep
the Name
box then click on
Chart Wizard
3:
Cell
C6 in your
Enter
appropriate
titles.
Characteristics
ofgraph
aspreadsheet.
Buffer:
X
Values: Click
in the X would
Valuesmove
box. Use the
A solution’s
composition
to select
the column
of [A] data
Click
. adding
alongmouse
the x-axis
by
acid ()
(G7:G27).
or
base
().will now appear.
Your
graph
X
Values: 1:
Click
in does
the Ythe
Values
box. Use the
Question
How
pH change
to acid?
select (UP
the column
of pH values.
whenmouse
you add
or DOWN)
(C7:C27).
Question
2: If the [A] is 1.0 mM and you add
0.7
of base, what is the change in pH? ____
ClickmM
Next.
Question 3: If the [A] is 3.9 and you add 0.7
mM base, what is the change in pH? ____
Question 4: Which point is a better buffer?
(1.0 mM A or 3.9 mM A)
3
Finish
Graph Cleanup:
Take the time to fix the font and
number format for the titles and
scales. To do this, click on the item
then use the font and formatting
buttons the button bar. Excel tends
to over emphasize labels making
your actual data less prominent.
10
Updated spreadsheet for disturbing the buffer system.
We will now add features to the spreadsheet so we can see the
effect of adding base to the buffer.
Start by inserting eight rows below “Buffer pKa”.
B
C
D
E
F
G
2
3
4
5
6
7
8
9
10
11
12
13
14
Name:
Armando Herbelin
Date:
7/20/07
Total Buffer Concentration:
Buffer pKa:
4.8
7.81
Disturbing a Buffer
[HA] (mM)
[A-] (mM)
[Added Base] (mM)
Disturbed pH
Buffer Graph:
#
pH
Initial
Final
2.4
2.4
-1.1
7.40
pH-pKa
[A-]/[HA]
3.45
1.35
[HA]
[A-]
Carbonate Buffer
12.0
10.0
pH
8.0
pH
6.0
Disturbed pH
4.0
2.0
0.0
0.0
1.0
2.0
3.0
[A-] (mM)
4.0
5.0
6.0
Labels:
labels
Rows
7-11
& 13.
1. SelectAdd
thethe
Excel
rowon
labels
from
Row
6 toNote
13.
that
we are labeling the graph
section now to
Concentrations:
2. Open the InsertEnter
menuinitial
and buffer
select Rows
differentiate
it
from
our
new
work.

concentrations
Calculations: of 2.4 mM for [HA] and [A ]. This
The
column titles
forcenter
the graph
data
should
corresponds
to the
of the
buffer
point.now
Final
[HA]
is
the
initial
minus
[Added
Base]:
Graphing:
be on Row We
14. will add a one-point series to the
Enter
graph
0.0
showing
for the
the
added
Disturbed
base.
pH.
We willadding
change
Investigating
the
Buffer:
Simulate
acid
[HA]
=
[HA]
–
[Added
Base]
final
initial
this
number
to
buffer later.
byon
decreasing
value
of [Added
1. the
Right-Click
the graph,the
select
Source
Data.
Base].
Adjust
it until thetab,
Disturbed
pHAdd.
is equal to
2.
Click
then click
Final
[A]on
is the
the Series
initial plus [Added
Base].
7.40,
average
physiologic
pH.
3. Setthe
Name
to Cell
B11.
4.
Set X Values
Cell
F9.
Question
5:
[AHow
]finalto
=much
[A]initial
acid
+ [Added
relative Base]
to the
5.
Set
Y
Values
to
Cell
E11.
overall buffer concentration do you have to add?
6.
Click Ok.
Disturbed
pH is calculated from the HendersonQuestion 6: Is the blood buffer at an optimal
Hasselbalch
equation.
sure
usemagenta
[HA]final
Your
should
now Be
have
an to
extra
point graph
for
resisting
more
base?
and
[Ait]final
.
dot on
representing
the disturbed pH.
Question 7: Is the blood buffer at an optimal
This
movemore
alongacid?
the graph as we modify
pointdot
for will
resisting
the added base value.
Justify your answers!
11
Definition and Meaning of Buffer Capacity
What is Buffer Capacity?
Introduction:
pH
A buffer
is a solution that resists
Older
Definition:
changes in pH when acid or base is
An older definition
of buffer capacity
Another
added. Approach:
was the amount of strong acid or
The
graph
axes
are
pHattempt
and Acid
Calculating
Buffer
Capacity:
Buffer
Capacity
is an
base required
to change
1 liter to
of the
Concentration.
The
slope
of
the
quantify
this
resistance.
buffer
solution
bycolumn
1Capacity
pH unit.
Graphing
1. Label
aBuffer
new
next to your
graph would be:
1.
Right-Click
on
graph,
select
data
If
Meaning
you
add“BC”
of
a lot
Buffer
of the
acid
Capacity:
or base,
you
For
biological
buffers,
this
definition
Slope
=
Change
in
pH
Source
Data,the
add
anotherofdata
can
overwhelm
is
not
verythe
useful.
Abuffer!
change
0.5
2.
Enter
slope
formula
in Cell
Question
8: Where
is buffer
Acid
Amount
series:
pH units
can kill you.
H16: highest?
capacity
Name = BC column label.
This is
the inverse of the definition
=1/SLOPE(C15:C17,G15:G17)
To study
for smaller
Xbuffer
data =capacity
[A ] data.
of buffer capacity.
changes
pH,paste
the
Yin
data
=we
BCinterpret
data.cell
3.
Copy
and
this
Question
9: Is
the
blood
pHformula
at an
buffer
capacity
definition
as
a
The
buffer
capacity
can
be
2.
Click
on
one
of thethrough
BC dotsratio:
to
down
the
column
optimal
buffer
capacity?
calculated
as new
the inverse
of the
select
the
series.
Cell Capacity
H34.
Buffer
=data
Amount
of Acid
slope
of
our
graph
at
a
given
point.
3.
Right
Click
on
the
same
dotof
Question 10: What 1ispH
theUnit
value
(If
you’ve
hadselect
calculus,
= pH?
and
then
Format
Data
the
buffer
at
theslope
blood
Note:
We capacity
cannot calculate
the slope
derivative).
TheSeries.
units
(mM/pH
unit).
for
thewould
first orbe
last
data point.
4. Click on the Axis tab and
Excel has an automatic function to
select Secondary Axis.
calculate the slope for us.
Carbonate Buffer
10.0
3.0
9.0
2.5
8.0
2.0
7.0
1.5
6.0
1.0
pH
Disturbed pH
BC
5.0
0.5
4.0
0.0
0.0
1.0
2.0
3.0
4.0
5.0
[A-] (mM)
12
How much CO2 do you lose per breath?
• Hyperventilation disturbs the blood pH by removing CO2 from your
blood faster than your metabolism produces it.
– This is equivalent to adding hydroxide and disturbing the buffer’s pH.
– On average, humans breathe at 24 breaths/minute (bpm).
– For this exercise, assume that hyperventilation removes about
0.00060 mM of CO2 per extra breath.
– Based on this information, how long can you hyperventilate at 300%
normal rate before reaching a dangerous blood pH?
• Solution:
– Determine the amount of hydroxide you would have to add to the blood
buffer to bring the pH from 7.40 to 7.80.
– Use dimensional analysis to convert from mM base to extra breaths
then minutes of hyperventilation:
 1 mM OH  
 

1 breath
1 minute



? mM A   1 mM A    0.00060

  
mM OH   72  24 extra breaths

 

13
How much CO2 do you lose per breath?
We will now add features to the spreadsheet so we can
calculate the time to death.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
B
C
D
Name:
Armando Herbelin
Date:
7/20/07
Total Buffer Concentration:
Buffer pKa:
E
F
G
4.8
7.81
Hyperventilation
#
pH
pH-pKa [A-]/[HA]
[HA]
[A-]
Normal
7.40
-0.41
0.39
3.456
1.344
Death
7.80
-0.01
0.98
2.428
2.372
Change in [A-] (mM):
1.028
Added base per breath (mM/breath):
0.00340
Hyperventilation breathing rate (breath/min):
72
Normal breathing rate (breath/min):
24
Extra breathing rate (breath/min):
48
Time before death (min):
6.3
Disturbing a Buffer
Initial
Final
Start by inserting 11 rows below the
“Buffer
a” row.
Labels:pKLabel
this section Hyperventilation.
Add
labels
Your the
Cheating:
Disturbing
Wein
need
a Rows
Buffer
to 11-16.
determine
section should
[A] atnow
two
start
different
on Row
pHskip
values.
18.the entries
We could
redo 8-10,
the second
Be sure
Calculations:
to
in Rows
we’re
example
buffer
calculation…
can cheat
going
1.
Enter
to cheat!
a formula
in Cell G11ortowe
calculate
the
Investigating
Hyperventilation:
Use
by
using the
we created earlier.
change
[Aformulas
].spreadsheet
(modify)inyour
to answer the
2.
Enter constants
for the unit conversions.
1. Select
following
questions.
Cells B25-G27.
3.
Calculate
the extra
rate.
2. Open
the Edit
menubreathing
and select
Copy.
Question
11:
How
long
would
you
last if you
4.
Apply
dimensional
analysis
to
calculate
the
3. Click on Cell B8.
were
really scared
and hyperventilated at 100
time
before
4. Open
the death.
Edit menu and select Paste.
bpm?
5. Change the row labels to Normal and
Death, and12:
Question
update
Whatthe
if you
pHwatched
values. a lame
science fiction movie and only breathe at 32
bpm?
Question 13: Is your answer to Question 12
realistic? Should a 33% higher breathing rate
really be dangerous?
14
End of Module Questions
I.
Answer Questions 1-13 in the previous slides.
II.
Add a column to your spreadsheet to calculate the percent of conjugate base
%A- = [A] /([HA]+[A])*100%. Modify your graphs so the x-axis is percent
conjugate base.
III.
Make a copy of your spreadsheet. (Right-click on the Sheet1 tab at the bottom of
the screen, select Move or Copy, check Create a Copy and click Ok.). Modify
your spreadsheet for a primitive alien species that uses a phosphate buffer
(pKa=7.2). Work through the spreadsheet process to answer the following
questions:
a. Find the amount of base needed to disturb the buffer to pH 7.40.
b. Compare the buffer capacity this alien has to humans.
c. How long can the aliens hyperventilate at 72 bpm?
d. Would the aliens be more sensitive to acidosis? Explain how you used your
spreadsheet to test this numerically. What boundary value will you use for pH?
IV.
We use a 0.025 M phosphate buffer to calibrate our electrodes (pH=7.00). If you
had 50 mL of this buffer and didn’t rinse the pH electrode, what effect would it
have on the calibration buffer if:
a. There was about 0.10 mL ( 2 drops) of neutral water on the electrode.
b. There were 2 drops of 0.1M HCl on the electrode.
15
Pre-Post Test
1. If log(x)=3, what is x?
pH
2. Use a calculator to determine the log of the numbers 0.05, 0.95,
1.0, and 5.3.
Which of these values is special for logarithms?
3. Identify the point on the graph (A, B, or C) that best answers the
following:
a. Which point represents the lowest slope?
b. Which point represents the solution composition that will best
resist pH change (y-axis) when acid or base is added (move
on the x-axis).
4. Use the Henderson-Hasselbalch equation (at right) to compute
the value of pH in the equation for [HA]=1.2 mM and [A]=24mM.
C
B
A
Added Base (mM)
 
 A 

pH  6.35 log


HA


5. Which value ([HA] or [A]) would you increase to lower the pH?
6. Compute the ratio [A]/[HA] for a solution with pH=6.2.
7. Without doing any math, would the ratio increase or decrease for
a pH of 7.2?
16
Buffer Review: Derivation of the Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation is
derived from the mass action equation
for a weak acid.
Chemical Equation:
HA ⇌ H+ + A[ H  ][A  ]
Mass Action Equation:
Ka 
[ HA]
 [ H  ][ A ] 

Step 1 : logKa   log
[
HA
]


 [ A ] 

Step 2 : logKa   log[ H ]  log
 [ HA] 

 [ A ] 

Step 3 :  log[ H ]  logKa   log
[
HA
]


Derivation (Click to start the steps):
1. Starting from the mass action equation,
take the base-10 log of both sides.
2. Selectively separate the terms on the
Step 4 :
+
right-hand side (split off [H ]).
3. Move log[H+] to the left-hand side.
4. Move log(Ka) to the right-hand side.
Step 5 :
5. The “p” in pH is an operator that means
“minus log” or “log10()”. Replace log[H+]
with pH.
Step 6 :
6.
Replace log(Ka) with pKa.

 [ A ] 

 log[ H ]   logKa   log
 [ HA] 

 [ A ] 

pH   logKa   log
[
HA
]


 [ A ] 

pH  pKa  log
 [ HA] 
Click here to return to the buffer review.
20
Buffer Review: Derivation of the Henderson-Hasselbalch Equation
Click here to return to the buffer review.
21