Why students should learn about negative pH Dr Kieran F. Lim, University of Canterbury
Nevertheless, there is much confusion about the permissible range of the pH scale. Whether or not negative pH values can (or cannot) exist is a common question on world-wide web
Dr Kieran Lim is an Associate Professor in the Faculty of Science and Technology at Deakin University. He is the recipient of the 2011 RACI Fensham Medal for Outstanding Contribution to Chemical Education, and a 2012 University of Canterbury Visiting Erskine Fellow.
FAQ sites (e.g., Rapp, 2003;
pH and the pH scale pH is defined as (McCarty & Vitz, 2006):
pH = -logl oa(Hp+ (aq))
Eq. (1)
In Eq. (1), a is the activity
pronouncements that there is
of aqueous hydronium ion (H 30+ (aq), often denoted as aqueous hydrogen ion, H+ (aq)).
fIno such thing as negative pH"
Activity measures the effective
(e.g., Acids with polyatomic ions, 2005). Even expert scientists
concentration and can be estimated by the Debye-Huckel
share the misconception (e.g.,
or other models. The base-l 0 logarithm scale is open-ended. At sufficiently low concentration
between 0 and 14. The possible
Acids with polyatomic ions, 2005; Argon Bulletin Board, 2001 ; Lake Access, n.d.; Muwanga-Zake,
origins ofthis misconception are discussed and strategies to avoid the misconception are presented.
2002; Negative pH's?, 1999; pH, 1993; Roberge, 1999a), before correction, sometimes several
Senese, 2005), with erroneous
A
common misconception is that the pH scale runs
and ionic strength, the activity can be approximated by the concentration: Eq . (2)
years later (Negative pH's?, 1999). Books that incorrectly state that the pH scale is between a (or 1)
Introduction pH is commonly used as a
and 14, include popular-science
measure of the hydronium ion
books (e.g., Bobick & Balaban, 2003;
concentration in chemistry,
Cobb & Fetterolf, 2005; Morgan,
biochemistry, soil science,
7995), textbooks (e.g., Burton, 2007;
wine science and other fields. The logarithmic pH scale is open-ended, allowing for pH values below 0 or above 14 (Lim, 2006). For example, commercially available concentrated HCI (37% by mass) solution has pH ::::: -1.1, while saturated NaOH solution has pH ::::: 15.0 (Dickerson, Gray, & Darensbourg, 7984). HCI-H 2SO 4 hot
springs near Ebeko volcano have estimated pH values as low as -l.7 (Ivanov, 7955;Nikitina, 7974).
Students have varied learning
Topping, & Caret, 2007; Hogendoorn et al., 2070; Kruszelnicki, 7997;
styles and preferences. Kolb distinguishes two modes
Lofts & Merett, 2000; Taylor, Ng,
of grasping experience:
Stubbs, Stokes, & James, 2007; Timberlake, 7999), revision guides
grasping through concrete experience (apprehension)
(e.g., Roebuck, 2000) and reference
and grasping through
books (e.g., Allaby, 7998; Clarke, 2003; Dictionary of Science,
abstract conceptualisation (comprehension) (Kolb, 7984;
2003; Dictionary of Science and
Towns, 2007). Bruner's theory
Techn9logy, 2003; Hayhew, 2004;
of childhood intellectual
Lafferty & Rowe, 7998; Thain &
development (Brunner, 7966), implies that novice learners
at Iron Mountain, CA, have pH
This paper discusses the probable
= -3.6 (Nordstrom &Alpers,
origins of this misconception and
7999;
acti~:>ns
to avoid the
Nordstrom, Alpers, Ptacek, & Blowes,
proposes
2000).
mistaken belief that the pH scale is between 0 (or 1) and 14.
10 LabTalk Vol 56 •
NO.3 • 2012
'\ I
I
Apprehension versus comprehension
Cochrane & Devlin, 2000; Denniston,
Hickman, 2004).
Waters from the Richmond Mine
The probable origins of the misconception
.
I
.
first act or interact with actual objects (enactic stage), then with concrete representations (iconic stage), before developing abstract representations (symbolic stage).
Features
Visual learning
Although many chemistry texts state or infer that negative pH values are possible, no examples are given (e.g. Table
I) .(a)
Learners,
especially novice learners, who favor apprehension or enactic
(without arrows on the pH-scale
Dunn and Dunn have categorized
Blain, & McCoy, 7996; Ganderton
auditory, tactile, kinesthetic (Dunn
& McLeod, 1996; Gellert, Gottwald,
Hellwich, Kastner, & Kiistner, 1989),
(words) and visual (external)
suggests that the pH scale is a
modes are most relevant to
conclude that negative pH values are merely a theoretical
closed line interval (Figure 2(a»),
learning from textbooks. This
rather the open-ended scale
duality can also be regarded as
construction without physical
shown in Figure 1(b) (d. Figure 2
words versus pictures sensory
reality. Table I. Common textbook
preference. Most texts have a diagram of a pH scale similar
examples of solutions with
to Figure 1 (a). Comparison of
--
varying pH
diagrams (e.g., Evans, Lipson, Jones,
several sensory modes: visual, & Griggs, 1988, 2000). The visual
and iconic modes of learning,
,-----
axis) to mathematical-textbook
...
(a)). Students who favor a visual (external) sensory mode more than a visual (words) mode will
the typical textbook diagram -(a)
Solution
approximate
pH scale
pH
I
I
I
I
0
3
5
6
< Gastric juice
7
8
10
11
12
13
. . ..
increa sing acidity
14
:>
Increasing baSICity
1.2 (b) pH scale
Lemonjuice
---r--T
2.1
·1
L-
Cola, vinegar
r-1 3
0
4
7
< .
Increasing acidity
I
I
8
9
I " 10
11
12
13
14
. . ..
15
:>
Increasing baSICity
Figure 1: Two pH scales.
2.8
(a) A typical textbook diagram. -
Apple juice
(b) arrows on the axis show that pH is measured on an open-ended scale. (a) interval
3.8
•
Rain
•
a
-
b
---
5.8 (b) ray
•
b
a
Lime water
10.4
---
(e) line
Household bleach
12.4
a
b
Figure 2: Typical mathematical textbook diagrams (e.g., Evans, et al., 7996;
Ganderton & McLeod, 1996; Gellert, et al., 7989). (a) Interval ab contains all points between two points, a and b. (b) Ray ab contains interval ab plus all points beyond point b in a one-sided collinear extrapolation of interval abo (c) Line ab contains interval ab plus all points beyond points a and b in a two-sided colinear extrapolation of interval abo
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LabTalk Vol 56 • No.3· 2012 11
Why students should learn about negative pH
(continued)
learn the untended misconception from the diagram, even when the textbook has an implied or explicit statement (i.e. words) to the effect that pH values outside the range 0
14 are possible.
Eq. (3)
Eq. (2) ia an approximation
Although concentrated acid
(McCarty & Vitz, 2006). Just as the
solutions are commercially
fact that gases deviate from Eq. (4)
available, the erroneous
places no bounds on the values of
extrapolation of Eq. (2) to high
the gas pressure, P, so too, the fact that aqueous acids deviate from
concentration (ef., right panel of Figure 2) has lead to the naNe
Misconception of ionic activity
Eq . (2) places no bounds on the
conception that it is not possible
values of the pH.
to prepare an acid solution with Hp+ activity equal to or exceeding 1 mol L -1 (e.g., Roberge, 7999b).
At high-school and university first-year level, Eq . (2) is used
there is little or no clue to indicate
Discussion Textbooks typically only give
to "define" pH (Burton, 2007). Students would normally not
Non-ideal behaviour
encounter ionic activity at these
In two different contexts,
stages in their studies. However,
textbooks typically present ideal
examples of positive pH values and use pH scales similar to Figure 1(a). Students, who favor grasping through concrete
teachers should be aware of the
behaviour such as Eq. (2) for
more correct Eq . (1). In many
aqueous acids, and the ideal gas
books, only the low concentration
law,
experience (apprehension) (Kolb, 7984; Towns, 2007) or who prefer
learning using pictures (Dunn &
limit (left panel of Figure 2) is
Eq. (4)
PV = nRT
shown: the numerical value of
Griggs, 7988, 2000), will construct
the ionic activity coefficient is less
Students might have some vague
the misconception that pH is
than 1, meaning that ionic activity
idea that real (non -ideal) gases
limited to the range 0-14, and
is Iftss than the concentration. In
do not always obey the ideal gas
that negative pH values are not
the low concentration limit,
law, just from the name. However,
possible. Gunstone refers to this
(a)
(b)
-
-
c
...
c
Q)
Q)
'u
'u
i: Q) o()
~
Q)
~
--m
>:~
+-'
()
()
m
.~
left/and panel -- ----- -- -- ,
,
()
c
c
o ..... o
.Q
..o ', : E . -.. - . - - -. -'" .c
E .c
-
-
. ;::
.;::
m CJl o
m
CJl
o
square root of concentration
square root of concentration
Figure 3: Schematic diagram for the ionic activity co.efficient (solid curves) and the Debye-Huckellimiting law
(straight lines). (a) Typical textbook diagram showing low concentration limit. (b) Behavior over an extended concentration range.
12 LabTalk Vol 56 • No.3' 2012
'1
Features as examples of how we teach (e.g., Table I and Figure 1(a)) influencing what we teach (i.e., the content) (Gunstone, 2005). This misconception is perpetuated in
Table II. Examples of solutions with pH at or below zero Solution
pH
HCI (aq) (1.228 mol L- l)
Monk (2004) 0
popular-science books (e.g., Bobick & Balaban, 2003; Cobb & Fetterolf, 2005; Morgan, 7995), textbooks
HCI (aq) (12 mol L- l; 37% by mass)
Dickerson (1984) -1. 1
(e.g., Burton, 2007; Cochrane
& Devlin, 2000; Denniston, et
HCI-H2S04 hot springs near
al., 2001; Hogendoorn, et al.,
Ebeko
2070; Kruszelnicki, 1997; Lofts & Merett, 2000; Tay/or, et al., 2007;
volcano, Kurillslands, Russia
Timberlake, 1999), revisi~n guides
Ivanov (1955); Nikitina (1974) as low as -1.7
(e.g., Roebuck, 2000), reference
books (e.g., Allaby, 1998; Clarke, 2003; Dictionary of Scienc~, 2003; Dictionary of Science and Technology, 2003; Hayhew, 2004;
Nordstrom
Acid mine waters at Iron Mountain, CA, USA
Lafferty & Rowe, 1998; Thain &
& Alpers -3 .6
(1999); Nordstrom, et al. (2000)
Hickman, 2004) and web sites (e.g., Acids with polyatomic ions, 2005; Argon Bulletin Board, 200 7;
~
Lake Access, n.d.; Muwanga-Zake, 2002; Negative pH's?, 1999; pH, 1993;Roberge, 1999a) and will
present difficulties for those graduates who proceed to work in acid-soil (Nordstrom & Alpers, 7999; Nordstrom, et al., 2000) remediation, the
Students should learn about negative pH to minimise this misconception; textbooks can help by listing extremely low pH examples (see Table II) and using pH scale diagrams similar to Figure 1 (b).
study of biological systems in low pH conditions (Ashcroft,
Acknowledgments
2000; Edwards, Bond, Gihring, & Banfield, 2000) and other areas.
The author thanks the University
Negative pH values are difficult
of Canterbury (New Zealand) for a
to measure (de Levie, 2010), but it
Visiting Erskine Fellowship.
is a misconception that negative pH values are not possible when solutions of Hp+ activity (or concentration) in excess of 1 molar are possible (see Table II). This misconception may also cause difficulties in learning concepts associated with pH and strong acids.
Note Negative pH values are difficult to measure experimentally (e.g., Harris, 2002; Skoog, West, Holler, & Crouch, 2004) and there has been a lack of suitable buffer standards for pH < l. It is easier to report H30 + concentrations or total acid concentrations in the 10° -102 mol L - I range than imprecise negative pH values.
Literature cited Acids with polyatomic ion s. (2005, 3 March 2005) Retrieved 7 June 2012, from http://www.able2know.com/ forum s/ about46629.html Allaby, M. (Ed.). (1998). Th e Oxford Dictionary of Ecology (2nd ed.). Oxford: Oxford University Press. Argon Bulletin Board. (2001, 16 January 2001) . Negative pH? Retrieved 21 April 2005, from http://forum .argon.acad .bg/ html/ Forum8/HTMLl000003.htm l Ashcroft, F. M. (2000). Life at the Extremes. Berkeley (CA): University of California Press. Bobick, J. E., & Balaban, N. E. (Eds.). (2003). The Handy Science An swer Book. Canton (M I) : Visibl e Ink Press. Brunner, J. S. (19(6). Toward a Theory of Instruction. New York: W. W. Norton & Company. Burton, R. F. (2007). Defining and teaching pH. Journal of Chemical Education, 84(7), 1129. doi: DOl: 10.1021 / ed084pl129 Clarke, A. N. (2003). Dictionary of Geography (3rd ed.). London : Penguin.
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LabTalk Vol 56 • NO.3· 2012
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Why students should learn about negative pH
Cobb, c., & Fetterolf, M. L. (2005). The Joy of Chemistry: The amazing science of familiar things. Amherst (NY): Prometheus Books. Cochrane, H., & Devlin, J. (2000). Heinemann Science Links 2. Port Melbourne: Heinemann. de Levie, R. (2010). Potentiometric pH measurements of acidity are approximations, some more useful than others. Journal of Chemical Education, 87 (11),1188-1194. doi : DOl : 10.1021 / ed1000262 Denni ston, K. J., Topping, J. J., & Caret, R. L. (2001). General, Organic, and Biological Chemistry (3rd ed.). New York: McGraw-HilI. Dickerson, R. E., Gray, H. B., & Darensbourg, M. Y. (1984). Chemical Principles (4th ed.). Menlo Park (CA) : Benjamin Cummings. Dictionary of Science. (2003). Glasgow: HarperCollins. Dictionary of Science and Technology. (2003). Bloomsbury. Dunn, R., & Griggs, S. A. (1988) . Learning Styles: Quiet Revolution in American Secondary Schools. Reston (VA) : National Asst)ciation of Secondary School Principals. Dunn, R., & Griggs, S. A. (Eds.). (2000) . Practical Approaches to Using Learning Styles In Higher Education. Westport (CT): Bergin & Garvey. Edwards, K. J., Bond, P. L., Gihring, T. M., & Banfield, J. F. (2000). An Archaeal iron-oxidizing extreme acidophile important in acid mine drainage. Science, 287(5459), 1796-1799. Evans, M., Lipson, K., Jones, P., Blain, D., & McCoy, T. (1996) . Essential Mathematical Methods. Units 3 & 4 (2nd ed.). Malvern (Vic): Coghill. Ganderton, G. D., & McLeod, J. M. (1996). Mathematics for Australian Schools. Year 7 (3rd ed.). South Melbourne (Vic): MacMillan Education Australia. Gellert, w., Gottwald, S., Hellwich, M., Ka stner, H., & Kustner, H. (Eds.). (1989). The VNR Concise Encyclopedia of Mathematics (2nd ed.). New York: Van Nostrand Reinhold. Gunstone, R. F. (2005). Rethinking physics content - How we teach impacts on what we teach [Keynote address] . Paper presented at the VCE Physics Teachers' Conference, Melbourne.
14 LabTalk Vol 56 • No.3' 2012
(continued)
Harris, D. C. (2002). Quantitative Chemical Analysis (6th ed.). New York: W.H . Freeman and Company. Hayhew, S. (2004). The Oxford Dictionary of Geography (3rd ed.). Oxford: Oxford University Press. Hogendoorn, B., Common s, c., Jarrett, S., McKenzie, c., Moseley, w., Porter, M., & Williamson, M. (2010). Heinemann Chemistry 2 (Enhanced 4th ed.). Port Melbourne: Pearson Education Australia. Ivanov, V. V. (1955). Geokhimiya, 1(1), 63 . Kolb, D. A. (1984). Experiential Learning : Experience as the Source of Learning and Development. Englewood Cliffs (NJ) : Prentice Hall. Kruszelnicki, K. (1997) . Flying La sers, Robofish and Cities of Slime. Pymble (NSW) : HarperCollins. Lafferty, P., & Rowe, J. (Ed s.). (1998). The Hutchinson Dictionary of Science (2nd ed.) . Oxford: Helicon. Lake Access. (n.d.). pH : Measuring the acidity and alkalinity of lakes Retrieved 7 June 201 2, from http://lakeaccess.org/ russ/ pH.htm Lim, K. F. (2006). Negative pH does exist. Journal of Chemical Education, 83(10), 1465. Lofts, G., & Merett, M. J. (2000). Science Quest 2 (2nd ed .). Milton (Qld): Jacaranda Wiley. McCarty, C. G., &Vitz, E. (2006). pH paradoxes: Demonstrating that it is not true that pH = -log[WJ . Journal of Chemical Education, 83 (5), 752-757. doi: DOl : 10.1021 / ed083p752
Nordstrom, D. K., & Alpers, C. N. (1999). Negative pH, efflorescent mineralogy, and con sequences for environmental restoration at the Iron Mountain Superfund site, California. Proceedings of the National Academy of Science (USA), 96(7),3455-3462. Nord strom, D. K., Alpers, C. N., Ptacek, C.
J., & Blowes, D. W. (2000). Negative pH and extremely acidic mine waters from Iron Mountain, California. Environmental Science and Technology, 34(2), 254 -258. pH. (1993) Retrieved 7 June 2012, from http://www.newton.dep.anl.gov / newton/ askasci / 1993/ chem/ CHEM028.HTM Rapp, N. (2003, 26 February 2003). Study Guide: Chapter 14, Acids and Bases and Chapter 15, Ionic Equilibria of Weak Electrolytes and Solubility Product Principle Retrieved 21 April 2005, from http://www.chemistrygeek.com/ c2c15 . htm Roberge, P. (1 999a, 2005). pH and corrosion Retrieved 7 June 2012, from http://www.corrosi 0 n-d octors.org/ Cooling-Water-Towers/ ph.htm Roberge, P. (1 999b, 2005). Standard hydrogen electrode (SHE) Retrieved 21 April 2005, from http://www. corrosion-doctors.org/ References/ hydrogen.htm Roebuck, C. M. (2000). Excel Preliminary Chemistry. Glebe (NSW): Pascal Press. Senese, F. (2005, 19 January 2005). Is a negative pH possible? Retrieved 21 ApriI2005,"from http://antoineJrostburg . edu/ chem/ senesei 101 / acidbase/ faq / negative-pH.shtml
Monk, P. (2004) . Physical Chemistry: Understanding our chemical world. Chichester (UK) : Wiley.
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Negative pH's? (1999) Retrieved 7 June 2012, from http://www.newton .dep.anl. gov/ askasci/ chem99/ chem99230.htm
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Volume 56 Number 3 - 2012
The Secondary Science Journal ofthe Science Teachers' Association of Victoria Inc.
~~'''''I:~
~~ Founded 1943
Contents
Labtal
Volume 56· Number 3 • 2012
LabTalk Vol 56 - No.3 LabTalk is the quarterly journal of the Science Teachers' Association of Victoria, which was founded in 1943. Articles in this journal primarily cover issues and discussions related to the teaching and learning of science at Secondary School level. LabTalk provides a means for communication between members and allows the sharing of ideas, perspectives, concerns and information with the aim of fostering . ff . • co -operative e orts to Improve science education.
Contents Page
Article
Author
2
President's viewpoint ..................................................... Soula Bennett
3
The square kilometre array: From dark energy to green energy ................................................................................... Professor Brian Boyle
5
Putting stars in their eyes .................................... Jacinta den Besten
8
Blow up the science laboratory - safely! .................. John Widmer
10
Why students should learn about negative pH ....................... .. Dr Kieran F. Lim
15
Posting science ........................................................................ John Gipps
18
Book reviews ................................................................................................. .
20
Science spriral crossword .....................................................Pat O'Shea
Graphic design & typesetting STAY Publications
21
Cryptic science ......................................................................... Pat O'Shea
Advertising STAV Publications Officer Email:
[email protected] u
22
Who or what am I? ..................................................................Pat O'Shea
Managing Editor STAV Publishing
...
Published by Science Teachers' Association of Victoria Inc. 5 Munro Street Coburg VIC 3058 Telephone: 9385 3999 Fax: 9386 6722 Website: www.stav.org.au ISSN 0159-2033
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Correspondence regarding thi s journal should be addressed to: LabTalk Managing Editor STAV PO Box 109 Coburg VIC 3058 or emai l:
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LabTalk Vol 56 • No.3 • 2012
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