Dealing With the pH Concept at High School

7/29/2019 Dealing With the pH Concept at High School

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J o h n n i e M u w a n g a Z a k e (B .Sc ., B .Ed ., M.Sc ., M.Ed ., Ph D, P.G.C.E., P.G.D.E.) P a g e 1 2 0 0 6 - 0 7 - 2 5 1

A theoretical framework of the pH concept at high school

Muwanga-Zake, J. W. F. (B.Sc., B.Ed., M.Sc., M.Ed., PhD, P.G.C.E., P.G.D.E.)Centre for the Advancement of Science and Mathematics Education (CASME),

University of KwaZulu Natal, Durban. South Africa.

Cell: (027) 0 730632051Office: (027) 0 31 2603418

CASME,University of KwaZulu Natal,P O Box 10607, Ashwood 3605.Republic of South Africa

Key words: Negative pH values; Super Acids; Weaknesses of the Lowry-Brnsted model

ABSTRACT

Literature shows that the concept of pH face conceptual challenges, especially outside the 0-14range that it requires further debate. The concern of this discussion is the aspects of pH taught atschool. I suggest how best to teach pH in such a way that pH values outside the normal 0 14range are understood and speculate on what negative pH values could mean. The discussion

does NOT provide an authoritative understanding of pH, that chemistry gurus might have.

INTRODUCTION

Although technology has eased the rigours of measurements, a conceptual understanding of pH is still vitalto improve conceptual understanding and technology further. Conceptual problems emanate from caseswhere the concentration of hydronium ions is beyond the range of 10 0 10-14 mol.dm-3, for which we haveto account for pH values of less than 0 or greater than 14. For example, 1.5 Molar acids would yield a pHof 0.17 assuming complete dissociation. I am particularly concerned with situations when the pH is lessthan 0 because 1 Molar or greater acid concentrations are common in school laboratories.

In order to gain entry into conceptual understanding for learners I propose that the teacher covers thefollowing topics first:

Chemical bonding, with focus on the uniqueness of hydrogen bonds, especially in water The structure and properties of the water molecule A mention of energies involved in the formation or dissociation of acids in water (Heat of

Dilution) Chemical equilibrium, and the meaning of equilibrium constants Logarithms, especially in Base 10

On addition, I think the following knowledge is important in introducing a lesson on pH.

THE MEANING OF K

The equilibrium constant K defines the ratio of the concentrations of the products (e.g. dissociatedions) and the reactants (e.g. un-dissociated molecules). For example, the dissociation constant K of

a molecule HA is given as[ ][ ]

[ ]HAAH

K+

= ; brackets denote concentration. K apparently originated

from: Arrheniuss theory that the molecule of an electrolyte can give rise to two or more electrically

charged atoms or ions; and The Law of Mass Action (by two Norwegians, Gulberg & Waage), that if the dissociation happens in

a solvent, at saturation, we can call the constant, a solubility constant. The dissociation processmight be endothermic or exothermic.

It should also be noted that an equilibrium sign does not apply to irreversible reactions, such as where agas is liberated and lost to the environment. Second, it is wrong to represent equilibrium by two unequalarrows pointing in opposite directions, as often seen in some textbooks. This mistake, often wronglyapplied to show which direction of the equilibrium is favoured, should be avoided. We have to differentiate

Important: Most constants referred to in chemistry such as Kc, Kw, Ka, and Kb are temperature-dependent, and often are assumed to be quoted at 25 C, i.e. average room temperature


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between the quantities yielded (perhaps as a result of a change in conditions surrounding the equilibrium i.e. Le Chateliers principle), and the state of dynamic equilibrium.

At equilibrium, the number of products being formed is exactly equal to the number being broken down tore-form reactants. That is, the RATE of the forward reaction is exactly equal to the rate of the reversereaction. Therefore, the arrows must be equal to indicate that the forward rate equals the reverse rate. Forexample, a weak acid (HA) dissociates reversibly in water:

WATER

Pure waterConsider 1000 ml of water with a density of 1.00 g/ml - this 1.00 litre (1000 ml or 1 dm. 3) would weigh 1000grams. This mass divided by the molecular mass of water (18.0152 g/mol) gives 55.5 moles. The "molarity"of this water would then be 55.5 mol / litre or 55.5 M.

Autoprotolysis of pure waterThe following equation describes the reaction of water with itself (called autoprotolysis):H2O + H2O H3O

+ + OH. The equilibrium constant for this reaction is written as follows:

[ ][ ]OHOHOHOH

K22

3+

=

However, in pure liquid water, [H2O] is a constant, and together with K produces Kc. Thus, Kc = [H3O+]

[OH]. This constant Kc, also known as Kw, is called the water autoprotolysis constant or waterautoionization constant. It is assumed to obtain in dilute solutions, and may not strictly apply toconcentrated solutions. Many factors such as temperature and the nature of solute would affect thisequilibrium.For example, while Kw has been shown to be 1.011 x 10

14 at 25 C (generally, a value of 1.00x 1014 is used), Kw = 10

-12.3 at 100 C.

The equation above shows that concentrations of H3O+ and OH are in the molar ratio of one-to-one, and

so [H3O+] = [OH]. Therefore, [H3O

+] and [OH] = Kw, which is 10-7 M in pure water at 250C. This leads to

important models of acids and bases, not least the pH scale, since most acids and bases express theirproperties when they are dissolved in water.

The implication of [H3O+][OH-] = 10-14 at 250CNote that [H3O

+][OH-] = 10-14 at 250C, and so [H3O+] = 10-7 in pure water implies that for every one H3O

+,

there are 10,000,000 (i.e. 107) un-dissociated water molecules at 250C. The amount of H3O+ increases by

adding acidic compounds. Adding an alkaline compound increases OH-. The range of both [H3O+], and

[OH-] is between 100 and 10-14 at 250C. That is, it is not possible to have, for example, a range of 1020 to10-34 for [H3O

+], and [OH-] even though 1020 x 10-34 = 10-14.

ACIDS AND BASES

Definitions evolve and change over time. There were definitions of acids and bases before the currentpopular ones such as:

1. Lavoisier (1776) an acid is an oxide of nitrogen, phosphorus, sulphur and the halogens (e.g.,SO3 + H2O forms H2SO4)

2. Liebig (1838) an acid is a compound in which the hydrogen can be replaced by a metal (e.g.,2HCl + Zn gives ZnCl2 + H2)3.

AcidAccording to Park (1998), the word acid comes from the Latin word acere, which means 'sour'. All acidstaste sour. Well known are vinegar, sour milk, lemon juice, aspirin (acetosallicylic acid).

Alkaline/baseThe word alkaline could be from the Arabic al-qily, which means, 'to roast in a pan" or "the calcinatedashes of plants. The word "base" might come from bassus, which is Latin for low. There are numerousdefinitions of acids and bases, most of which relate with water solutions.

Why bases are slippery between our fingers!

Bases feel slippery, sometimes people say soapy. This is because they dissolve the fatty acidsand oils from your skin and this cuts down on the friction between your fingers as you rub themtogether. In essence, the base is making soap out of you, because the preparation of soap is analkali plus a lipid.


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ArrheniusA Swedish chemist, Svante August Arrhenius (1859-1927), defined an acid as a substance, which releaseshydrogen ions in solution, and a base as a substance, which forms hydroxyl ions. Wilhelm Ostwaldfollowed up this idea and calculated the dissociation constants Ka, which is a measure of an acid'sstrength, starting with water as a neutral compund. Thus, the Arrhenius-Ostwald definition is based uponthe Autoprotolysis of water. In 1904, H. Friedenthal recommended that the hydrogen and hydroxyl ionconcentration be used to characterize solutions, since the [OH-] = 10-14 [H3O

+].

Now, it is widely argued that hydrogen ions cannot exist in water because hydrogen ions are actuallyprotons, and so have a high electric field intensity because of their small size. Furthermore, bases such asNH3 that do not have the OH

- group are excluded from Arrheniuss definition.

Lowry and BrnstedIn 1923, Johannes Nicolaus Brnsted (Denmark) and Thomas Martin Lowry (England) publishedessentially the same theory about how acids and bases independently of one another, so both names havebeen used for the theory name. Cited in Hawkes (1992)

Brnsted: " acids and bases are substances that are capable of splitting off or taking up hydrogenions, respectively." Here is a more recent way to say the same thing:

An acid is a substance from which a proton can be obtained. A base is a substance that can remove a proton from an acid.

T. M. Lowry, in his paper "The Uniqueness of Hydrogen" Chemistry, and Industry 42 (19 January 1923) pp.43-47, argued:

"It is a remarkable fact that strong acidity is apparently developed only in mixtures and never in purecompounds'. For example, pure H2SO4 is weak and hydrogen chloride only becomes an acid whenmixed with water. This can be explained by the extreme reluctance of a hydrogen nucleus to lead anisolated existence. It seems that plenty of water is needed to enable the release of all protons and thisis probably why the Lowry- Brnsted seems to have problems with concentrated acids.

Note:1. The difference between Lowry and Brnsted; - Brnsted used H+, but Lowry, used the H3O

+ that iscommonly used today.

2. A substance acts as an acid or base in relation to a solvent usedbecause there are a variety of

solvents in which a transfer of protons can happen. The acid increases the cationic species(hydrogen ions) natural to the solvent. For enrichment, consider dissolving acetic acid in water,and then in sulphuric acid, and in alcohol..

3. With regard to Lowry - Brnsted, acidity is really a measure of how strong the water molecule is,compared to the base in the acid molecule (H-Base).

Note that Energy is required to break the bond between the Hydrogen proton and the base in the acid Energy is probably released from the bonding between the Hydrogen protons with a water molecule. The balance between these energies plays a role in determining whether an acid dissociates or not,

whether the acid is strong or weak, and whether the dissolution process would be endothermic orexothermic.

In conclusion, we can take an acid to be a substance in which hydronium ions are more concentrated than

hydroxyl ions and a base as a substance in which the hydroxyl ions are more concentrated than hydroniumions.

IT IS NOT EXACTLY CORRECT TO SAY THAT ACIDS "DONATE PROTONS"

It is unlikely that acids simply donate protons since those protons have to be broken off a base i.e., thebase holds on its dear proton. Hence, the formation of acids requires energy. Bases have different affinitiesfor protons. A base has to be stronger than the one in the acid to pull off the proton from the acid.Therefore, the acid molecule does not "give" or "donate" as stated for example in Brink & Jones (1979;160), and Toon & Ellis (1973: 475). Bases that have a greater desire for protons take possession of theproton by force, except in some rare cases where complex ions repulse protons. I have therefore replaced'donor' by 'loser' in this paper.

STRENGTH OF ACIDS AND BASES

When an acid is added, the water molecule acts as a base and pulls the proton from the acid molecule.The acid is strong when the base in it is weaker than the water molecule and the acid is weak when thebase in it is stronger than the water molecule.


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Strong acids and basesThe key point is that strong means 100% ionised and K is extremely high that talking of equilibrium ofstrong acids and bases in dilute solutions does not make much sense. The water molecule is stronger than the base in strong acids. It is assumed that all the acid

dissociates, and all its protons are in solution. Examples of strong acids in schools includeHydrochloric acid, Sulphuric acid, and Nitric acid.

The water molecule is stronger than the acid in the base. When a base is added to water, thewater molecule acts as an acid. The base molecule pulls the hydrogen proton from water, leavingbehind the OH- behind. There are almost no un-dissociated base molecules in solutions of strongbases. Strong bases at school include Sodium hydroxide and Ammonium Hydroxide.

Weak acids and basesThe K value is often less than 1 in weak acids and bases. With weak acids and bases, we can talk ofequilibrium because the acids or bases partially dissociate. This is because water cannot grab all theprotons from such acids or all the hydroxyl ions from bases. Consequently, for acids, a measurement of[H+] does not give the total amount of hydrogen ions available because some of the hydrogen remainsassociated with bases in acid molecules. However, if a weak acid is titrated against a dilute base, theundissociated molecules progressively dissociate and eventually the total hydrogen ion concentration canbe found. This is why the "titratable acid" is distinguished from the actual acidity (pH). With strong acids,the titratable acid and acidity are assumed the same.

K values of polyprotic acidsWhile monoprotic acids release only one proton per acid molecule, polyprotic acids are able to lose morethan one proton per acid molecule. A diprotic acid (here symbolized by H2A) can undergo one or twodissociations depending on the pH. Each dissociation has its own dissociation constant, K a1 and Ka2.

H2A(aq) + H2O(l) H3O+(aq) + HA(aq) Ka1: and HA

(aq) + H2O(l) H3O+(aq) + A2(aq) Ka2

The first dissociation constant is typically greater than the second; i.e., Ka1 > Ka2 , the reason being that thebase in the acid molecule hangs on to the protons left more strongly. For example, sulphuric acid (H 2SO4)can lose one proton to form the bisulphate anion (HSO4

), for which Ka1 is very large; then it can lose asecond proton to form the sulphate anion (SO4

2), wherein the Ka2 is intermediate strength.

Conjugate Acid-Base Pairs

Let's look at the reaction of NH3 and H2O again:(1) NH3 + H2O NH4

+ + OH-The reverse of this reaction is:

(2) NH4 + OH- NH3 + H2O

In this case, NH4+ acts as an acid, which loses a proton to OH-. OH- acts as a base. An acid and a base

that are related by the gain and loss of a proton are called a conjugate acid-base pair. For example, NH4+

is the conjugate acid of NH3, and NH3 is the conjugate base of NH4+. Every acid has associated with it a

conjugate base. Likewise, every base has associated with it a conjugate acid.

Conjugate Acid-base Pairs tend towards weaker acids and basesTake the example: HCl + H2O H3O

+ + Cl-. In general, in acid-base reactions such as this,equilibrium favours the production of the weaker acid (e.g. H3O

+) and base (e.g. Cl). Put simply, the acid

produced has a stronger base than that in the acid, which lost the proton (i.e. H 2O base is stronger than Cl

-

). We may in fact consider acid-base reactions as a competition in which bases fight for protons.

Amphoteric substancesAn Amphoteric substance can behave as an acid or as a base depending upon the surroundings,especially the pH. For example, aluminium hydroxide reacts with acids as a base:

Al(OH)3 + 3H+ Al3+ + 3 H2O and as a base with acids; and in reaction with bases it will act as an acid

Al(OH)3 + 2OH- AlO2

- + H2O

WHAT IS pH?

Origins of the symbol pHThere are varied claims about the origins of the symbol pH. Wikipedia (at http://en.wikipedia.org/wiki/PH)

gives various sources. It states that this concept was introduced in 1909 by the Danish chemist SrenSrensen as a convenient way of expressing acidity. pH purportedly means "pondus hydrogenii" in Latin.Other sources attribute the name to the French termpouvoir hydrogne, while in English, pH can stand for


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"power of hydrogen," or "potential of hydrogen." While Srensen used to write PH, the Compact OxfordEnglish Dictionary states that the modern notation 'pH' was first adopted in 1920 by W. M. Clark (inventorof the Clark oxygen electrode) for typographical convenience, and claims that the "p" stands for theGerman word for "power",potenz, so pH is an abbreviation for "power of hydrogen". Thus, "p-Functions"have also been adopted for other concentrations. For example, "pCa = 5.0" means a concentration ofcalcium ions equal to 10-5 M.

DefinitionThe IUPAC definitionIUPAC endorsed a pH scale based on comparison with a standard buffer of known pH usingelectrochemical measurements. IUPAC restricted the pH range to dilute aqueous solutions of less than 10 -1 mol.dm3: 2


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WHAT DO YOU MEAN pH = -1?

A pH = -1 implies that [H3O+] = 10 M or 101 moles/dm3. Any concentration of H3O

+ (i.e. [H3O+], and not of

the acid molecules) greater than 1M would translate into a pH that is < 0; i.e. would be negative. A 12MH2SO4 would have a pH of 1.08 and then 1.38, 11M HCl would have a pH of 1.04, etc. However, suchpH values might be meaningless in the Lowry- Brnsted model.

What does this argument say about water?

Water acts as a base when an acid is introduced into it, and water has to be stronger than the base in theacid to pull the proton away from the acid, if a substance is to fit the definition of a Lowry- Brnsted acid.For example, the pull that water exerts upon the proton in HCl, is stronger than the pull between theHydrogen ion (proton) and the Chloride ion (base). What is not clear though is how many water moleculessurround or pull the Hydrogen ion.

Heat of Dilution of Acids tables show that the overall process of acid dilution is generally exothermic, but,apparently, as long as there are enough water molecules to pull those protons. Once the proton has beentorn off the acid molecule, it has a very high electrical field intensity (because it is very small) that forces itinto water molecules. It seems that a lot of water molecules are needed to break away H + ions from acidmolecules given that in pure water, every H+ mole is associated with 107 moles of water. We earlierestablished that 1 mole of H3O

+ is accommodated by 55.5 moles of water molecules. Or1 molecule ofH3O

+ requires 55.5 x 6 x 1023 molecules of waterin a Molar solution of an acid. Hence the capacity of

water to tear off and accommodate acidity(H3O+

ions) is limited.

Let us take a 2M acid molecules - in the Lowry-Bronsted model, it can only release 1M of H 3O+ ions in 1

dm3 and beyond that a solution cannot take anymore H3O+ ions or more protons because the Lowry-

Bronsted pH cannot be negative. A 2M acid is not at liberty to release more than 1 mole of its hydrogenions into a dm3. Put differently, the Lowry-Bronsted model tells us that no more H3O

+ ions can be formedbeyond [H3O

+] = 1M or 100 moles/dm3 at 250C. Another limitation could be energy requirements, sincewater molecules must find energy to pull the hydrogen ions away from the bases in the acid. Any otherH3O

+ ion introduced increases the Molarity beyond 1M (i.e., beyond 100M) and would lower internal energyof the solution further.

These un dissociated H+ ions are however accessible, firstly because water and acids mix in allproportions. The H+ ions are accessible and measurable by titration because the base introduces more

water as well as basic ions. This implies that the extra water liberates more H+

ions from the acidmolecules to form a surplus of H3O

+ beyond [H3O+] = 1M or 100 moles/dm these lower the pH to negative

values. Thus, a negative pH becomes meaningless to the Lowry - Brnsted model since it contradicts itselfto the possibility that [H3O

+] can exceed 100M, at 250C, but is measurable.

THE CONCEPT OF SUPER ACIDS

With suitable equipment, we can prepare pure acids with no water in them (and would not be acids by theLowry - Brnsted model because they do not have H3O

+). Such acids would have a pH < 0 because everydrop of water introduced is consumed and are called super acids (Cotton, Wilkinson, & Gaus, 1987: 221).Super acids are used to provide protons, and are believed to force substances to accept protons. Similarly,there are super bases.

According to Cotton, Wilkinson, & Gaus (1987: 221), super acids are necessarily non aqueous since theacidity of any aqueous system is limited by the fact that the strongest acid that can exist in the presence ofwater is H3O

+. In that system, a stronger acid than H3O+ loses its proton to H2O to form more of H3O

+. Theacidity scale goes beyond the normal pH scale, and uses the Hammett acidity function: H0= pkBH

+- log

[BH+]/[B], where B is the base and BH+ is its protonated form. pKBH+ is log K for the dissociation of BH+.

By using bases with very negative pKBH+ values, the H0scale may be extended to negative values. The H0

scale becomes identical to the pHscale in dilute aqueous solution. On this scale, pure H2SO4 (1012 M) has

a H0value of 12 (instead of the LowryBrnsted value of 1.08), and for Oleum, aboutH0 = 15, etc. Takenote that the Hammett acidity function clearly avoids water in its equation.

In other cases, pH has been defined as pH = -log aH+ where aH+ is the hydrogen ion activity. In solutionsthat contain other ions and under varied conditions, activity and concentration are not the same. Theactivity indicates the hydrogen ions that are active, rather than the true concentration; it accounts for the

fact that other ions and conditions surrounding the hydrogen ions might shield them and affect their abilityto participate in chemical reactions.


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How about other factors?We have already seen that temperature is a factor. Other conditions include substances in solution, thenature of solvent, as well as pressure. These factors are likely to be even more effective in acids that candissociate or evaporate to form gases such as hydrogen chloride. Thus, two solutions with the sameamount of hydrogen could have different amounts of hydrogen ions (protons) available, and thereforedifferent pH values. Similar hydrogen ion (proton) concentrations would register different pH values indifferent solvents because the neutral pH is different for each solvent. For example, the concentration ofhydrogen ions in pure ethanol is about 1.58 10

-10M, so ethanol is neutral at pH 9.8. A solution with a pH

of 8 would be considered acidic in ethanol, but basic in water!Think about a solution of water in anacid.Again, we see a limitation to the application of the pH scale based on the Lowry- Brnsted theory.

ACIDITY IS NOT LIMITED TO TRANSFER OF HYDROGEN IONS

IntroductionThere are other definitions of acids and bases that are often never mentioned in school curricula. Thissection is therefore enrichment for a school science teacher

Lewis Theory of Acids and Bases acidity as a transfer of chargesIn 1923, an American Gilbert Newton Lewis (1875-1946) argued that acids and bases are not tied to wateror restricted to transfer of protons (i.e., to protic,(lso known as protolytic, protonic reactions). Lewissuggested that it is the charges that move between acids and bases: Well, it is true that a proton is apositive charge and, in fact, Lowry mentioned a transfer of H+ between octets in protic reactions. However,Lewis is concerned with electron transfer: an acid is an electron-pair acceptor, and a base is an electron-

pairloser. (e.g., BF3 acid + CH3N base CH3N:BF3) This definition bears similarity with the

Usanovich model (1939) (e.g., Na base+ Cl acid NaCl)

Firstly, the Lewis model bears similarity with Lowry- Brnsted model in terms of charge. The Lowry-Brnsted acid also gets its oxidation number reduced by losing a proton (H +) and the Lowry- Brnstedbase gets its oxidation state increased by stealing a proton.

Secondly, the Lewis definition bears resemblance with definitions of a reducing agent and an oxidisingagent respectively. The difference is that Lewiss definition applies to an un-shared pair of electrons in theouter energy level. Check out Lewis hard and soft acids and bases for enrichment.

Lux-Flood definition of acids and bases.Derived in 1939, the Lux-Flood model regards an acid as an oxide (O 2-) acceptor and a base as an oxide(O2-) loser. Again, we can see a similarity with Lewis's notion of charge transfer. By an acid accepting (O2-),it is actually accepting an extra pair of electrons. This is an important definition in geological chemistry.

IMPLICATIONS FOR TEACHING/LEARNING ABOUT pH

ProblemsThere are often problems with demonstrating or proving concepts in a school environment. I am not evensure whether negative pH should be taught at all, although I think that knowledge improves the conceptualunderstanding of pH. Knowledge about other ways of measuring acidity suffers from analysis based in theLowry- Brnsted model. Yet, one way of challenging or scrutinising the Lowry- Brnsted model might be

outside the Lowry- Brnsted model itself, especially with regard to the limitations and constraints that theLowry- Brnsted model places upon the pH.

A need to investigateWe should develop a culture of consulting widely and of opening up to new conceptual frameworks thatchallenge our current schemas. School curricula often leave out fundamental assumptions that surroundimportant concepts. The pH concept is an example in this regard. However, rather than waiting for someauthority to provide already shifted knowledge, teachers should try to test some claims in a schoollaboratory or through logical but open discussions with their colleagues and learners.

What should we teach and how?Traditionally, we tend to teach Arrheniuss definition first. However, learners seem to easily confuseArrheniuss definitions with the more acceptable Brnsted-Lowry definitions. Hawkes (1992) argues

It is inherent in human nature that we accept what we are told first and relinquish or change it withdifficult. The Brnsted-Lowry approach should be presented first, because it is simpler.


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Whatever you start with, make sure that you broaden your learners' minds about limitations in the pHmodels.

CONCLUSION

Educators have to critically debate issues that seem to be taken for granted and form networks throughwhich they can share knowledge, especially drawing upon their experiences in class, and be ready toprovide logical answers to their learners when they end up with funny values such as negative pH values.

It might be necessary to introduce the concept of Super Acids to learners since they are exposed to acidswhose Molarity is greater than 1 at school.

REFERENCES

Brink, B. P. & Jones, R. C. 1979.Physical Science 10.Juta & Co, Ltd. Cape Town.

Cotton, F. A., Wilkinson, G., & Gaus, P. L. 1987. Basic Inorganic Chemistry. John Wiley & Sons.New York.

CRCHandbook of Chemistry and Physics. 1st

Student Edition. 1987

Ellis, H. Eds.1984. Revised Nuffield Advanced Science Book of Data. Longman Group (FE) Ltd.Hong Kong.

Hawkes, S. J., 1992. Arrhenius Confuses Students. Journal of Chemical Education, Vol. 69, No. 7; July1992; pages 542-543.

IUPAC Online [Available] www.iupac.org [15th July 2002]

Park, J. L., 1998. Acids and bases. Online. [Available] http://dbhs.wvusd.k12.ca.us/AcidBase/Acid-Base[7th July 2002]

Toon, E. R. & Ellis, G. L. 1973. Foundations of Chemistry. Holt, Rinchart & Winston, Inc. New York.

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Dealing With the pH Concept at High School