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*Litmus is a natural dye found in certainlichens. The name is of Scandinavian origin,e.g. lit (color) + mosi (moss) in Icelandic."Litmus test" has acquired a meaning thattranscends both Chemistry and science todenote any kind of test giving a yes/noanswer.

On this page:

Acids

Acids and the hydrogen ion

Bases

Neutralization

What you should be able to do

Concept map

Chem1 General Chemistry Virtual Textbook → Acid­base concepts → Introduction

Introduction What is an acid? What is a base?

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The concepts of an acid, a base, and a salt are very oldones that have undergone several major refinements aschemical science has evolved. Our treatment of thesubject at this stage will be mainly conceptual andqualitative, emphasizing the definitions and fundamentalideas associated with acids and bases. We will not covercalculations involving acid-base equilibria in theselessons.

1 AcidsThe term acid was first used in the seventeenth century; it comes from theLatin root ac­, meaning “sharp”, as in acetum, vinegar. Some early writerssuggested that acidic molecules might have sharp corners or spine­likeprojections that irritate the tongue or skin.

Acids have long been recognized as a distinctive class of compounds whoseaqueous solutions exhibit the following properties:

A characteristic sour taste(think of lemon juice!);

ability to change the color oflitmus* from blue to red;

react with certain metals toproduce gaseous H2;

react with bases to form a saltand water.

How oxygen got mis­named

The first chemistry­based definition of an acid turned out to be wrong: in1787, Antoine Lavoisier, as part of his masterful classification ofsubstances, identified the known acids as a separate group of the “complexsubstances” (compounds). Their special nature, he postulated, derivedfrom the presence of some common element that embodies the “acidity”

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principle, which he named oxygen, derived from the Greek for “acidformer”.

Lavoisier had recently assigned this name to the new gaseous elementthat Joseph Priestly had discovered a few years earlier as the essentialsubstance that supports combustion. Many combustion products (oxides)do give acidic solutions, and oxygen is in fact present in most acids, soLavoisier’s mistake is understandable. In 1811 Humphrey Davy showedthat muriatic (hydrochloric) acid (which Lavoisier had regarded as anelement) does not contain oxygen, but this merely convinced some thatchlorine was not an element but an oxygen­containing compound.Although a dozen oxygen­free acids had been discovered by 1830, it wasnot until about 1840 that the hydrogen theory of acids became generallyaccepted. By this time, the misnomer oxygen was too well established aname to be changed. The root oxy comes from the Greek word οξνς,which means "sour".

2 Acids and the hydrogen ionThe key to understanding acids (as well as bases and salts) had to awaitMichael Faraday’s mid­nineteenth century discovery that solutions of salts(known as electrolytes) conduct electricity. This implies the existence ofcharged particles that can migrate under the influence of an electric field.Faraday named these particles ions (“wanderers”). Later studies onelectrolytic solutions suggested that the properties we associate with acidsare due to the presence of an excess of hydrogen ions in the solution. By1890 the Swedish chemist Svante Arrhenius (1859­1927) was able toformulate the first useful theory of acids:

"an acidic substance is one whosemolecular unit contains at leastone hydrogen atom that candissociate, or ionize, whendissolved in water, producing ahydrated hydrogen ion and an

anion."

[image link]hydrochloric acid HCl → H+(aq) + Cl–(aq)

sulfuric acid H2SO4→ H+(aq) + HSO4–(aq)hydrogen sulfiteion HSO3–(aq) → H+(aq) + SO32–(aq)

acetic acidH3CCOOH → H+(aq) +H3CCOO–(aq)

Strictly speaking, an “Arrhenius acid” must contain hydrogen. However,there are substances that do not themselves contain hydrogen, but stillyield hydrogen ions when dissolved in water; the hydrogen ions come fromthe water itself, by reaction with the substance. A more useful operationaldefinition of an acid is therefore the following:

An acid is a substance that yields an excess of hydrogenions when dissolved in water.

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The word “alkali” is often applied tostrong inorganic bases. It is of Arabicorigin, from al­kali ("the ashes") whichrefers to the calcined wood ashes thatwere boiled with water to obtain potash

There are three important points to understand about hydrogen in acids:

Although all Arrhenius acids contain hydrogen, not all hydrogen atoms in asubstance are capable of dissociating; thus the –CH3 hydrogens of acetic acidare “non­acidic”. An important part of knowing chemistry is being able topredict which hydrogen atoms in a substance will be able to dissociate intohydrogen ions; this topic is covered in a later lesson of this set.

Those hydrogens that do dissociate can do so to different degrees. The strongacids such as HCl and HNO3 are effectively 100% dissociated in solution. Mostorganic acids, such as acetic acid, are weak; only a small fraction of the acid isdissociated in most solutions. HF and HCN are examples of weak inorganicacids.

Acids that possess more than one dissociable hydrogen atom are known aspolyprotic acids; H2SO4 and H3PO4 are well­known examples. Intermediateforms such as HPO42–, being capable of both accepting and losing protons, arecalled ampholytes.

H2SO4sulfuric acid

→HSO4– hydrogensulfate ("bisulfate")ion

→ SO42–

sulfate ion

H2Shydrosulfuricacid

→ HS–hydrosulfide ion

→S2–

sulfide ion

H3PO4phosphoricacid

→H2PO4–

dihydrogen phosphateion

→HPO42–

hydrogen phosphateion

→ PO43–

phosphate ion

HOOC­COOHoxalic acid → HOOC­COO–

hydrogen oxalate ion→

–OOC­COO–

oxalate ion

You will find out in a later section of this lesson that hydrogen ions cannotexist as such in water, but don't panic! It turns out that chemists still findit convenient to pretend as if they are present, and to write reactions thatinclude them.

3 BasesThe name base has long been associated with a class of compounds whoseaqueous solutions are characterized by:

a bitter taste;

a “soapy” feeling when applied to the skin;

ability to restore the original blue color of litmus that has been turned red byacids;

ability to react with acids to form salts.

react with certain metals to produce gaseous H2;

Just as an acid is a substancethat liberates hydrogen ions intosolution, a base yieldshydroxide ions when dissolvedin water:

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which contains the strong base KOH,used in soap making. The element namepotassium and its symbol K (from theLatin kalium) derive from these sources.

NaOH(s) → Na+(aq) + OH–(aq)

Sodium hydroxide is anArrhenius base because itcontains hydroxide ions. However, other substances which do not containhydroxide ions can nevertheless produce them by reaction with water, andare therefore also classified as bases. Two classes of such substances arethe metal oxides and the hydrogen compounds of certain nonmetals:

Na2O(s) + H2O → [2 NaOH] → 2 Na+(aq) + 2 OH–(aq)

NH3 + H2O → NH4+(aq) + OH–(aq)

We can therefore define a base as follows:

A base is a substance that yields an excess of hydroxideions when dissolved in water.

4 NeutralizationAcids and bases react with one another to yield two products: water, andan ionic compound known as a salt. This kind of reaction is called aneutralization reaction.

This "molecular" equation is convenient to write, but we need to re­cast itas a net ionic equation to reveal what is really going on here when thereaction takes place in water, as is almost always the case.

H+ + Cl– + Na+ + OH–→ Na+ + Cl– + H2O

If we cancel out the ions that appear on both sides (and therefore don'treally participate in the reaction), we are left with the net equation

H+(aq) + OH–(aq) → H2O (1)

which is the fundamental process that occurs in all neutralization reactions.

Confirmation that this equation describes all neutralization reactions thattake place in water is provided by experiments indicating that no matterwhat acid and base are combined, all liberate the same amount of heat(57.7 kJ) per mole of H+ neutralized.

In the case of a weak acid, or a base that is not very soluble in water,more than one step might be required. For example, a similar reaction canoccur between acetic acid and calcium hydroxide to produce calciumacetate:

2 CH3COOH + Ca(OH)2 → CH3COOCa + 2 H2O

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If this takes place in aqueous solution, the reaction is really between thevery small quantities of H+ and OH– resulting from the dissociation of theacid and the dissolution of the base, so the reaction is identical with (1):

H+(aq) + OH–(aq) → H2O

If, on the other hand, we add solid calcium hydroxide to pure liquid aceticacid, the net reaction would include both reactants in their "molecular"forms:

2 CH3COOH(l) + Ca(OH)2 (s) → 2 CH3COO– + Ca2+ + 2 H2O

The “salt” that is produced in a neutralization reaction consists simply ofthe anion and cation that were already present. The salt can be recoveredas a solid by evaporating the water.

What you should be able to do

Make sure you thoroughly understand the following essential ideas whichhave been presented above.

Suggest simple tests you could carry out to determine if an unknownsubstance is an acid or a base.

State the chemical definitions of an acid and a base in terms of their behaviorin water.

Write the formula of the salt formed when a given acid and base arecombined.

Concept Map

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⇐index intro | pH | Brønsted | competition | electrons | structures | gallery

© 2007 by Stephen Lower ­ Simon Fraser University ­ Burnaby/Vancouver Canada

For information about this Web site or to contact the author, please see the Chem1 Virtual Textbook home page.

This work is licensed under a Creative Commons Attribution­NonCommercial 2.5 License.

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All chemical reactions thattake place in a singlephase (such as in asolution) are theoretically"incomplete" and are saidto be reversible.

On this page:

Ion product of water

pH ­ definition

The pH scale

Acid­base titration

What you should be able to do

Concept map

Chem1 General Chemistry Virtual Textbook →Acid­base concepts →pH and titration

pH and titration Aqueous solutions of acids and bases

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As you will see in the lesson that follows this one, water plays an essential role in acid-base chemistry as weordinarily know it. To even those who know very littleabout chemistry, the term pH is recognized as ameasure of "acidity", so the major portion of this unit isdevoted to the definition of pH and of the pH scale. Butsince these topics are intimately dependant on theproperties of water and its ability do dissociate intohydrogen and hydroxyl ions, we begin our discussion withthis topic. We end this lesson with a brief discussion ofacid-base titration— probably the most frequentlycarried-out chemistry laboratory operation in the world.

1 Dissociation of waterThe ability of acids to react with bases depends on thetendency of hydrogen ions to combine with hydroxideions to form water:

H+(aq) + OH–(aq) → H2O (1)

This tendency happens to be very great, so the reaction is practically complete— but not "completely" complete; a few stray H+ and OH– ions will always bepresent. What's more, this is true even if you start with the purest waterattainable. This means that in pure water, the reverse reaction, the"dissociation" of water

H2O → H+(aq) + OH–(aq) (2)

will proceed to a very slight extent. Both reactions take place simultaneously,but (1) is so much faster than (2) that only a minute fraction of H2O moleculesare dissociated.

Liquids that contain ions are able to conduct an electric current. Pure water ispractically an insulator, but careful experiments show that even the most highlypurified water exhibits a very slight conductivity that corresponds to aconcentration of both the H+ ion and OH– ions of almost exactly 1.00 × 10–7mol L–1 at 25°C.

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The quantity 1.00 x 10–14is commonly denoted byKw. Its value variesslightly with temperature,pressure, and thepresence of other ions inthe solution.

Problem Example 1

What fraction of water molecules in a litre of water are dissociated

Solution: 1 L of water has a mass of 1000 g. The number of moles in 1000 g ofH2O is

(1000 g)/(18 g mol–1) = 55.5 mol. This corresponds to (55.5 mol)(6.02E23 mol­1)= 3.34E25 H2O molecules.

An average of 10­7 mole, or (10­7)(6.02E23) = 6.0E16 H2O molecules will bedissociated at any time. The fraction of dissociated water molecules is therefore(6.0E16)/(3.3E25) = 1.8E–9.

Thus we can say that only about two out of every billion (109) water molecules willbe dissociated.

Ion product of water

The degree of dissociation of water is so small that you might wonder why it iseven mentioned here. The reason stems from an important relationship thatgoverns the concentrations of H+ and OH– ions in aqueous solutions:

[H+][OH–] = 1.00 × 10–14 (3) must know this!

in which the square brackets [ ] refer to theconcentrations (in moles per litre) of the substancesthey enclose.

This expression is known as the ion product ofwater, and it applies to all aqueous solutions, not justto pure water. The consequences of this are far­reaching, because it implies that if the concentration ofH+ is large, that of OH– will be small, and vice versa. This means that H+ ionsare present in all aqueous solutions, not just acidic ones.

This leads to the following important definitions, which you must know:

acidic solution [H+] > [OH–]

alkaline ("basic")solution [H+] < [OH–]

neutral solution [H+] = [OH–] = 1.00×10–7

mol L–1

Take special note of the followng definition:

A neutral solution is one in which the concentrations of H+ andOH– ions are identical.

The values of these concentrations are constrained by Eq. 3. Thus, in a neutralsolution, both the hydrogen­ and hydroxide ion concentrations are 1.00 × 10–7 mol L–1:

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[H+][OH–] = [1.00 × 10–7][1.00 × 10–7] =1.00 × 10–14

Hydrochloric acid is a typical strong acid that is totally dissociated in solution:

HCl → H+(aq) + Cl–(aq)

A 1.0M solution of HCl in water therefore does not really contain any significantconcentration of HCl molecules at all; it is a solution in of H+ and Cl– in whichthe concentrations of both ions are 1.0 mol L–1. The concentration of hydroxideion in such a solution, according to Eq 2, is

[OH–] = (Kw)/[H+] = (1.00 x 10–14) / (1 mol L–1) = 1.00 x 10–14 mol L–1.

Similarly, the concentration of hydrogen ion in a solution made by dissolving1.0 mol of sodium hydroxide in water will be 1.00 x 10–14 mol L–1.

2 pH

When dealing with a range of values (such as the variety of hydrogen ionconcentrations encountered in chemistry) that spans many powers of ten, it isconvenient to represent them on a more compressed logarithmic scale. Byconvention, we use the pH scale to denote hydrogen ion concentrations:

pH = – log10 [H+] (4) must know this!

or conversely, [H+] = 10–pH .

This notation was devised by the Danish chemist SørenSørensen (1868­1939) in 1909. There are several accounts ofwhy he chose "pH"; a likely one is that the letters stand for theFrench term pouvoir hydrogène, meaning "power ofhydrogen"— "power" in the sense of an exponent. It has sincebecome common to represent other small quantities in "p­notation". Two that you need to know in this course are thefollowing:

pOH = – log10 [OH–]

pKw = – log Kw (= 14 when Kw = 1.00 × 10–14)

Note that pH and pOH are expressed as numbers without any units, sincelogarithms must be dimensionless.

Recall from Eq 3 that [H+][OH–] = 1.00 × 10–14; if we write this in "p­notation" it becomes

pH + pOH = 14 (5) must know this!

In a neutral solution at 25°C, pH = pOH = 7.0. As pH increases, pOHdiminishes; a higher pH corresponds to an alkaline solution, a lower pH to anacidic solution. In a solution with [H+] = 1 M , the pH would be 0; in a0.00010 M solution of H+, it would be 4.0. Similarly, a 0.00010 M solution of

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NaOH would have a pOH of 4.0, and thus a pH of 10.0. It is very important thatyou thoroughly understand the pH scale, and be able to convert between [H+]or [OH–] and pH in both directions.

Problem Example 2

The pH of blood must be held very close to 7.40. Find the hydroxide ionconcentration that corresponds to this pH.

Solution: The pOH will be (14.0 – 7.40) = 6.60.[OH–] = 10–pOH = 10–6.6 = 2.51 x 10–7 M

The pH scale

The range of possible pH valuesruns from about 0 to 14.

The word "about" in the abovestatement reflects the factthat at very highconcentrations (10 Mhydrochloric acid or sodiumhydroxide, for example,) asignificant fraction of the ionswill be associated into neutralpairs such as H+·Cl–, thusreducing the concentration of“available” ions to a smallervalue which we will call theeffective concentration. It isthe effective concentration ofH+ and OH– that determinesthe pH and pOH. For solutionsin which ion concentrationsdon't exceed 0.1 M, theformulas pH = –log [H+] andpOH = –log[OH–] aregenerally reliable, but don't expect a 10.0 M solution of a strong acid to have apH of exactly –1.00!

The table shown here will help give you a general feeling for where commonsubstances fall on the pH scale. Notice especially that

most foods are slightly acidic;

the principal "bodily fluids" are slightly alkaline, as is seawater— not surprising,since early animal life began in the oceans.

the pH of freshly­distilled water will drift downward as it takes up carbon dioxidefrom the air; CO2 reacts with water to produce carbonic acid, H2CO3.

the pH of water that occurs in nature varies overa wide range. Groundwaters often pick upadditional CO2 respired by organisms in the soil,but can also become alkaline if they are in contactwith carbonate­containing sediments. "Acid" rainis by definition more acidic than pure water inequilibrium with atmospheric CO2, owing mainlyto sulfuric and nitric acids that originate fromfossil­fuel emissions of nitrogen oxides and SO2.

pH indicators

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The colors of many dye­like compounds depend on the pH, and can serve asuseful indicators to determine whether the pH of a solution is above or belowa certain value.

Here is a list of ordinary foods and household substances that can serve as indicators

Natural indicator dyes

Thebest

known of these is of course litmus,which has served as a means ofdistinguishing beween acidic andalkaline substances since the early18th century.

Manyflower

pigments are also dependent onthe pH. You may have noticed thatthe flowers of some hydrangeashrub species are blue when grownin acidic soils, and white or pink inalkaline soils.

Red cabbage is a popular make­it­yourself indicator. Here is a typical recipe.

Universal indicators

Most indicator dyes show only one color change, andthus are only able to determine whether the pH of asolution is greater or less than the value that ischaracteristic of a particular indicator. By combining avariety of dyes whose color changes occur at differentpHs, a "universal" indicator can be made.Commercially­prepared pH test papers of this kind areavailable for both wide and narrow pH ranges.

3 TitrationSince acids and bases readily react with each other, it isexperimentally quite easy to find the amount of acid in a solutionby determining how many moles of base are required toneutralize it. This operation is called titration, and you shouldalready be familiar with it from your work in the Laboratory.

We can titrate an acid with a base, or a base with an acid. Thesubstance whose concentration we are determining (the analyte)is the substance being titrated; the substance we are adding inmeasured amounts is the titrant. The idea is to add titrant untilthe titrant has reacted with all of the analyte; at this point, the number ofmoles of titrant added tells us the concentration of base (or acid) in the

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solution being titrated.

36.00 ml of a solution of HCl was titrated with 0.44 M KOH. The volume of KOHsolution required to neutralize the acid solution was 27.00 ml. What was theconcentration of the HCl?

Solution: The number of moles of titrant added was (.027 L)(.44 mol L–1) = .0119 mol. Because one mole of KOH reacts with one moleof HCl, this is also the number of moles of HCl; its concentration is therefore(.0119 mol) ÷ (.036 L) = 0.33 M .

Titration curves

The course of a titration can be followedby plotting the pH of the solution as afunction of the quantity of titrant added.The figure shows two such curves, onefor a strong acid (HCl) and the other fora weak acid, acetic acid, denoted by HAc.Looking first at the HCl curve, notice howthe pH changes very slightly until theacid is almost neutralized. At that point,which corresponds to the vertical part ofthe plot, just one additional drop ofNaOH solution will cause the pH to jump to a very high value— almost as highas that of the pure NaOH solution.

Compare the curve for HCl with that of HAc. For a weak acid, the pH jump nearthe neutralization point is less steep. Notice also that the pH of the solution atthe neutralization point is greater than 7. These two characteristics of thetitration curve for a weak acid are very important for you to know.

If the acid or base is polyprotic, there will bea jump in pH for each proton that is titrated.In the example shown here, a solution ofcarbonic acid H2CO3 is titrated with sodiumhydroxide. The first equivalence point (atwhich the H2CO3 has been convertedentirely into bicarbonate ion HCO3–) occursat pH 8.3. The solution is now identical toone prepared by dissolving an identicalamount of sodium bicarbonate in water.

Addition of another mole equivalent of hydroxide ion converts the bicarbonateinto carbonate ion and is complete at pH 10.3; an identical solution could beprepared by dissolving the appropriate amount of sodium carbonate in water.

Finding the equivalence point: indicators

When enough base has been added to react completely with the hydrogens of amonoprotic acid, the equivalence point has been reached. If a strong acid andstrong base are titrated, the pH of the solution will be 7.0 at the equivalencepoint. However, if the acid is a weak one, the pH will be greater than 7; the

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“neutralized” solution will not be “neutral” in terms of pH. For a polyprotic acid,there will be an equivalence point for each titratable hydrogen in the acid.These typically occur at pH values that are 4­5 units apart, but they areoccasionally closer, in which case they may not be readily apparent in thetitration curve.

The key to a successful titration is knowing when the equivalance point hasbeen reached. The easiest way of finding the equivalence point is to use anindicator dye; this is a substance whose color is sensitive to the pH. One suchindicator that is commonly encountered in the laboratory is phenolphthalein; itis colorless in acidic solution, but turns intensely red when the solutionbecomes alkaline. If an acid is to be titrated, you add a few drops ofphenolphthalein to the solution before beginning the titration. As the titrant isadded, a local red color appears, but quickly dissipates as the solution isshaken or stirred. Gradually, as the equivalence point is approached, the colordissipates more slowly; the trick is to stop the addition of base after a singledrop results in a permanently pink solution.

Different indicators change color at different pH values; see here for anillustrated list. Since the pH of the equivalance point varies with the strength ofthe acid being titrated, one tries to fit the indicator to the particular acid. Onecan titrate polyprotic acids by using a suitable combination of severalindicators, as is illustrated above for carbonic acid.

What you should be able to do

Make sure you thoroughly understand the following essential ideas which havebeen presented above. It is especially imortant that you know the precisemeanings of all the highlighted terms in the context of this topic.

Define the ion product of water, and know its room­temperature value.

State the criteria, in terms of H+ and OH– concentrations, of an acidic, alkaline,and a neutral solution.

Given the effective hydrogen ion concentration in a solution, calculate the pH.Conversely, find the hydrogen­ or hydroxide ion concentration in a solution having agiven pH.

Find the pH or pOH of a solution when either one is known.

Describe the process of acid­base titration, and explain the significance of theequivalence point.

Sketch a typical titration curve for a monoprotic or polyprotic acid.

Concept Map

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Page last modified: 17.02.2007

⇐index | intro pH Brønsted | competition | electrons | structures | gallery<

© 2007 by Stephen Lower ­ Simon Fraser University ­ Burnaby/Vancouver Canada

For information about this Web site or to contact the author, please see the Chem1 Virtual Textbook home page.

This work is licensed under a Creative Commons Attribution­NonCommercial 2.5 License.