Chapter 14

Principles of Neutralization Titrations

Neutralization titrations are widely used to determine theamounts of acids and bases and to monitor the progress ofreactions that produce or consume hydrogen ions.

Standard Solutions

The standard reagents used in acid/base titrations are alwaysstrong acids or strong bases, such as HCl, HClO4, H2SO4, NaOH,and KOH.

Weak acids and bases are never used as standard reagentsbecause they react incompletely with analytes.

Acid/Base Indicators

An acid/base indicator is a weak organic acid or a weak organicbase whose undissociated form differs in color from its conjugatebase or its conjugate acid form.

An acid-type indicator, HIn:

HIn + H2O In- + H3O+

A base-type indicator, In:

In + H2O InH+ + OH-

The equilibrium-constant expressionfor the dissociation of an acid-typeindicator takes the form:

Ka = [H3O+][In-]

[HIn]

phenolphthalein

The human eye is not very sensitive to color differences in asolution containing a mixture of HIn and In-.

HIn, exhibits its pure acid color when

[HIn]/[In-] 10/1

and its base color when

[HIn]/[In-] 1/10

Therefore, the range of hydronium ion concentrations needed forthe indicator to change color can be estimated.

For full acid color,

[H3O+] = 10Ka

and for the full base color,

[H3O+] = 0.1Ka

To obtain the indicator pH range, we take the negative logarithms ofthe two expressions:

pH (acid color) = -log(10Ka) = pKa – 1

pH (basic color) = -log(0.1Ka) = pKa + 1

Indicator pH range = pKa 1

There are two types of titration error in acid/base titrations:

Determinate error that occurs when the pH at which the indicatorchanges color differs from the pH at the equivalence point.

Indeterminate error that originates from the limited ability of thehuman eye to distinguish reproducibly the intermediate color of theindicator.

The pH interval over which a given indicator exhibits a color changeis influenced by temperature, the ionic strength of the medium, andthe presence of organic solvents and colloidal particles.

Titration of strong acids and bases

The hydronium ions in an aqueous solution of a strong acid havetwo sources:

(1) the reaction of the acid with water and (2) the dissociation ofwater itself.

For a solution of HCl with a concentration greater than about 10-6 M:

[H3O+] = cHCl + [OH-] cHCl

where [OH-] represents the contribution of hydronium ions fromthe dissociation of water.

For a solution of a strong base, such as sodium hydroxide:

[OH-] = cNAOH + [H3O+] cNAOH

Three types of calculations must be done to construct thehypothetical curve for titrating a solution of a strong acid with astrong base.

Preequivalence: compute the concentration of the acid from itsstarting concentration and the amount of base added.

Equivalence: the hydronium ion concentration can be calculateddirectly from the ion-product constant for water, Kw.

Postequivalence: the analytical concentration of the excess base iscomputed, and the hydroxide ion concentration is assumed to beequal to or a multiple of the analytical concentration.

(1) Kw = [H3O+][OH-]

(2) – log Kw = – log [H3O+][OH-] = – log[H3O+] – log[OH-]

(3) pKw = pH + pOH

The Effect of Concentration

Choosing an Indicator

Titrating a Strong Base with a Strong Acid

Titration curves for weak acids/bases

1. At the beginning, the solution contains only a weak acid or aweak base, and the pH is calculated from the concentration of thatsolute and its dissociation constant.

2. After various increments of titrant have been added (up to, butnot including, the equivalence point), the solution consists of aseries of buffers. The pH of each buffer can be calculated from theanalytical concentrations of the conjugate base or acid and theconcentrations of the weak acid or base that remains.

3. At the equivalence point, the solution contains only the conjugateof the weak acid or base being titrated (that is, a salt), and the pH iscalculated from the concentration of this product.

4. Beyond the equivalence point, the excess of strong acid or basetitrant suppresses the acidic or basic character of the reactionproduct to such an extent that the pH is governed largely by theconcentration of the excess titrant.

The analytical concentrations of acid and conjugate base areidentical when an acid has been half neutralized.

At the half-titration point in a weak-acid titration:

[H3O+] = Ka and pH = pKa

In the titration of a weak base:

At the half-titration point in a weak-base titration:

[OH-] = Kb and pOH = pKb

The buffer capacities of each of the solutions are at a maximum atthis point.

The Effect of Concentration

Curve for the titration of acetic acid with sodium hydroxide.

The initial pH values are higher

and the equivalence-point pH is

lower for the more dilute solution

(Curve B).

At intermediate titrant volumes,

the pH values differ only slightly

because of the buffering action

of the acetic acid/sodium acetate

system that is present in this region.

The Effect of Reaction Completeness

The effect of acid strength (dissociation constant) on titration curves.

Titration curves for 0.1000 M

solutions of acids with different

dissociation constants are

shown.

The pH change in the

equivalence point region

becomes smaller as the acid

becomes weaker.

Titration curves for weak bases

Hypothetical titration curves for a series of weak bases ofdifferent strengths.

The composition of solutions during acid/base titrationsThe straight lines show the change in relative amounts of HOAc(0) and OAc- (1) during the titration of 50.00 mL of 0.1000 Macetic acid.

Chapter 15

Complex Acid/Base Systems

I. Mixtures of strong and weak acids or strong and weak bases25 mL

II. Polyfunctional acids and bases

A species are said to exhibit polyfunctional acidic or basic behaviorif it has two or more acidic or basic functional groups.

With a polyfunctional acid such as phosphoric acid (H3PO4), theprotonated species (H3PO4, H2PO4

-, HPO4-2) differ enough in their

dissociation constants that they exhibit multiple end points in aneutralization titration.

The Phosphoric Acid System

H3PO4 + H2O H2PO4- + H3O+ Ka1 = [H3O+][H2PO4

-]= 7.11 10-3

[H3PO4]

H2PO4- + H2O HPO4

-2 + H3O+ Ka2 = [H3O+][HPO4-2]= 6.32 10-8

[H2PO4-]

HPO4-2+ H2O PO4

-3 + H3O+ Ka3 = [H3O+][PO4-3]= 4.5 10-13

[HPO4-2]

Ka1 > Ka2 often by a factor of 104 to 105 because of electrostatic forcesand statistical reasons.

Addition of two adjacent stepwise equilibria:

H3PO4 + 2H2O HPO4-2 + 2H3O+ Ka1Ka2 = [H3O+]2[HPO4

-2]= 4.49 10-10

[H3PO4]

Similarly, Ka1Ka2Ka3 = [H3O+]3[PO4-3]

[H3PO4]

The Carbon Dioxide/Carbonic Acid System

When carbon dioxide is dissolved in water:

CO2(aq) + H2O H2CO3 Khyd = [H2CO3] = 2.8 10-3

[CO2(aq)]

H2CO3 + H2O H3O+ + HCO3- K1 = [H3O+][HCO3

-] = 1.5 10-4

[H2CO3]

HCO3- + H2O H3O+ + CO3

-2 K2 = [H3O+][CO3-2] = 4.69 10-11

[HCO3-]

Combining the first two,

CO2(aq) + 2H2O H3O+ + HCO3- Ka1 = [H3O+][HCO3

-] = 4.2 10-7

[CO2(aq)]

HCO3- + H2O H3O+ + CO3

-2 Ka2 = 4.69 10-11

Buffer solutions involving polyprotic acids

Two buffer systems can be prepared from a weak dibasic acid andits salts:

The first consists of free acid H2A and its conjugate base NaHA, andthe second makes use of the acid NaHA and its conjugate base Na2A.

The pH of the NaHA/Na2A system is higher than that of theH2A/NaHA system because the acid dissociation constant for HA- isalways less than that for H2A.

Calculation of the pH of solutions of NaHA

Salts that are amphiprotic are formed during neutralizationtitrations of polyfunctional acids and bases. The pH of which isdetermined as follows:

HA- + H2O A-2 + H3O+ and HA- + H2O H2A + OH-

The relative magnitudes of the equilibrium constants for theseprocesses determine whether a solution of NaHA is acidic or basic.

Ka2 = [H3O+] [A2-] Kb2 = Kw = [H2A] [OH-]

[HA-] Ka1 [HA-]

If Kb2 is greater than Ka2, the solution is basic. It is acidic if Ka2

exceeds Kb2.

To derive an expression for the hydronium ion concentration of asolution of HA-, we first write the mass-balance equation:

cNaHA = [HA-] + [H2A] + [A2-]

The charge-balance equation is

[Na+] + [H3O+] = [HA-] + 2[A2-] + [OH-]

Since the sodium ion concentration is equal to the molar analyticalconcentration of NaHA,

cNaHA + [H3O+] = [HA-] + 2[A2-] + [OH-]

Subtracting the mass-balance equation from the charge-balanceequation:

[H3O+] = [A-2] + [OH-] - [H2A]

Rearranging the acid-dissociation constant expressions forH2A and HA-:

[H2A] = [H3O+][HA-] [A2-] = Ka2[HA-]

Ka1 [H3O+]

Substitution [H3O+] = [A-2] + [OH-] - [H2A] yields,

[H3O+] = Ka2[HA-] + Kw - [H3O+][HA-]

[H3O+] [H3O+] Ka1

Finally, we get

This simplifies to: 1

2

1

2

3/1/][1

][][

aNaHA

wNaHAa

a

wa

Kc

KcK

KHA

KHAKOH

+

+=

+

+=

−

−

+

213 ][ aa KKOH =+

Titration curves for polyfunctional acids

Compounds with two or more acidic functional groups yield multipleend points in a titration if the functional groups differ sufficiently instrength as acids.

Titration of 20.00 mL of 0.1000 M

H2A with 0.1000 M NaOH.

If Ka1/Ka2 > 103, the theoretical

titration curves can be calculated.

Curves for the titration of polyprotic acids. A 0.1000 M NaOHsolution is used to titrate 25.00 mL of 0.1000 M H3PO4 (curve A ),0.1000 M oxalic acid (curve B ), and 0.1000 M H2SO4 (curve C ).

In titrating a polyprotic acid

or base, two usable end points

appear if the ratio of dissociation

constants is greater than 104 and

if the weaker acid or base has

a dissociation constant greater

than 10-8.

Titration curves for polyfunctional bases

The titration of 25.00 mL of 0.1000 M Na2CO3 with 0.1000 M HCl:

Two end points appear in the titration.

The important equilibrium constants are

CO32- + H2O OH- + HCO3

-

Kb1 = Kw = 1.00 x 10-14 = 2.13 x 10-4

Ka2 4.69 x 10-11

HCO3- + H2O OH- + CO2(aq)

Kb2 = Kw = 1.00 10-14 = 2.4 10-8

Ka1 4.2 10-7

III. Titration curves for amphiprotic species

An amphiprotic substance when dissolved in a suitable solventbehaves both as a weak acid and as a weak base.

If either of its acidic or basic characters predominates, titration ofthe substance with a strong base or a strong acid may be feasible.

Ex.

H2PO4-

HPO4-2

Amino acid

Composition of polyprotic acid solutions as a function of pHAlpha values are useful in visualizing the changes in theconcentration of various species that occur in a titration.

cT: the sum of the molar concentrations of the maleate-containingspecies in the solution throughout the titration.The free acid 0 is defined as:

0 = [H2M]cT

where cT = [H2M] + [HM-] + [M2-]

The alpha values for HM- and M2- are:

1 = [HM-] 2 = [M2-]

cT cT

The sum of the alpha values for a system must equal one:

0 + 1 + 2 = 1

The three curves plotted show the alpha values for eachmaleate-containing species as a function of pH.

Fractions of H3PO4 species as a function of pH.

Titration of 25.00 mL of 0.1000 M maleic acid with 0.1000 MNaOH. These curves give a comprehensive picture of allconcentration changes that occur during the titration.

Chapter 16

Applications of Neutralization Titrations

Neutralization titrations are used to determine the concentration ofacidic or basic analytes or analytes that can be converted to acids orbases by suitable treatment.

Reagents for neutralization titrations

Strong acids and strong bases produce the largest change in pH atthe equivalence point. Hence, standard solutions for neutralizationtitrations are always prepared from these reagents.

Preparation of Standard Acid Solutions

HCl solutions, Perchloric acid, and sulfuric acid are stable standardsolutions.

To obtain most standard acid solutions, a solution of an approximateconcentration is first prepared by diluting the concentrated reagent.The diluted acid solution is then standardized against a primary-standard base.

The Standardization of Acids

Sodium carbonate is the most frequently used reagent forstandardizing acids. Primary-standard-grade sodium carbonate isavailable commercially or can be prepared by heating purifiedsodium hydrogen carbonate between 270 to 300°C for 1 hr:

2NaHCO3(s) → Na2CO3 + H2O +CO2 (g)

Other Primary Standards for Acids

Tris-(hydroxymethyl)aminomethane, (HOCH2)3CNH2, known also asTRIS or THAM, is available in primary-standard purity fromcommercial sources. The main advantage is its much greater massper mole of protons consumed (121.1 g/mol) than sodiumcarbonate (53.0 g/mol).

A high mass per proton consumed is desirable in a primary standardbecause a larger mass of reagent must be used, thus decreasing therelative weighing error.

Preparation of Standard Solutions of Base

Sodium hydroxide, potassium hydroxide, and barium hydroxide arethe most common bases for preparing standard solutions.

The Effect of Carbon Dioxide on Standard Base Solutions

The hydroxides of sodium, potassium, and barium react rapidly withatmospheric carbon dioxide to produce the corresponding carbonate:

CO2(g) + 2OH- → CO32- + H2O

Absorption of carbon dioxide by a standardized solution of sodium orpotassium hydroxide leads to a negative systematic error, calledcarbonate error, in analyses in which an indicator with a basic rangeis used.

Carbonate ion in standard base solutions decreases the sharpness ofend points and is usually removed before standardization.

The Standardization of Bases

Several primary standards are available for standardizing bases.Most are weak organic acids that require the use of an indicatorwith a basic transition range.

Potassium Hydrogen Phthalate

KHC8H4O4 is a nearly ideal primary standard.

It is a nonhygroscopic crystalline solid with a relatively large molarmass (204.2 g/mol).

Other Primary Standards for Bases

Benzoic acid can be obtained in primary-standard purity and usedfor the standardization of bases. Benzoic acid has limited solubilityin water, so it is usually dissolved in ethanol prior to dilution withwater and titration.

Typical applications of neutralization titrations

Neutralization titrations are used to determine the many inorganic,organic, and biological species that possess acidic or basicproperties.

Elemental Analysis

Several important elements such as carbon, nitrogen, chlorine,bromine, fluorine, that occur in organic and biological systems areconveniently determined by methods that have an acid/basetitration as the final step.

Nitrogen

The most common method for determining organic nitrogen is theKjeldahl method, which is based on a neutralization titration.

It is the standard process for determining the protein content ofgrains, meats, and biological materials.

The sample is decomposed in hot, concentrated sulfuric acid toconvert the bound nitrogen to ammonium ion.

It is then cooled, diluted, and made basic, a process that convertsthe ammonium ions to ammonia.

The ammonia is distilled from the basic solution, collected in anacidic solution, and determined by a neutralization titration.

Sulfur

Sulfur in organic and biological materials is determined by burningthe sample in a stream of oxygen.

The sulfur dioxide (as well as the sulfur trioxide) formed is collectedby distillation into a dilute solution of hydrogen peroxide:

SO2(g) + H2O2 → H2SO4

The Determination of Inorganic Substances

Ammonium salts are determined by conversion to ammonia with astrong base followed by distillation.

Nitrates and nitrites are first reduced to ammonium ion by reactionwith an alloy of 50% Cu, 45% Al, and 5% Zn (Devarda’s alloy).Granules of the alloy are introduced into a strongly alkaline solutionof the sample in a Kjeldahl flask.

Carbonate and carbonate mixtures require two titrations with astrong acid: one using an alkaline-range indicator, such asphenolphthalein, and the other with an acid-range indicator, such asbromocresol green.

In the Winkler method, both components are titrated with astandard acid with an acid-range indicator, such as bromocresolgreen. An unmeasured excess of neutral barium chloride is thenadded to a second aliquot of the sample solution to precipitate thecarbonate ion, following which the hydroxide ion is titrated to aphenolphthalein end point.

Titration curves and indicator transition ranges for the analysis ofmixtures containing hydroxide, carbonate, and hydrogen carbonateions using a strong-acid titrant.

The Determination of Organic Functional Groups

Carboxylic and Sulfonic Acid Groups

Most carboxylic acids have dissociation constants that rangebetween 10–4 and 10–6, and thus, these compounds are readilytitrated.

Many caboxylic acids are not soluble in water; the acid can bedissolved in ethanol and titrated with aqueous base.

Alternatively, the acid can be dissolved in an excess of standardbase followed by back-titration with standard acid.

Amine groupsAliphatic amines generally have base dissociation constants on theorder of 10-5 and can be titrated directly with a solution of strongacid.

Cyclic amines with aromatic character, such as pyridine and itsderivatives, are usually too weak for titration in aqueous solutions.

Many saturated cyclic amines tend to resemble aliphatic amines intheir acid/base behavior and can thus be titrated in aqueous media.

Many amines that are too weak to be titrated as bases in water areeasily titrated in nonaqueous solvents.

Ester groups

Esters are commonly determined by saponification with ameasured quantity of standard base:

R1COOR2 + OH- → R1COO- + HOR2

The excess base is then titrated with standard acid.

Esters vary widely in their rates of saponification.

Saponification is the process by which an ester is hydrolyzed inalkaline solution to give an alcohol and a conjugate base.

Hydroxyl groupsHydroxyl groups in organic compounds can be determined byesterification with various carboxylic acid anhydrides or chlorides.

The two most common reagents are acetic anhydride and phthalicanhydride.

Carbonyl groupsMany aldehydes and ketones can be determined with a solution ofhydroxylamine hydrochloride.

The reaction produces an oxime and the liberated HCl is titratedwith a base.

The Determination of Salts

The total salt content of a solution can be determined accuratelyby acid/base titration.

The salt is converted to an equivalent amount of an acid or baseby passing a solution containing the salt through a column packedwith an ion-exchange resin.