Chapter 14. Principles of Neutralization Titrations

Chapter 14

Principles of Neutralization Titrations

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

Standard Solutions

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

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

Acid/Base Indicators

An acid/base indicator is a weak organic acid or a weak organic base whose undissociated form differs in color from its conjugate base 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 expression for the dissociation of an acid-type indicator takes the form:

K_a = [H₃O⁺][In^-] [HIn]

phenolphthalein

The human eye is not very sensitive to color differences in a solution 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 for the indicator to change color can be estimated.

For full acid color,

[H₃O⁺] = 10K_a and for the full base color,

[H₃O⁺] = 0.1K_a

To obtain the indicator pH range, we take the negative logarithms of the 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 indicator changes color differs from the pH at the equivalence point.

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

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

Titration of strong acids and bases

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

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

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

[H₃O⁺] = c_HCl + [OH^-]  c_HCl

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

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

[OH^-] = c_NAOH + [H₃O⁺]  c_NAOH

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

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

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

Postequivalence: the analytical concentration of the excess base is computed, and the hydroxide ion concentration is assumed to be equal to or a multiple of the analytical concentration.

(1) K_w = [H₃O⁺][OH^-]

(2) – log K_w = – log [H₃O⁺][OH^-] = – log[H₃O⁺] – log[OH^-] (3) pK_w = 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 a weak base, and the pH is calculated from the concentration of that solute and its dissociation constant.

2. After various increments of titrant have been added (up to, but not including, the equivalence point), the solution consists of a series of buffers. The pH of each buffer can be calculated from the analytical concentrations of the conjugate base or acid and the concentrations of the weak acid or base that remains.

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

4. Beyond the equivalence point, the excess of strong acid or base titrant suppresses the acidic or basic character of the reaction product to such an extent that the pH is governed largely by the concentration of the excess titrant.

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

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

[H₃O⁺] = K_a and pH = pK_a In the titration of a weak base:

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

[OH^-] = K_b and pOH = pK_b

The buffer capacities of each of the solutions are at a maximum at this 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 of different strengths.

The composition of solutions during acid/base titrations

The straight lines show the change in relative amounts of HOAc (₀) and OAc^- (₁) during the titration of 50.00 mL of 0.1000 M acetic acid.

Chapter 15

Complex Acid/Base Systems

I. Mixtures of strong and weak acids or strong and weak bases

25 mL

II. Polyfunctional acids and bases

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

With a polyfunctional acid such as phosphoric acid (H₃PO₄), the protonated species (H₃PO₄, H₂PO₄^-, HPO₄^-2) differ enough in their dissociation constants that they exhibit multiple end points in a neutralization titration.

The Phosphoric Acid System

H₃PO₄ + H₂O  H₂PO₄^- + H₃O⁺ K_a1 = [H₃O⁺][H₂PO₄^-]= 7.11  10^-3 [H₃PO₄]

H₂PO₄^- + H₂O  HPO₄^-2 + H₃O⁺ K_a2 = [H₃O⁺][HPO₄^-2]= 6.32  10^-8 [H₂PO₄^-]

HPO₄^-2+ H₂O  PO₄^-3 + H₃O⁺ K_a3 = [H₃O⁺][PO₄^-3]= 4.5  10^-13 [HPO₄^-2]

K_a1 > K_a2 often by a factor of 10⁴ to 10⁵ because of electrostatic forces and statistical reasons.

Addition of two adjacent stepwise equilibria:

H₃PO₄ + 2H₂O  HPO₄^-2 + 2H₃O⁺ K_a1K_a2 = [H₃O⁺]²[HPO₄^-2]= 4.49 10^-10 [H₃PO₄]

Similarly, K_a1K_a2K_a3 = [H₃O⁺]³[PO₄^-3] [H₃PO₄]

The Carbon Dioxide/Carbonic Acid System When carbon dioxide is dissolved in water:

CO₂(aq) + H₂O  H₂CO₃ K_hyd = [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^- K_a1 = [H₃O⁺][HCO₃^-] = 4.2  10^-7 [CO₂(aq)]

HCO₃^- + H₂O  H₃O⁺ + CO₃^-2 K_a2 = 4.69  10^-11

Buffer solutions involving polyprotic acids

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

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

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

Calculation of the pH of solutions of NaHA

Salts that are amphiprotic are formed during neutralization titrations of polyfunctional acids and bases. The pH of which is determined as follows:

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

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

K_a2 = [H₃O⁺] [A^2-] K_b2 = K_w = [H₂A] [OH^-]

[HA^-] K_a1 [HA^-]

If K_b2 is greater than K_a2, the solution is basic. It is acidic if K_a2 exceeds K_b2.

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

c_NaHA = [HA^-] + [H₂A] + [A^2-] The charge-balance equation is

[Na⁺] + [H₃O⁺] = [HA^-] + 2[A^2-] + [OH^-]

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

c_NaHA + [H₃O⁺] = [HA^-] + 2[A^2-] + [OH^-]

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

[H₃O⁺] = [A^-2] + [OH^-] - [H₂A]

Rearranging the acid-dissociation constant expressions for H₂A and HA^-:

[H₂A] = [H₃O⁺][HA^-] [A^2-] = K_a2[HA^-]

K_a1 [H₃O⁺]

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

[H₃O⁺] = K_a2[HA^-] + K_w - [H₃O⁺][HA^-] [H₃O⁺] [H₃O⁺] K_a1

Finally, we get

This simplifies to: ¹

2 1

2

3 1 [ ]/ 1 /

] ] [

[

a NaHA

w NaHA

a a

w a

K c

K c

K K

HA

K HA

O K

H +

= + +

= ₋⁻ +

+

2 1

3 ]

[H O⁺ = K_a K_a

Titration curves for polyfunctional acids

Compounds with two or more acidic functional groups yield multiple end points in a titration if the functional groups differ sufficiently in strength 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 NaOH solution 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 CO₃^2- + H₂O  OH^- + HCO₃^-

K_b1 = K_w = 1.00 x 10^-14 = 2.13 x 10^-4 K_a2 4.69 x 10^-11

HCO₃^- + H₂O  OH^- + CO₂(aq)

K_b2 = Kw = 1.00  10^-14 = 2.4  10^-8 K_a1 4.2  10^-7

III. Titration curves for amphiprotic species

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

If either of its acidic or basic characters predominates, titration of the 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 pH

Alpha values are useful in visualizing the changes in the concentration of various species that occur in a titration.

c_T: the sum of the molar concentrations of the maleate-containing species in the solution throughout the titration.

The free acid ₀ is defined as:

₀ = [H₂M]

c_T where c_T = [H₂M] + [HM^-] + [M^2-]

The alpha values for HM^- and M^2- are:

₁ = [HM^-] ₂ = [M^2-]

c_T c_T

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 each maleate-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 M NaOH. These curves give a comprehensive picture of all concentration changes that occur during the titration.

Chapter 16

Applications of Neutralization

Titrations

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

Reagents for neutralization titrations

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

Preparation of Standard Acid Solutions

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

To obtain most standard acid solutions, a solution of an approximate concentration 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 for standardizing acids. Primary-standard-grade sodium carbonate is available commercially or can be prepared by heating purified sodium 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 as TRIS or THAM, is available in primary-standard purity from commercial sources. The main advantage is its much greater mass per mole of protons consumed (121.1 g/mol) than sodium carbonate (53.0 g/mol).

A high mass per proton consumed is desirable in a primary standard because a larger mass of reagent must be used, thus decreasing the relative weighing error.

Preparation of Standard Solutions of Base

Sodium hydroxide, potassium hydroxide, and barium hydroxide are the 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 with atmospheric carbon dioxide to produce the corresponding carbonate:

CO₂(g) + 2OH^- → CO₃^2- + H₂O

Absorption of carbon dioxide by a standardized solution of sodium or potassium hydroxide leads to a negative systematic error, called carbonate error, in analyses in which an indicator with a basic range is used.

Carbonate ion in standard base solutions decreases the sharpness of end 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 indicator with a basic transition range.

Potassium Hydrogen Phthalate

KHC₈H₄O₄ is a nearly ideal primary standard.

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

Other Primary Standards for Bases

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

Typical applications of neutralization titrations

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

Elemental Analysis

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

Nitrogen

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

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

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

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

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

Sulfur

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

The sulfur dioxide (as well as the sulfur trioxide) formed is collected by 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 a strong base followed by distillation.

Nitrates and nitrites are first reduced to ammonium ion by reaction with an alloy of 50% Cu, 45% Al, and 5% Zn (Devarda’s alloy).

Granules of the alloy are introduced into a strongly alkaline solution of the sample in a Kjeldahl flask.

Carbonate and carbonate mixtures require two titrations with a strong acid: one using an alkaline-range indicator, such as phenolphthalein, and the other with an acid-range indicator, such as bromocresol green.

In the Winkler method, both components are titrated with a standard acid with an acid-range indicator, such as bromocresol green. An unmeasured excess of neutral barium chloride is then added to a second aliquot of the sample solution to precipitate the carbonate ion, following which the hydroxide ion is titrated to a phenolphthalein end point.

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

The Determination of Organic Functional Groups Carboxylic and Sulfonic Acid Groups

Most carboxylic acids have dissociation constants that range between 10^–4 and 10^–6, and thus, these compounds are readily titrated.

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

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

Amine groups

Aliphatic amines generally have base dissociation constants on the order of 10^-5 and can be titrated directly with a solution of strong acid.

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

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

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

Ester groups

Esters are commonly determined by saponification with a measured 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 in alkaline solution to give an alcohol and a conjugate base.

Hydroxyl groups

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

The two most common reagents are acetic anhydride and phthalic anhydride.

Carbonyl groups

Many aldehydes and ketones can be determined with a solution of hydroxylamine hydrochloride.

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

The Determination of Salts

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

The salt is converted to an equivalent amount of an acid or base by passing a solution containing the salt through a column packed with an ion-exchange resin.