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Acid-Base Equilibria

Brønstead-Lowry Acids and Bases

The Arrhenius definition of an acid and a base:

Acids - substances that when dissolved in water release H+ ions

Bases - substances that when dissolved in water release OH- ions

The definition of an Arrhenius acid and base emphasizes the H+ and OH

- ions in water

Proton Transfer Reactions

HCl is an Arrhenius acid:

When HCl dissolves in water it actually transfers a proton to a water molecule:

HCl(g) + H2O(l) H3O+(aq) + Cl

-(aq)

The recognition that the release of H+ ions by acids involves H

+ transfer led to a new proposal for

the definition of what is an acid, and what is a base

The Brønstead-Lowry definition of an acid and a base:

Acids - a substance that can transfer a proton to another substance

Base - a substance that can accept a proton from another substance

These definitions emphasize proton transfer, and can include solvents other than water (aqueous

solutions are not part of the definition, proton transfer is the key feature)

The definition was developed independently in 1923 by Johannes Brønstead and Thomas Lowry

HCl(g) + H2O(l) H3O+(aq) + Cl

-(aq)

In the reaction of HCl with H2O, HCl is a Brønstead-Lowry acid (donates a proton to H2O), and

the H2O (in this particular reaction) is a Brønstead-Lowry base (accepts a proton from the HCl)

HCl(g) + NH3(g) Cl-(g) + NH4

+(g)

In the reaction of HCl with NH3, a proton is transferred from the HCl to the NH3.

o The HCl is the Brønstead-Lowry acid

o NH3 is the Brønstead-Lowry base

o H2O is not involved in the reaction (or definition) of the acid or base in this reaction

NH3(aq) + H2O(l) NH4+(aq) + OH

-(aq)

In the above reaction of ammonia with water, the ammonia is a Brønstead-Lowry base, and the

H2O is acting as a Brønstead-Lowry acid

A molecule that can act as both a Brønstead-Lowry acid or a Brønstead-Lowry base (depending on the

reaction in question) is termed amphoteric

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The ammonia is also an Arrhenius base (it increases the concentration of OH- ions in water)

An acid and a base always work together to transfer a proton

A substance can only work as a Brønstead-Lowry acid (i.e. donates a proton), if another substance

simultaneously acts as a Brønstead-Lowry base (i.e. accepts the proton)

o To be a Brønstead-Lowry acid, a molecule must have a H atom that can it can lose as an

H+ ion

o To be a Brønstead-Lowry base, a molecule must have a non-bonding pair of electrons

that it can use to bind the H+ atom (this non-bonding pair will form the basis of the

"shared" electrons in the new covalent bond with the H atom)

Conjugate Acid-Base Pairs

In any acid-base equilibrium both the forward and reverse reactions involve proton transfer reactions. For

example, the general reaction of a Brønstead-Lowry acid with water proceeds as follows:

HA(aq) + H2O(l) A-(aq) + H3O

+(aq)

acid + base base + acid

In the forward reaction, HA donates a proton to H2O

o HA is the Brønstead-Lowry acid

o H2O is the Brønstead-Lowry base In the reverse reaction, H3O

+ donates a proton to A

-

o H3O+ is the Brønstead-Lowry acid

o A- is the Brønstead-Lowry base

When HA behaves as an acid and donates a proton, what remains is A-, which behaves like a base

When H3O+ behaves as an acid and donates a proton, what remains is H2O, which (in this reaction)

behaves like a base (although H2O is amphoteric)

HA and A- are termed a conjugate acid-base pair. They differ only in the presence or absence of a

proton.

o A- is the conjugate base of HA

H3O+ and H2O are also a conjugate acid-base pair.

o H3O+ is the conjugate acid of H2O

In any acid-base proton transfer reaction there will be conjugate acid-base pairs

Relative Strengths of Acids and Bases

A strong acid is a molecule that has a strong preference to donate a proton.

Thus, its conjugate base will have a weak tendency to accept a proton

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A strong base is a molecule that has a strong preference to accept a proton

Thus, its conjugate acid will have a weak tendency to donate a proton

There is an inverse relationship between the strength of an acid and its conjugate base (likewise a strong

base and its conjugate acid)

All molecules of a strong acid in water will donate their protons (to H2O)

The conjugate base has no tendency to be protonated.

Weak acids have conjugate bases that have a moderate tendency to be protonated.

Thus, in solution, only a fraction of the molecules of a weak acid will donate a proton. There will

be a significant concentration of both the acid and conjugate base forms in solution

What about molecules that contain H atoms, e.g. methane (CH4), but do not appear to have any acidic

character?

Their conjugate bases must be quite strong!

o CH3- is the conjugate base if CH4 behaves as an acid

o CH3- is such a strong base that it strips H

+ from H2O with such vigor that NO CH3

- will

remain in solution

o Thus, CH4 (the conjugate acid to CH3-) is technically an incredibly weak acid - absolutely

NO molecules will donate a proton

If we were to consider the "reaction" of methane with water we would have:

CH4(g) + H2O(l) CH3-(aq) + H3O

+(aq)

acid + base base + acid

The reaction proceeds entirely to the left

o When comparing CH3- and H2O (both are bases in this reaction), the CH3

- is the stronger

base o When comparing CH4 and H3O

+, the H3O

+ is the stronger acid

CH4(g) + H2O(l) CH3-(aq) + H3O

+(aq)

acid + base stronger base + stronger acid

In acid-base reactions, the reaction proceeds in the direction where a proton is transferred from the

stronger acid to the stronger base

Strong Acids and Bases

Strong acids and bases are strong electrolytes and exist in solution entirely as ions.

There are relatively few common strong acids and bases

Strong Acids

The monoprotic (one proton) strong acids:

HCl (hydrochloric acid)

HBr (hydrobromic acid)

HI (hydroiodic acid)

HNO3 (nitric acid)

HClO3 (chloric acid)

HClO4 (perchloric acid)

The diprotic (two protons) strong acid:

H2SO4 (sulfuric acid)

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These acids are completely ionized in H2O(l). Thus, the reaction is represented with a single arrow in the

direction of proton donation:

HCl(aq) + H2O(l) Cl-(aq) + H3O

+(aq)

Or an equally valid equation for an aqueous solution of HCl:

HCl(aq) Cl-(aq) + H

+(aq)

The protons from an aqueous solution of a strong acid are typically in such vast excess to the natural

ionization of water that their concentration determines the [H+] of an aqueous solution

Strong Bases

There are few common strong bases. They are typically the ionic hydroxides of group 1A metals, and some

of the heavier group 2A metals:

LiOH, NaOH, KOH, etc.

Ca(OH)2, Sr(OH)2, Ba(OH)2

These molecules ionize completely in aqueous solution.

The [OH-] of an aqueous solution of a strong base is determined by the concentration of the base -

it is in vast excess to the natural ionization of water

Strongly basic solutions can also be produced by certain substances that react with water to form OH- ions

Oxide ion (O2-

) is an example of this (in the form of metal oxides, e.g. CaO)

O2-

(aq) + H2O(l) 2OH-(aq)

CaO(aq) + H2O(l) 2OH-(aq) + Ca

2+(aq)

O2-

will react completely with H2O to produce OH- ion (i.e. it is a strong base)

Other strong bases like O2-

include H- and N

3-

Periodic table and acid/base properties of compounds

Bimolecular compounds of the form X-H (i.e. group 7 hydrides) will have different acid strengths

depending on the ease with which the proton can be released (i.e. the ease with which the X-H bond can be

broken).

The further the bonding electrons are from the nucleus, the less energy is required to ionize them

completely.

In this regard, as you move down the periodic table the atomic radii increases and valence

electrons are further away from the nucleus.

Thus, bond strengths generally decrease as you move down the periodic table, and it requires less

energy to ionize a proton in an X-H compound.

The easier it is to release a proton, the more acidic the compound. Thus, group 7 hydrides are

stronger acids as you move down the periodic table:

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Similarly, the electronegativity of the elements generally increases as you move to the right of the periodic

table.

For any two elements that are bonded together, it is easier to break the bond and ionize the two

atoms if there is a large difference in electronegativities.

The extreme case would be a metal halide - the large electronegativity difference means that they

don't share bonding electrons, rather they ionize readily (since the metal wants to give up its

valence electron and the halide wants to get one).

Thus, the greater the electronegativity difference between a hydrogen and the other atom in a H-X

bond, the easier to ionize and thus the stronger the acid. The electronegativity of H is about the

same as carbon.

So, as you move right in the periodic table beyond carbon, the stronger the acid for X-H bonds

(i.e. CH4 < NH3 < H2O < HF as far as acid strength):

Another effect upon the ability to ionize an X-H bond is the effect of an electron-withdrawing group (i.e. a

group with a large electronegativity) in the proximity of an X-H bond. This is most often observed for

halides bound to various locations within carboxylic acid compounds.

The closer they are bonded to the carboxylic acid ionizable proton (-O-H bond) the stronger the

carboxylic acid. The reason for this is that their high electronegativity tends to delocalize electrons

and withdraw them towards the halide.

This effect can be distributed over the molecule and influence the electrons comprising the X-H

bond.

If they are withdrawn away from the H, then it is easier to ionize the H (and the acid will be

stronger). Here are examples:

Dissociation of Water

Acids and Bases - Brief Review

Acids have a sour or tart taste (but don't use this method to identify if a compound is an acid)

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Bases have a bitter taste, and have a slippery feel

When bases are added to acids, they lower the amount of acid. When acids and bases are mixed

together in appropriate proportions, they are completely neutralized (and their characteristic

acid/base properties disappear altogether)

1830 - It was known that all acids contain hydrogen, but not all hydrogen-containing compounds were

acids

1889 - Svante Arrhenius (he of the Arhhenius equation) connected acidic properties with the presence of

H+ions and basic properties with the presence of OH

- ions

If a solution contained more H+ than OH

- ions, then it was acidic

If a solution contained more OH- than H

+ ions, then it was basic

H+ and OH

- ions can react with each other to form H2O molecules during neutralization reactions

The Dissociation of Water

Pure water consists almost entirely of H2O molecules. While this may seem like a redundant statement, the

point is that H2O is essentially a non-electrolyte.

Pure water is a poor conductor of electricity because it does not ionize to any great extent.

What little ionization of water does occur results in the production of H+ and OH

- ions. At room

temperature, one in a billion water molecules will ionize:

H2O(l) H+(aq) + OH

-(aq)

This process is termed the auto-ionization of water

The equilibrium expression for the auto-ionization reaction is:

The concentration of pure H2O is about 55M. The concentration of water is essentially unchanged

during chemical reactions involving dilute aqueous solutions (i.e. where the "solute" is in very low

concentrations compared to the pure 55M water).

As a result, the term for the concentration of water is considered to be a constant in the

equilibrium equations involving dilute aqueous reactions. Therefore:

The constant, Kw, is called the ion-product constant. At 25°C, the value of Kw is 1 x 10-14

The presence of other ions in dilute aqueous solution does not significantly perturb this

equilibrium constant. Therefore, this value is used for pure water and such solutions.

Based on this equilibrium constant, if we know the concentration of either H+ or OH

- ions in

solution, then we can derive the concentration of the other ion

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[H+] = 1 x 10

-14 / [OH

-]

[OH-] = 1 x 10

-14 / [H

+]

A solution for which [H+] = [OH

-] is said to be neutral

[H+][OH

-] = 1 x 10

-14

if at neutrality [H+] = [OH

-] then we can substitute into the above equation to yield:

[H+][H

+] = 1 x 10

-14

[H+]

2 = 1 x 10

-14

[H+] = 1 x 10

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(true for neutral solutions)

o Most aqueous solutions are not neutral

o As the concentration of one of these ions increases, the other must decrease according to

the equilibrium constant

The Proton in Water

The auto-ionization of water:

H2O(l) H+(aq) + OH

-(aq)

An H+ ion is a hydrogen atom that has lost its (one and only) valence electron. In other words, it is a naked

proton.

This proton is quite reactive; it wants two valance electrons in order to form a stable noble gas

valence electron configuration (like He)

The proton in solution has a high affinity for a non-bonding pair of electrons in neighboring water

molecules, and will form a covalent bond to the oxygen atom in water molecules:

The H3O+(aq) ion is called a hydronium ion

o Chemists use H+ and H3O

+ terms interchangeably to represent the hydrated proton in

acidic aqueous solutions

o The H+ ion is most often used because its simple and convenient, but H3O

+ is more

closest the physical state of this hydrogen ion in solution

o Production of the hydronium ion from the auto-ionization of water is often written not in

two distinct steps, but as resulting from the interaction of two water molecules:

H2O(l) H+(aq) + OH

-(aq)

H+(aq) + H2O(l) H3O

+(aq)

H2O(l) + H2O(l) H3O+(aq) + OH

-(aq)

Or

2H2O(l) H3O+(aq) + OH

-(aq)

The equilibrium equation for this ionization would be:

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o This would seem to give a different constant than the above expression for the

equilibrium constant arising from a single water molecule. However, since the

concentration of H2O(l) is constant, the [H2O]2 term is also a constant.

o Thus, the value of the equilibrium constant is the same (i.e. it depends on the product of

the concentration of the OH- ion and the H

+ or H3O

+ ion). And [H

+] is interchangeable

with [H3O+]

Thus, H

+ is interchangeable with H3O

+

The pH Scale

The concentration of H+ ion in solution is a pretty small number that can, nonetheless, vary over a

considerable range.

To conveniently represent the magnitude and range of concentration that the H+ ion can have in

aqueous solutions, the term pH is used

pH is defined as the negative logarithm (base 10) of the H+ ion concentration

pH = -log [H+]

-pH = log[H+]

10 -pH

= [H+]

What is the pH of a neutral solution at 25°?

Under this condition, the concentration of hydrogen ion is 1.0 x 10-7

M

pH = -log(1.0 x 10-7

) = -(-7.0) = 7.0

What is the pH of an acidic solution?

An acidic solution is one where we have an increase in [H+]

If a neutral solution has a [H+] of 1 x 10

-7M, then an acidic solution must have a [H

+] that is

greater than 1 x 10-7

M

For example, a solution with a [H+] = 1 x 10

-6M will be acidic. What will be the pH of this

solution?

pH = -log(1.0 x 10-6

) = -(-6.0) = 6.0

Because of the negative sign in the log term of the definition of pH, acidic solutions (i.e. those

with increasing concentrations of H+ ions) will have increasingly lower values of pH (i.e. pH 1.0 is

a potent acid and this pH is used to help digest your food in your stomach).

What is the pH of a basic solution?

A basic solution is one in which the [OH-] is greater than 1 x 10

-7M

For example, a solution has a [OH-] = 1.0 x 10

-5M (this is greater than 1 x 10

-7M, and so this

solution is basic)

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Basic solutions will have increasingly higher values of pH (i.e. pH 12 would be a potent base)

The nature of the pH scale, based upon the -log[H+], is that a 10 x fold change in [H

+] results in a single

unit change in the pH value.

A pH 7.0 solution has a [H+] of 1 x 10

-7M. If we increase the concentration 10 x fold (to 1 x 10

-

6M) the pH decreases by 1 unit (to pH 6.0)

A pH 4.0 solution has a [H+] of 1 x 10

-4M. If we decrease the concentration 10 x fold (to 1 x 10

-

5M) the pH increases by 1 unit (to pH 5.0)

Although the concentration of [H+] may seem very low indeed, even small changes can have a big impact

on chemical reactions that include [H+] as a component in their reaction

For reactions that are first order in [H+] doubling the concentration (even though the starting

concentration is a very small amount) can double the reaction rate

Blood is approximately pH 7.4. If the pH of blood varies by as much as 0.5 pH units outside this

value, illness and death may result

Other "p" Scales

By convention, the negative log of a quantity is labeled p(quantity)

For example, we could reference the quantity of OH- ions directly:

pOH = -log [OH-]

From the definition of Kw:

Kw = [H+][OH

-] = 1 x 10

-14

-log(Kw) = (-log([H+]) - log([OH

-]) = 14

-log(Kw) = pH + pOH = 14

Measuring pH

pH meters; detect changes in voltage in response to changes in pH

Indicator dyes; change colors at different pH's.

o Bromthymol Blue - changes color from yellow (pH 6) to blue (pH 7.4) - physiologically

useful indicator

o Phenolphthalein - changes color from colorless (pH 8) to pink (pH 9) - often used to

determine the endpoint in an acid/base titration

Weak Acids

Most acids are weak acids - they only partially ionize in aqueous solution

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If weak acids only partially ionize, then the [H+] that is produced is less than the total

concentration of acid added to the solution (note: a strong acid dissociates completely and

therefore the [H+] is equal to the concentration of acid added to a solution).

Since the [H+] produced by the ionization of weak acids is less than the concentration of acid

added to the solution, you cannot calculate the pH directly from the concentration of acid (again,

this would only be possible with strong acids that dissociate completely).

The extent of their ionization can be expressed by using the equilibrium constant and equilibrium

equation:

HA(aq) H+(aq) + A

-(aq)

Ka is the equilibrium constant for the ionization of an acid, often referred to as the acid

dissociation constant

What happens if the hydrated proton is represented by H3O+(aq) instead of H

+(aq)?

HA(aq) + H2O(l) H3O+(aq) + A

-(aq)

o Here the H2O is in liquid form, and therefore, its concentration never changes (and we

can consider it to be a constant in the expression

o And Ka is the same expression in both cases

Weak acids are often composed entirely of C, H and O atoms

H atoms are often bonded to either C or O atoms

o C electronegativity = 2.5

o H electronegativity = 2.1

o O electronegativity = 3.5

The H atoms bonded to C do not ionize (not a polar bond)

It is one or more H atoms bonded to an O atom that can ionize in water (due to difference in

electronegativity)

Weak acids are often carboxylic acids:

The magnitude of Ka is an indication of the tendency of the H atom to ionize

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o If Ka is large, it means that the concentration of H+ ion is large, and this means the acid

likes to ionize (the more it ionizes, the stronger the acid)

o Thus, the larger the value of Ka, the stronger the acid

Values for Ka for weak acids is typically less than 1 x 10-3

Polyprotic Acids

Many acids have more than 1 ionizable H atom. Such atoms are known as polyprotic acids

Sulfurous acid is a polyprotic acid:

H2SO3(aq) H+(aq) + HSO3

-(aq) Ka1 = 1.7 x 10

-2

HSO3(aq) H+(aq) + SO3

2-(aq) Ka2 = 6.4 x 10

-8

Ka1 is the equilibrium constant for ionization of the first proton

Ka2 is the equilibrium constant for ionization of the second proton

Ka2 is much smaller than Ka1

Its more difficult to remove the second proton. This is because the second proton has to be

removed from a negatively charged species (HSO3-) which will have an electrostatic attraction for

this second proton

It is always easier to remove the first proton from a polyprotic acid (Ka values become successively smaller

as protons are removed)

Usually Ka values for successive protons in polyprotic acids differ by a value of 103 or greater

We can estimate pH values by considering only the Ka1 value for polyprotic acids

Weak Bases

Weak bases in water react to release a hydroxide (OH-) ion and their conjugate acid:

Weak Base(aq) + H2O(l) Conjugate Acid(aq) + OH-(aq)

A common weak base is ammonia (NH3). Its conjugate acid is the ammonium ion (NH4+):

NH3(aq) + H2O(l) NH4+(aq) + OH

-(aq)

Since the H2O is the liquid state, and the concentration effectively doesn't change:

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Kb is the base-dissociation constant (analogous to the Ka dissociation constant for acids)

Kb always refers to the equilibrium in which a base reacts with H2O to form the conjugate acid and OH-

The structures of weak bases contain one or more lone pairs of electrons

A lone pair is necessary to form a bond with an H+ ion (producing the conjugate acid and releasing

OH- from H2O)

The lone pairs are typically located on Nitrogen atoms in the base

Other weak bases are actually the anion forms of weak acids (i.e. the conjugate bases of weak

acids)

(note: lone electron pairs to bond with H

+ are located on O atoms in this case)

Types of Weak Bases

How can you tell from the formula whether a compound will behave as a weak base?

There are two general categories of weak bases:

1. Neutral compounds containing a non-bonding pair of electrons that can form a bond

with a proton (i.e. can function as an acceptor of a proton)

o Most of this type of base contains nitrogen (and it's the lone pair on the N that accepts the

proton)

o These include ammonia (NH3) and related compounds called amines

o An amine is like ammonia, except one or more of the N-H bonds are replaced by a N-C

bond. For example, the compound methylamine has the structure:

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o Amines can extract a proton from H2O by forming a covalent bond with the lone pair of

electrons on the Nitrogen atom

2. The second category includes anions of weak acids

o The compound sodium hypochlorite (NaClO) dissociates to yield Na+ and ClO

- ions

In acid/base neutralization reactions, the Na+ ion would be a spectator ion

However, the ClO- ion is the conjugate base of HClO (hypochlorous acid), a

weak acid

Therefore, the ClO- ion can potentially extract a proton from H2O:

ClO-(aq) + H2O(l) HClO(aq) + OH

-(aq)

o This is the definition of a base, and therefore ClO- is a weak base in

water

Relationship Between Ka and Kb

Strong acids have weak conjugate bases

Strong bases have weak conjugate acids

The product of the acid-dissociation constant for an acid (i.e. Ka) and the base-dissociation constant for

its conjugate base (i.e. Kb) is the ion-product constant for water

Ka * Kb = Kw

What are the implications of this relationship?

o The product of Ka * Kb must always equal 1 x 10-14

o If Ka is large (i.e. if the acid is a strong acid), then Kb must be small (i.e. the conjugate

base is a weak base)

o If Kb is large (i.e. if the base is a strong base), then Ka must be small (i.e. the conjugate

acid is a weak acid)

In tables of dissociation constants for acids or bases, often only the value for the acid-dissociation

constants is given.

o The base-dissociation constants can be determined from the relationship:

Kb = Kw/Ka

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Acid-Base Properties of Salt Solutions

Ions can exhibit acidic or basic properties

NH4+ can donate a proton (i.e. act as an acid)

F- can accept a proton (i.e. act as a base)

Can salt solutions have acidic or basic properties?

Salts are strong electrolytes - they are completely ionized in solution.

Any acid or base properties must therefore be due to the properties of their cations or anions

Many ions are able to react with H2O(l) to produce H+(aq) or OH

-(aq) ions. This is termed Hydrolysis.

When weak acids dissociate, they produce anions that are the conjugate base

HA(aq) A-(aq) + H

+(aq)

The A- ion conjugate base can react with H2O(l) to produce a hydroxide ion, and is therefore a

base

A-(aq) + H2O(l) AH(aq) + OH

-(aq)

The anions of strong acids, by definition, are such weak bases that they do not react with H2O(l) to

produce OH-(aq) ions and thus, don't affect the pH of aqueous solutions

Amphoteric ions can behave as either an acid or a base

HSO3- ions can accept a proton, and behave as a base

HSO3- ions also have a proton they can still donate, thus, they may act as an acid

Their behavior in water will be determined by the relative magnitudes of Ka and Kb.

Cations

All cations, with the exception of group 1 metals, and the heavy group 2 metals (i.e. Ca2+

, Sr2+

, Ba2+

) act as

weak acids in aqueous solution

Predicting the pH of salt solutions:

The ions in a salt represent the spectator ions left over after the neutralization reaction

NaOH(aq) + HCl(aq) Na+(aq) + Cl

-(aq) + H2O(l)

o In the above reaction, the cation (Na+) is the conjugate acid of the base NaOH, and the

anion (Cl-) is the conjugate base of the acid HCl.

o NaOH is a strong base, and therefore, the conjugate acid (Na+) is so weak as to not have

any acidic properties at all

o HCl is a strong acid, and therefore, the conjugate base (Cl-) is so weak as to not have any

basic properties at all

Thus, the salt NaCl is composed of ions that do not have any acid or base properties, and will not affect the

pH of an aqueous solution

and

One can predict whether a salt will have acidic or basic properties by considering the nature of its

conjugate acid and base

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1. A salt derived from a strong acid and a strong base: As conjugate acid to a strong base and

conjugate base to a strong acid both salt ions will be so weak as to have no acid or base properties

(see above for NaCl ions)

2. A salt derived from a strong acid and a weak base: The conjugate base to the strong acid (i.e. the

anion of the salt) will have no basic properties. The conjugate acid to the weak base (i.e. the

cation) will have significant acidic property. Thus, this type of salt in aqueous solution will be

acidic in nature.

3. A salt derived from a weak acid and a strong base: The conjugate acid to the strong base (i.e. the

cation of the salt) will have no acidic properties. The conjugate base to the weak acid (i.e. the

anion) will have significant base property. Thus, this type of salt will be basic in nature.

4. A salt derived from a weak acid and a weak base: The conjugate acid to the weak base (i.e. the

cation) will have significant acidic properties and the conjugate base to the weak acid (i.e. the

anion) will have significant basic properties. Both cation and anion hydrolyze. The overall affect

on pH is dependent upon which is the stronger.

Acid-Base Behavior and Chemical Structure

How does the chemical structure of a substance determine whether it will behave as an acid, base, or

neither?

Factors that Affect Strength of Acids and Bases

For a molecule to donate a proton, the bond between the molecule and the hydrogen in question must be

polarized such that the shared electrons in the bond are attracted away from the leaving hydrogen, and

towards the rest of the molecule:

H has an electronegativity of 2.1 and carbon 2.5. This bond is slightly polar, but does not promote

withdrawal of the bonding electrons towards carbon. Thus, compounds containing exclusively C-

H bonds do not behave as acids

Na has an electronegativity of 0.9, in comparison to hydrogen's 2.1. Thus, in metal hydride

compounds (e.g. NaH) the shared electrons are actually withdrawn towards the hydrogen. In this

case, the hydrogen may be present as the hydride ion (H-) and act as a proton acceptor

In addition to appropriate polarity, the overall strength of the H-X bond is important in determining

whether the molecule can donate a proton

The H-F bond is the most polar bond that H can engage in. Although the polarity is such that the

shared electrons are withdrawn towards the F atom, H-F is actually considered to be a weak acid.

This is because the H-F bond is somewhat difficult to break (although when it does break, the

hydrogen leaves the bonding electrons behind).

Another consideration is the nature of the conjugate base that will form (X-).

If this compound is stable (i.e. chemically unreactive), then H-X will behave as an acid.

14

If X- is entirely unstable (for example, will readily react with H2O to produce HX and OH

-), then

H-X will not behave as an acid

Binary Hydrides

Are there periodic trends for hydrogen compounds of elements (i.e. hydrides)? The answer: somewhat.

Towards the left, hydride compounds will generally be basic

Towards the right, hydride compounds will generally be acidic

Elements on the left (i.e. the more metallic elements) want to give up valence electrons to achieve an octet,

and form cations

In this case, in a bond with hydrogen, the metal tends to give electrons to the departing hydrogen,

forming a hydride ion, H-. The hydride ion acts as a base, i.e. it will accept a proton to form H2(g).

Elements on the right (i.e. non-metals) want to accept valence electrons to achieve an octet, and form

anions

In this case, in a bond with hydrogen, the non-metal tends to keep the shared electrons, and the

departing hydrogen leaves as H+. This is the definition of an acid

What about moving down the periodic table?

Larger elements have weaker bonds due to reduced orbital overlap

A weaker H-X bond means that the compound is more likely to donate a proton. Thus, a hydride

compound is generally more acidic as we move down the periodic table

Oxyacids

Acids in which OH groups (and potentially other O atoms) are bonded to a central atom are called

oxyacids:

Sulfuric acid (H2SO4) - a strong acid!

Being an acid, H2SO4 donates a proton during chemical reactions

OH groups are also found in bases. However, in bases, the entire OH group is released (as OH

- ion) and H

+

is not released

What factors determine whether an OH group in a molecule will release a proton (H+), or the OH

- ion?

15

Consider the effects of the other atoms in the molecule. In particular, the atom that the OH group is bonded

to:

If Y has low electronegativity, the Y-O bond will most likely be ionic in nature and separate with

O retaining the shared electrons. This would be the case if Y was a metal (giving a basic metal

hydroxide)

If Y has higher electronegativity, the Y-O bond would be more covalent in character. In this case,

it is unlikely that the Y-O bond will break, and more likely that the O-H bond will break, yielding

a proton. This would be the case for Y = nonmetals, and the compound would most likely

represent an oxyacid.

As a general rule, as the electronegativity of Y increases, the acidic character of the compound increases

The high electronegativity of Y is felt by the H atom also. The attraction of Y for electrons helps to

"withdraw" the electrons in the O-H bond towards the Oxygen atom. The O-H bond becomes more

polar with increasing electronegativity of the neighboring Y atom.

In order for the resulting anion, Y-O-, to recombine with a proton, there must be a freely available

non-bonding pair of electrons on the oxygen. As the electronegativity of Y increases, it tends to

withdraw the non-bonding electrons of the oxygen (making them less available for a proton).

Thus, the greater the electronegativity of Y, the more stable the conjugate base (oxyanion)

Likewise, the more electronegative atoms (e.g. O) bonded to the central Y atom, the more they

help to withdraw electrons from the Y-O bond in question. The strength of an acid will increase as

additional electronegative groups are bonded to the central atom.

For oxyacids that have the same number of oxygen atoms, acid strength increases with increasing

electronegativity of the central atom

For oxyacids that have the same central atom, Y, acid strength increases as the number of oxygen atoms

attached to Y increases

Carboxylic Acids

Carboxylic acids are organic compounds that have the general formula R-COOH, where R is either a

hydrogen or a chain of carbon-based groups:

The -COOH portion of the structure is known as the carboxyl group

Acids that contain carboxyl groups are known as carboxylic acids

Lewis Acids and Bases

Recall the Arrhenius description of acids and bases:

An Arrhenius acid reacts in water to release a proton

16

An Arrhenius base reacts in water to release a hydroxide ion

In the Bronstead-Lowry description of acids and bases:

A B-L acid reacts to donate a proton

A B-L base accepts a proton

A B-L base, therefore, is a compound with an unshared pair of electrons that can from a bond with a

proton:

G.N.Lewis thought about acids and bases in terms of donation and acceptance of unshared pairs of

electrons:

A Lewis acid is defined as an electron-pair acceptor

A Lewis base is defined as an electron-pair donor

In the above example with ammonia, the ammonia is acting as a Lewis base (donates a pair of

electrons), and the proton is a Lewis acid (accepts a pair of electrons)

The description of an acid and a base by Lewis is consistent with the description by Arrhenius, and with the

definition by Bronstead-Lowry. However, the Lewis description, a base is not restricted in donating its

electrons to a proton, it can donate them to any molecule that can accept them.

Since we are so used to thinking about aqueous solutions and protons as the electron pair acceptor (i.e.

acid), any molecule like BF3 that can act as an "acid" according to Lewis' definition is explicitly referred to

as a "Lewis acid" (and not just as an "acid").

Lewis acids include molecules that have less than an octet of electrons in the valence shell

Many simple cations can function as Lewis acids. For example, Fe3+

can interact strongly with

cyanide ions to form Ferricyanide ion, Fe(CN)63-

. The Fe3+

ion has vacant valence shell orbitals

that can accept electrons from the cyanide ions (thus forming a covalent bond). The Fe3+

ion is

acting as a Lewis acid. Many metal ions can thus behave as acids (in the Lewis definition).

Compounds with multiple bonds can also behave as Lewis acids (i.e. they can accept pairs of

electrons and form new bonds:

17

The CO2 is acting as a Lewis acid - it can accept a pair of electrons because the multiple bonds

means there is a deficiency of valence electrons around the carbon. The product shown is unstable.

The O- group will act as a Lewis base and the neighboring H will act as a Lewis acid. This will

result in an O-H bond (and the O on the left will have two unshared pair of electrons).

Hydrolysis by Metal Ions

The solutions of many metal ions exhibit acidic properties

Metal ions are cations. The positive charge attracts an unshared pair of electrons on a water

molecule.

The water molecules surrounding a metal ion serve to hydrate (solvate) the ion. However, the

charge on the ion helps to increase the polar nature of the O-H bond of the water molecule - the

metal draws electrons away from the oxygen, the oxygen in turn draws the shared electrons in the

O-H bond away from the H atom.

This increase in the polar nature of the O-H bond shifts the Kw of these particular waters, and they

are more acidic than bulk solvent water molecules.

The waters involved in hydration of a metal ion give up protons (i.e. are ionized) more readily

than bulk solvent waters

Fe(H2O)63+

(aq) Fe(H2O)5(OH)2+

(aq) + H+(aq)

Ka = 2 x 10-3

Hydrolysis reactions generally increase with increasing ionic charge and decreasing ionic radius of the

metal ion

The Common-Ion Effect

A weak acid or weak base will partially ionize in aqueous solution. For example,

Weak acids often have Ka values < 1.0 x 10-3

Only a small percentage of the acid dissociates in aqueous solution

Ionic compounds (i.e. salts) dissociate completely in aqueous solution

Some salts may contain ions derived from weak or strong acids, or bases

Ions derived from strong acids or bases will not alter the pH (the conjugate base or conjugate

acid of a strong acid or strong base have no tendency to either accept or donate a proton)

Ions derived from weak acids or bases will have a certain tendency to either donate or accept

a proton (i.e. the reverse process to the ionization reaction that produced them), and will affect the

pH of the sample

18

What happens if a salt is added to a solution of a weak acid, and that salt contains a conjugate base to the

weak acid?

Example: Acetic acid (HC2H3O2)

The ionization of acetic acid, a weak acid, is as follows:

HC2H3O2(aq) C2H3O2-(aq) + H

+(aq)

Now let's add some Sodium Acetate salt.

Sodium acetate will dissociate completely in solution:

NaC2H3O2(aq) Na+(aq) + C2H3O2

-(aq)

We have increased the acetate conjugate base concentration (without increasing the concentration

of H+)

Le Chatelier's principle would predict that the equilibrium will shift to the left in order to minimize

the perturbing effects of the added concentration of conjugate base:

HC2H3O2(aq) C2H3O2-(aq) + H

+(aq)

This shift to the left will also result in a decrease in the H+ concentration

A reduction in the [H+] will raise the pH of the solution (i.e. be more basic)

A shift to the left means that less acid will dissociate

The "Common Ion Effect":

The dissociation of a weak electrolyte is decreased by adding to the solution a strong electrolyte (i.e. a salt)

that has an ion in common with the weak electrolyte

A similar type of result would be observed for the ionization of a weak base and the addition of a salt that

represents the conjugate acid

For example, ammonia (NH3) is a weak base that ionizes in H2O to produce ammonium ion

(NH4+) and hydroxide ion (OH

-)

NH3(aq) + H2O(l) NH4+(aq) + OH

-(aq)

The addition of ammonium sulfate salt (NH4)2SO4 would add ammonium ions (the conjugate

acid).

o This would shift the equilibrium concentration to the left

o This would reduce the [OH-] concentration and lower the pH

o Note that the sulfate ion, SO42-

, is the conjugate base of a strong acid (H2SO4, sulfuric

acid) and therefore has no basic properties (and is a spectator ion in the above ionization

reaction of ammonia)

Buffered Solutions

Solutions of a weak acid, and its conjugate base, establish an equilibrium:

HA H+ + A

-

From Le Chatelier's principle, the equilibrium opposes changes in the [H+] of the solution

o Addition of H+ will shift the equilibrium to the left (reducing [H

+])

o Removal of H+ will shift the equilibrium to the right (increasing [H

+])

19

Solutions that resist a change in pH upon addition of small amounts of acid or base are called

"Buffered" solutions (or just "Buffers")

Buffered solutions of weak acid/base conjugate pairs, and salts of that acid or base

Consider the weak acid HA:

HA(aq) H+(aq) + A

-(aq)

The corresponding acid dissociation constant, Ka, is:

We are interested in the possible buffering effects upon [H

+], so solving for [H

+] gives:

This simple analysis provides a clue as to the various entities that can influence the [H

+], and therefore, the

pH:

The value of the acid dissociation constant Ka

The ratio of the concentration of acid to conjugate base

How does the pH change with the addition of either H+ or OH

- ions?

OH- ions will react with H

+ ions to produce H2O(l). This is the neutralization reaction, or the

reverse of the water ionization reaction. In any case, it results in removal of H+ ions. The removal

of H+ ions will increase the pH (remember, pH = -log[H

+]; the smaller the value of [H

+] the greater

the value of -log)

o However, from Le Chatelier's principle the equilibrium will respond by shifting to the

right, increasing the [H+]

o If the equilibrium shifts to the right, however, [HA] will decrease and [A-] will increases.

Thus, the ratio [HA]/[A-] will get smaller. This is another way of saying that even though

the equilibrium shifts to the right to oppose the loss of [H+], it can't make up for the loss

entirely and the [H+] has to decrease somewhat

If the concentrations of [HA] and [A-] are large to begin with, and if the added concentration of OH

- is

small, the change in pH upon addition of the OH- will be small (the pH of the solution will be buffered)

What about the addition of H+ ions?

o From Le Chatelier's principle, the reaction will respond by shifting to the left, to reduce

the [H+]

o This is another way of saying the H+ reacts with the conjugate base, A

-, to produce the

acid HA

o Thus, in shifting to the left, A- is consumed and HA is produced. Therefore, the ratio

[HA]/[A-] will get larger. This is another way of saying that even though the system

responds by reducing [H+], it can't reduce the added H

+ entirely and the [H

+] has to rise

somewhat

Again, if the concentrations of [HA] and [A-] are large to begin with, and if the added concentration of

H+ is small, the change in pH upon addition of the H

+ will be small (the pH of the solution will be

buffered)

Weak acid/conjugate base pairs can therefore effectively buffer pH changes in either direction (i.e. buffer

against either an increase or decrease in [H+])

20

However, since the important aspect of buffering is to have the change in [HA] and [A-] be small

in response to the added [H+] or [OH

-], buffers work best when the ratio of [HA]/[A

-] is 1.0. (In

other words, if the concentration of either HA or A- is small, the solution can't buffer very well)

From the above equation, if [HA]/[A-] = 1.0, then [H

+] = Ka

Thus, for any give weak acid/conjugate base pair, there will be a pH at which it has the greatest buffering

capacity.

This pH will be where the [H+] = Ka.

In other words, best buffer pH = -log(Ka) = pKa

For example, if you want to buffer a solution at pH = 8.5 choose a weak acid/base conjugate pair

whose pKa = 8.5. (log Ka = -8.5, Ka = 3.16 x 10-9

; hypobromous acid is sort of close, pKa = 2.5 x

10-9

)

Buffer Capacity and pH

The two important characteristics of a buffer are:

The pH at which the buffer is most effective (this will be equal to the pKa for that buffer)

How much acid or base can be added before the pH starts to change

The greater the concentrations of both [HA] and [A-] (i.e. the acid/conjugate base-pair) the greater the

buffering capacity

How do the other components (i.e. conjugate base and undissociated acid when considering weak acids)

affect the pH?

From the equation relating [H+] to the concentration of acid/conjugate base:

It can be seen that [H

+], and therefore, the pH, is dependent upon the relative concentrations of the acid

(HA) and conjugate base (A-)

Thus, pH is determined not only by the pKa of the acid/conjugate base-pair, but also the concentration of

the acid and conjugate base

This relationship is known as the Henderson-Hasselbalch equation.

It allows one to determine the pH of a solution from knowing the pKa of the buffer and the concentration of

the acid and conjugate base components

A buffer works best when the concentration of the acid component (HA) is equal to the

concentration of the conjugate base (A-)

However, we know that for weak acids, only a small percentage of the acid will dissociate at

equilibrium. Therefore, the concentration of conjugate base will be quite small

21

How can we get the concentration of conjugate base to be equivalent to the concentration of the acid

component?

We can use the common ion effect

The acid and conjugate base components share a common ion

HC3H5O3(aq) H+(aq) + C3H5O3

-(aq)

(lactic acid) (protons) + (lactate ion)

The conjugate base ion can be added as a salt, where the cation component is from a strong base

NaC3H5O3

Sodium Lactate salt

The sodium lactate salt will dissociate completely, releasing Na+ and C3H5O3

-

NaC3H5O3(aq) Na+(aq) + C3H5O3

-(aq)

The Na+(aq) is the conjugate acid of a strong base (NaOH), and will therefore, not change the pH

(it has no desire to react with an OH- group)

The C3H5O3-(aq) will raise the concentration of this component in the solution. (Normally,

increasing this conjugate base will shift the equilibrium to the left. However, this will only happen

if an equivalent amount of H+ is around. Since we added the C3H5O3

- as the sodium salt, no H

+

was added (or is available)).

Finally, in the Henderson-Hasselbalch equation, the concentrations of [conjugate base] and [acid]

refer to the concentrations at equilibrium. However, since such a small percentage of the acid will

dissociate in solution, and such a small percentage of added conjugate base will be protonated, we

can use the starting concentrations of acid and conjugate base as relatively accurate values in

the calculation

Thus, most buffer solutions are made of a weak acid with the conjugate base (in approximately equal

concentration) supplied as a salt (where the cation is the conjugate acid of a strong base). [similarly with

buffers of a weak base]

Addition of Strong Acids or Bases to Buffers

As long as we do not exceed the buffering capacity of the buffer, we can assume that a strong acid, or

strong base, reacts completely with the buffer

To calculate the effect upon the pH, assume that all the H+ of an added strong acid reacts with the

conjugate base of the buffer, to produce an equivalent concentration of the acid form of the buffer.

Likewise, to calculate the effect upon the pH, assume that all the OH- of a strong base reacts with

the acid form of the buffer (i.e. it neutralizes an equivalent concentration of H+, this in turn is

obtained by a stoichiometrically equivalent amount of buffer acid that must dissociate) to produce

an equivalent concentration of conjugate base form of the buffer.

Acid-Base Titrations

In an acid-base titration a solution containing a known concentration of base is slowly added to an acid

until the acid is completely neutralized. Alternatively, a known concentration of acid is slowly added to a

basic solution until the base is completely neutralized.

22

The equivalence point is the point at which a stoichiometrically equivalent amount of base has

been added to the acid

This situation can be identified by noting an appropriate (pH-induced) color change in an

indicator dye that is added to the solution. Or a pH meter can be used to measure the pH of the

solution as a function of added base

A graph or plot of the pH as a function of added titrant (e.g. base solution) is called a titration

curve

o A titration curve can help to figure out when the equivalence point occurs, and also the

value of the acid or base dissociation constant (i.e. Ka, or Kb). The titration curve can also

help identify what type of indicator dye would be most useful in following the acid-base

neutralization reaction

Strong Acid - Strong Base Titrations

A strong acid ionizes completely in solution. Likewise, a strong base.

The conjugate base of the strong acid has no tendency to combine with a H+. Likewise, the

conjugate acid of the strong base has no tendency to combine with OH- to produce a H2O.

Therefore, when a strong acid is combined with a strong base it produces a salt (anion from strong acid,

cation from a strong base) that has no tendency to affect the pH of a solution

Example:

HCl(aq) + NaOH(aq) NaCl(aq) + H2O(l)

What happens when a stoichiometrically equivalent amount of strong base is added to a solution of a strong

acid?

All of the H+ ions present in the acid react with an equivalent amount of OH

- ions from the base;

and there are no net H+ or OH

- ions left over (i.e. [H

+] = [OH

-]). The reaction of the H

+ and OH

-

ions produces H2O(l)

Also, [Na+] = [Cl

-], and we essentially have a solution of H2O and NaCl(aq)

Since the NaCl produced has no effect upon pH, when an equivalent amount of NaOH is added to

a solution of HCl the solution has a neutral pH (i.e. pH = 7.0)

What happens if a less-than-stoichiometrically equivalent amount of strong base is added to the strong acid

solution?

For the NaOH that is added, all of it will ionize, and all of the OH- ions added will react with acid

(to produce Na+ and H2O(l))

Since the NaOH that was added is less than the concentration of HCl acid, there will be remaining

H+ ions and Cl

- ions

The solution will contain H+, Cl

- and Na

+ ions (essentially no OH

- ions)

The [Cl-] will be greater than [Na

+] in this case, but who cares? We have already determined that

they don't affect the pH anyway. Thus, the solution will be acidic if less-than-stoichiometrically

equivalent amount of base is added

The concentration of [H+] ion will be equal to the starting concentration minus the amount that is

neutralized. The amount that is neutralized is equal to the concentration of added base. The pH of

the solution will be determined by the amount of [H+] remaining after this neutralization

What happens if a greater-than-stoichiometrically equivalent amount of base is added to the acid solution?

All H+ from the acid are neutralized (essentially no H

+ from the acid remains)

There will be Cl- ions, Na

+ ions and OH

- ions in solution. Thus, the solution will be basic.

23

The [Na+] will be greater than [Cl

-], but who cares? These ions don't affect pH. Thus, the pH will

depend upon the concentration of the OH- ions in solution.

The concentration of OH- ions will be equal to the amount of basic solution added minus the

amount that is neutralized. The amount neutralized is equal to the concentration of acid in the

original sample.

Here is what a titration curve of a strong-acid/strong-base titration experiment might look like:

As we approach the equivalence point, the concentration of [H

+] gets very small, and therefore, small

additions of base will make a large relative change in the concentration of [H+].

Because of this, there is a large change in pH near the equivalence point

This behavior also means that we can use an indicator dye to show when we are very close to the

equivalence point, even though the indicator may change color at a pH that is not exactly equal to

pH 7.0

The Addition of a Strong Base to a Weak Acid

This gets a little complicated because the conjugate base of the weak acid will affect the pH of the solution

(i.e. it will have some tendency to combine with a proton and produce the weak acid, thus affecting the

concentration of H+)

Thus, we need to consider the stoichiometry between the acid and the base, and the equilibrium

reactions of the species that remain

The amount of strong base that is added will ionize completely, to produce a stoichiometric

amount of OH-(aq) and conjugate acid (e.g. Na

+)

o The stoichiometric amount of OH-(aq) will react completely with an equivalent amount

of H+ ion released by the weak acid

o Therefore, a stoichiometric amount of weak acid will ionize and be neutralized.

o This will also result in the production of a stoichiometric amount of conjugate base:

HA(aq) + OH-(aq) A

-(aq) + H2O(l)

This amount of conjugate base has to be factored into the equilibrium expression to determine the [H+]

The remaining weak acid (after the neutralization) is the concentration for the pH calculation

24

Titration Curves of Weak Acids with a Strong Base

At the equivalence point the solution contains only the salt

o However, for a weak acid, the salt contains the conjugate base, which is able to

recombine with a proton.

Thus, at the equivalence point of the titration of a weak acid with a strong base, the solution is slightly

basic

After the equivalence point, the solution contains salt and excess (i.e. non-neutralized) base (OH-).

The pH of the solution after the equivalence point is determined mainly by the excess OH- ions

provided by the strong base

Notice that after one-half of the acid has been stoichiometrically titrated the [HA] = [A-]. At this

point the pH = pKa. If you look at the above curves you will notice that the titration profile is

relatively flat around the pH = pKa point. This means that within this region the pH is not

changing much upon the addition of small amounts of base. This is the definition of a "buffered"

solution, and explains why the most effective buffering is at a pH value equal to the pKa.

Notice also that the transition is sharp at the equivalence point. This is the opposite property that

we would want for a buffered solution. It means that the pH changes a lot with small changes of

added base. At the equivalence point all the acid has been titrated and essentially none of the [HA]

form remains. Thus, there is no longer any ability to neutralize added base (and so, the solution

can no longer buffer against such changes)

The Titration of a Weak Base with a Strong Acid

Similar features are observed for the titration of a weak acid/base with a strong base/acid

In the case of a weak base titrated with a strong acid, the pH after the equivalence point is

determined by the excess [H+] from the strong acid

At the equivalence point, the solution contains conjugate base of the strong acid (e.g. Cl-; does not

affect pH) and conjugate acid (e.g. NH4+ which will affect pH - i.e. has some tendency to release

H+ ions). The conjugate acid can donate a proton, thus, at the equivalence point the pH is lower

than neutral (pH 7.0)

25

Titrations of Polyprotic Acids

Polyprotic acids can potentially donate more than one proton

Each proton will have an associated Ka value

The titration curve will reflect the separate Ka values

o There will be two unique equivalence points, associated with the separate Ka values

© 2000 Dr. Michael Blaber

Additional Aspects of Aqueous Equilibria

Solubility Equilibria

It is time to consider another type of equilibrium: solubility equilibrium

An ionic solid may dissolve in water, but, how much will dissolve?

If enough ionic solid is added to a solvent, some will dissolve but some will be left as undissolved

solid

Is there a way to predict how much of a particular ionic solid will dissolve in a solution?

The Solubility-Product Constant, Ksp

Barium sulfate (BaSO4) is an ionic solid that has a certain solubility in H2O(l). If enough BaSO4 is added to

a solution of H2O(l) the solution will become saturated, and some solid BaSO4 will remain.

In the case of the saturated solution, an equilibrium is established between the solid and dissolved

ions of BaSO4

BaSO4(s) Ba2+

(aq) + SO42-

(aq)

This is an example of a heterogeneous equilibrium (the reactants and products are not all in the

same phase)

o In writing the equilibrium expression we omit the "concentration" of the solid

component(s)

26

Ksp is the solubility product constant (or just the solubility product)

Note that although the concentration for the solid component(s) is omitted, for the equilibrium to exist

some undissolved BaSO4 must be present

o In other words, Ksp = [Ba2+

(aq)][SO42-

(aq)] is true only when some solid BaSO4 is present

in the solution

Ksp describes the equilibrium concentrations of dissolved ions that exists under conditions of

saturation with the solid form

o The smaller the value of Ksp, the lower the solubility of the ions of an ionic solid

o Writing the expression of Ksp is similar for other equilibrium constants; it is equal to the

product of the concentrations of the dissolved ions raised to the power of the coefficients

from the balanced equation

Solubility and Ksp

Solubility

The amount of a substance that dissolves when producing a saturated solution

o Solubility can be expressed in g/L or as molar solubility (i.e. mol/L)

Solubility product constant (Ksp)

Describes the concentration(s) of dissolved ions, or substance(s), at saturation equilibrium

The solubility of a substance may change as the concentrations of various ions change (including H+),

however, the value of Ksp is unique for a given solute at a specified temperature.

Factors that Affect Solubility

The solubility product constant, Ksp, varies with temperature, therefore, temperature will influence

the solubility of a compound.

However, the presence of other solutes (i.e. other dissolved ions or compounds) can also influence

the solubility - although they do not alter Ksp

There are three effects upon the solubility of a compound that we need to consider:

1. The presence of common ions

2. The pH of the solution (i.e. the effect of [H+] or [OH

-] on the solubility)

3. The presence of complexing agents

Common Ion Effect

In the solubility equilibrium of CuCl we have:

CuCl(s) Cu+(aq) + Cl

-(aq)

Ksp = 1.21 x 10-6

27

From Le Chatelier's principle, addition of Cu+ ion, or Cl

- ion, will shift the equilibrium to the left

o This will favor formation of the solid, and reduce the concentration of solvated ions, and

the solubility of the compound will decrease

The solubility of a partially soluble salt is reduced by the presence of a second solute that provides a

common ion

Solubility and pH

Magnesium hydroxide is an ionic compound that dissociates to produce magnesium ions and hydroxide

ions:

Mg(OH)2(s) Mg2+

(aq) + 2OH-(aq)

Ksp = [Mg2+

] [OH-]

2 = 1.8 x 10

-11

If X = the concentration of Mg(OH)2 that dissolves at equilibrium, then the solubility product constant, Ksp,

can be defined as follows:

Ksp = [X] * [2X]2 = 1.8 x 10

-11

4X3 = 1.8 x 10

-11

X = 1.04 x 10-4

M

The [Mg2+

] at equilibrium equals 1.04 x 10-4

The [OH-] at equilibrium equals 2.08 x 10

-4M

The pOH therefore equals 3.68, and pH is therefore (14.0 - 3.68) = 10.3

If the same Mg(OH)2 solution is made in a buffer at pH 9.0, what is the effect upon the solubility?

At pH = 9.0, the pOH = (14 - 9.0) = 5.0

Therefore, the [OH-] = 1.0 x 10

-5M

Since the solution is buffered, the [OH-] at equilibrium will also be 1 x 10

-5M

Ksp = 1.8 x 10-11

= [Mg2+

]*[OH-]

2

1.8 x 10-11

= [Mg2+

]*[1.0 x 10-5

]2

[Mg2+

] = 0.18M

Note from above that at the pH of 10.6 the concentration of dissolved Mg2+

ion was 2.08 x 10-4

.

Therefore, more of the Mg(OH)2 salt dissolved at pH 9.0 compared to pH 10.6

In this case, lowering the pH reduces the equilibrium [OH-] and from Le Chatelier's principle, this will

drive the reaction to the right (i.e. more salt will dissolve)

Consider the dissolution of CaF2:

CaF2(s) Ca2+

(aq) + 2F-(aq)

The F-(aq) ion is a weak base and can combine with H

+(aq) to produce the weak acid HF:

F-(aq) + H

+(aq) HF(aq)

In aqueous solution, therefore, the overall (balanced) equation for the dissolution of CaF2(s) would

consist of two consecutive reactions whose net reaction would be:

CaF2(s) + 2H+(aq) Ca

2+(aq) + 2HF(aq)

Thus, from Le Chatelier's principle, as the [H+] increases (i.e. as pH decreases) the reaction is

driven to the right (more of the solid dissolves)

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In both of the above cases (i.e. Mg(OH)2 and CaF2) we have seen that solubility increases with increasing

[H+] (decreasing pH)

In both cases the solid dissolves to produce an anion that is basic in nature. Increasing the [H+]

essentially removes the free anion from solution by forming the weak acid. This drives the

reaction to the right and more solid dissolves.

The solubility of slightly soluble salts containing basic anions increases as [H+] increases (as pH is

reduced)

The more basic the anion, the more pronounced the effect

Formation of Complex Ions

Metal ions characteristically act as Lewis acids towards H2O(l)

They accept a non-bonding pair of electrons from H2O(l) which behaves as a Lewis base

Other compounds can act as Lewis bases towards metal ions

Such interactions can affect the solubility of the metal ion

AgCl(s) has a low solubility in H2O(l), but can be solubilized in H2O(l) with the addition of ammonia

(NH3)

AgCl(s) Ag+(aq) + Cl

-(aq)

Ag+(aq) + 2NH3(aq) Ag(NH3)2

+(aq)

AgCl(s) + 2NH3(aq) Ag(NH3)2+(aq) + Cl

-(aq)

The presence of NH3(aq) will drive the dissolution of AgCl(s) because it effectively removes free

Ag+(aq) ions from solution (thus, the top reaction above is driven to the right by Le Chatelier's

principle)

The metal ion is hydrated (surrounded, separated and dispersed) by H2O(l) molecules

In order for the NH3(aq) molecules to act as a Lewis base with the metal ions, they must have a

greater affinity for the metal ion than do the H2O(l) molecules

An assembly of a metal ion and the Lewis bases bonded to it, is called a complex ion

o The stability of a complex ion can be judged by the magnitude of the equilibrium

constant for its formation

What is the concentration of Ag

+(aq) in a 0.01M solution of AgNO3(s) at equilibrium if NH3(aq) is added

to give an equilibrium concentration of NH3(aq) of 0.20M. Don't worry about any volume change when the

ammonia is added. The equilibrium equation for the formation of the complex ion of Ag+(aq) with NH3(aq)

is:

Ag+(aq) + 2NH3(aq) Ag(NH3)2

+(aq)

And

Kf = 1.7 x 107

The concentration of Ag+(aq) at equilibrium = XM

The concentration of NH3(aq) at equilibrium is given as 0.20M

What about the equilibrium concentration of Ag(NH3)2+(aq)?

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Kf is fairly large. Therefore, NH3(aq) will be quite effective at removing the Ag+(aq) ion. Since we

have an excess of NH3(aq) compared to AgNO3(s) we can assume that almost all of the AgNO3(s)

will be converted to either Ag+(s) or complex ion

Thus, at equilibrium the concentration of Ag(NH3)2+(aq) = (0.01 - X)M

6.8 x 10

5X + X = 0.01

6.8 x 105X ~ 0.01

X = 1.47 x 10-8

M

The presence of NH3(aq), and the formation of the complex ion with Ag+(aq), significantly reduces the

equilibrium concentration of Ag+(aq) ion, and thus drives the dissolution of AgNO3(s)

If a metal forms a complex with a Lewis base, such as NH3, CN- or OH

-, the solubility will increase

Amphoterism

If a metal hydroxide, or metal oxide, is amphoteric (i.e. can act as either an acid or a base), then it may be

soluble in both acidic and basic solutions (even though it may not be soluble in neutral solutions)

Acids promote dissolving of compounds containing basic anions

Bases promote dissolving of compounds containing acidic cations

Precipitation and Separation of Ions

Solubility, and the establishment of a saturated solution, is an equilibrium process

At equilibrium the rate of solubilization of molecules is equal to the rate of crystallization of the

solid

Note: crystallization denotes an orderly lattice arrangement of molecules as they are desolvated. However,

desolvation may also result in a disordered arrangement of desolvated molecules - known as a precipitate

The equilibrium condition can be reached from either direction. Consider the establishment of equilibrium

for a saturated solution of NaCl:

NaCl(s) Na+(aq) + Cl

-(aq)

Ksp = [Na+(aq)]*[Cl

-(aq)]

We could start with NaCl(s) and add water.

o In this case, at the start of the experiment there are no solvated ions of Na+ or Cl

-

o The reaction proceeds to the right as equilibrium is achieved

In principle, we could also start by combining solutions that contained Na+(aq) and Cl

-(aq) ions

and no solid NaCl

o If the product of the ion concentrations was greater than Ksp then solid NaCl would start

to form

o The reaction would proceed to the left as equilibrium is achieved

Determination of the reaction quotient, Q, for reactions has previously allowed us to determine the

direction that a given reaction will proceed. The same is true for figuring out whether a solution of ions will

precipitate

We will compare the value of Q to the value of the solubility product constant, Ksp

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For equilibrium expressions involving solubility, Q is calculated omitting the concentrations of

solid or liquid components (their concentrations don't change)

o In the above case, for example, Q = [Na+(aq)]*[Cl

-(aq)]

o In other words, the determination of Q (and Ksp) involves only consideration of the

concentrations of the soluble ions in the solution. Thus, Q is referred to as the ion

product

When comparing the value of the ion product to the solubility product, there are three possible situations

and we can draw the following conclusions:

1. Q > Ksp : in this case we are starting with a situation where the product of the concentrations of the

soluble ions is greater than the expected value at equilibrium. Therefore, the concentration of

soluble ions must decrease as equilibrium is achieved. In other words, the reaction is driven to the

left, and solid compound is produced.

2. Q = Ksp : in this case we are starting with a situation where the product of the concentrations of the

soluble ions is equal to the value expected at equilibrium. In other words, we are already in an

equilibrium situation and overall ion concentrations (and mass of solid) will not change.

3. Q < Ksp : in this case we have a situation where we are starting with insufficient concentration of

soluble ions. At equilibrium more soluble ions will be present. Therefore, the reaction must

proceed to the right, and some amount of the solid form of the compound must dissolve and

release more soluble ions.

How can situation #1 arise? How can we start with Q > Ksp? In short, how can we have essentially a greater

concentration of ions than the solubility product constant will allow?

The concentration of ions may arise from different solutions of salts or compounds. For example,

when considering the concentration of Na+ and Cl

- ions and the possibility of NaCl precipitating or

crystallizing, it may be the case that Na+ ions are being provided by another ionic compound (i.e.

NaOH) and the Cl- ions are also being provided by another solution (i.e HCl).

These solutions may be quite soluble as separate solutions, but when mixed, the concentrations of

ions may be too great for the solubility of NaCl(s).

Ions can be separated from each other based on the solubility’s of their salts

AgCl is not particularly soluble, whereas, CuCl2 is highly soluble

If Cl- ions are added to a solution of Ag

+(aq) and Cu

2+(aq) ions, the Ag

+(aq) ions will selectively

precipitate as AgCl(s)

Separation of ions in an aqueous solution by using a reagent that forms a precipitate with one of the ions is

called selective precipitation

Qualitative Analysis of Metal Ions

Metathesis Reactions

In many aqueous reactions it seems that the reaction involves the ionic compounds swapping their ionic

partners. For example, in the reaction involving the ionic compounds silver nitrate and potassium chloride

we have:

31

The silver cation exchanges its nitrate anion partner for the chloride anion. Likewise, the potassium cation

exchanges chloride anion for the nitrate anion:

This swapping of ions in aqueous reactions can be symbolically represented as follows:

This type of reaction is known as a Metathesis reaction

Note: metathesis is not pronounced "meta-thesis", but rather "meh-TATH-eh-sis" (apparently the Greeks

prefer to pronounce it that way)

There is something subtle in the above example that is important to note.

Take a look at the state of the silver chloride ion pair.

The AgCl(s) is a solid, and therefore the ions are not dispersed in solution. In fact, they precipitate

out of solution.

The precipitation effectively removes the AgCl ions from the solution, and this is the driving

force for the observed metathesis reaction

The driving force for metathesis reactions is the removal of ions from solution

What are the ways in which ions can be removed from solution and thus drive a metathesis reaction?

1. Certain ions can associate to form an insoluble precipitate (as with the formation of AgCl(s))

2. Certain ions can chemically combine to form a neutral molecular compound (resulting in

either a non-electrolyte, or a weak electrolyte).

o Acid/base neutralization reactions that produce water from H+ and OH

- ions are an

example of this.

o Being a non-electrolyte (or weak electrolyte) the formation of the molecular compound

from the constituent ions is essentially an irreversible process

3. Certain ions can chemically combine to form a gas, and the gas physically escapes from the

solution

Precipitation Reactions

Metathesis reactions that result in an insoluble precipitate are called precipitation reactions

Solubility refers to the amount of a substance that can be dissolved in a given quantity of water.

This is a consideration of the relative strength of water:ion versus ion:ion attractive forces. If

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the ion:ion attractive forces are greater than water:ion attractive forces, then the ion:ion

interaction will predominate, resulting in precipitation (i.e. lack of solvation)

The solubility of an ionic compound determines whether it will precipitate or not

Any substance with a solubility less than 0.01 moles/L will be considered as essentially insoluble

The solubility of NaCl is around 10 moles/L (it is highly soluble and won't drive a metathesis

reaction). The solubility of PbI2 is around 0.0012 moles/L (it is essentially insoluble, and can drive

a metathesis reaction).

The reaction of KI and Pb(NO3)2:

The PbI2 is an insoluble ionic compound that will precipitate and drive the metathesis reaction:

Can we predict whether an ionic compound will be soluble or not?

If an ionic compound is insoluble it means that neighboring ions have an attraction for each other

that is greater than the attraction of water for the ions (i.e. water molecules cannot separate,

surround and disperse the ions in the ionic solid)

Unfortunately, there are no clear rules for solubility based on physical properties of ions.

However, some general behaviors of certain ions are observed:

Qualitative Analysis

Qualitative analysis is a type of analysis that informs you of the presence of a substance, but does not tell

you exactly how much of the substance there is. It is like being able to get a "yes" or "no" answer to the

question "is a particular metal ion present in this sample?"

If the ion in question is not present, then a qualitative analysis will provide a quantitative answer,

i.e. 0

Although automated instrumentation has superceded many qualitative methods, a general method for

qualitative analysis of metal ions in solution is still in use. The general outline of the method is as follows:

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This method will divide a wide collection of soluble metal ions into 5 general groups. These are (in order of

the experimental steps needed to separate them):

1. Insoluble chlorides

2. Acid-insoluble sulfides

3. Base-insoluble hydroxides and sulfides

4. Insoluble phosphates

5. Alkali metal ions and ammonia

Additional analytical methods are required to identify the individual components in each group

© 2000 Dr. Michael Blaber