Lecture 6. Acids, Bases and Solvent Systems.

Bartley Lab with pH indicator colours
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An acid (from the Greek oxein then Latin acidus/acére meaning sour) is a chemical substance whose aqueous solutions were characterized by a sour taste, the ability to turn blue litmus red, and the ability to react with bases and certain metals (like calcium) to form salts. Aqueous solutions of acids have a pH smaller than 7. The lower the pH, the higher the acidity and thus the higher the concentration of hydrogen ions in the solution (using the Arrhenius or Brønsted-Lowry definition).

Some notes on acids-bases, pH and the use of logarithms in calculations are available.

There are a number of common definitions for acids, for example, the Arrhenius, Brønsted-Lowry, and the Lewis definition. The Arrhenius definition defines acids as substances which increase the concentration of hydrogen ions (H+), when dissolved in water. The Brønsted-Lowry definition is an expansion of this and defines an acid as a substance which can act as an H+ donor. By this definition, any compound which can be easily deprotonated can be considered an acid. Examples include alcohols and amines which contain O-H or N-H fragments. A Lewis acid is a substance which can accept a pair of electrons to form a covalent bond. Examples of Lewis acids include all metal cations, and electron-deficient molecules such as boron trifluoride and aluminium trichloride.

Common examples of acids include hydrochloric acid (a solution of hydrogen chloride gas in water, this is the acid found in the stomach that activates digestive enzymes), acetic acid (vinegar is a dilute solution, generally under 5%), sulfuric acid (used in wet-cell car batteries), and tartaric acid (a solid used in baking). As these examples show, acids can be solutions or pure substances, and can be derived from solids, liquids, or gases.

HCl(aq) + NaOH(aq) ⇄ NaCl + H2O
HOAc(aq) + NaOH(aq) ⇄ NaOAc + H2O
H2SO4(aq) + 2NaOH(aq) ⇄ Na2SO4 + 2H2O
HO2CCH(OH)CH(OH)CO2H(aq) + 2NaOH(aq) ⇄ Na2Tartrate + 2H2O


The "modern" concept of a base in chemistry, stems from Guillaume-François Rouelle who in 1754 suggested that a base was a substance which reacted with acids "by giving it a concrete base or solid form" (as a salt). In addition they gave aqueous solutions which were characterized as slippery to the touch, tasted bitter, changed the colour of indicators (e.g., turned red litmus paper blue), and promoted certain chemical reactions (base catalysis). Examples of bases are the hydroxides of the alkali and alkaline earth metals (NaOH, Ca(OH)2, etc.).

For a substance to be classified as an Arrhenius base, it must produce hydroxide ions in solution. In order to do so, Arrhenius believed the base must contain hydroxide in the formula. This made the Arrhenius model limited, as it did not readily explain the basic properties of aqueous solutions of ammonia (NH3.aq, often written as NH4OH to better fit the Arrhenius model) or its organic derivatives (amines). In the more general Brønsted-Lowry acid-base theory, a base is a substance that can accept hydrogen ions (H+). In the Lewis model, a base is an electron pair donor.

Oxides and Hydroxides

An early classification of substances arose from the differences observed in their solubility in acidic and basic solutions. This led to the classification of oxides and hydroxides as being either acidic or basic. Acidic oxides or hydroxides either reacted with water to produce an acidic solution or were soluble in aqueous base. Basic oxides and hydroxides either reacted with water to produce a basic solution or readily dissolved in aqueous acids. The diagram below shows there is strong correlation between the acidic or basic character of oxides (ExOy) and the position of the element, E, in the periodic table.

Oxides of metallic elements are generally basic oxides, and oxides of nonmetallic elements acidic oxides. Take for example, the reactions with water of calcium oxide, a metallic oxide, and carbon dioxide, a nonmetallic oxide:

CaO(s) + H2O(l) → Ca(OH)2
CO2(g) + H2O(l) → H2CO3(aq)

Calcium oxide reacts with water to produce a basic solution of calcium hydroxide, whereas carbon dioxide reacts with water to produce a solution of carbonic acid.

classification of oxides
There is a gradual transition from basic oxides to acidic oxides from the lower left to the upper right in the periodic table.

Basicity of the oxides increase with increasing atomic number down a group:
BeO < MgO < CaO < SrO < BaO

Note as well that acidity increases with increasing oxidation state of the element:
MnO < Mn2O3 < MnO2 < Mn2O7
in keeping with the increase in covalency.

Oxides of intermediate character, called amphoteric oxides, are located along the diagonal line between the two extremes. Amphoteric species are molecules or ions that can react as an acid as well as a base. The word has Greek origins, amphoteroi (άμφότεροι) meaning "both". Many metals (such as copper, zinc, tin, lead, aluminium, and beryllium) form amphoteric oxides or hydroxides. Amphoterism depends on the oxidation state of the oxide.

For example, zinc oxide (ZnO) reacts with both acids and with bases:
In acid: ZnO + 2H+ → Zn2+ + H2O
In base: ZnO + 2OH- + H2O→ [Zn(OH)4]2-
This reactivity can be used to separate different cations, such as zinc(II), which dissolves in base, from manganese(II), which does not dissolve in base.

Aluminium hydroxide is another amphoteric species:
As a base (neutralizing an acid): Al(OH)3 + 3HCl → AlCl3 + 3H2O
As an acid (neutralizing a base): Al(OH)3 + NaOH → Na[Al(OH)4]

Acid-Base theories and concepts

Arrhenius acids and bases
Although the term proton is often used for H+, this should really be reserved for H (protium) not D (deuterium) or T (tritium). The more general term, hydron covers all isotopes of hydrogen.

The Swedish chemist Svante Arrhenius attributed the properties of acidity to hydrogen ions (H+) in 1884. An Arrhenius acid is a substance that, when added to water, increases the concentration of H+ ions in the water. Note that chemists often write H+(aq) and refer to the hydrogen ion when describing acid-base reactions, but the free hydrogen nucleus does not exist alone in water, it exists in a hydrated form which for simplicity is often written as the hydronium (hydroxonium) ion, H3O+. Thus, an Arrhenius acid can also be described as a substance that increases the concentration of hydronium ions when added to water. This definition stems from the equilibrium dissociation (self-ionization) of water into hydronium and hydroxide (OH-) ions:

H2O(l) + H2O(l) ⇌ H3O+(aq) + OH-(aq)

Kw is defined as [H+][OH-] and the value of Kw varies with temperature, as shown in the table below where at 25 °C Kw is approximately 1.0*10-14, i.e. pKw= 14.

Water temperature Kw / 10-14 pKw
0 °C 0.112 14.95
25 °C 1.023 13.99
50 °C 5.495 13.26
75 °C 19.95 12.70
100 °C 56.23 12.25

In pure water the majority of molecules are H2O, but the molecules are constantly dissociating and re-associating, and at any time a small number of the molecules (about 1 in 107) are hydronium and an equal number are hydroxide. Because the numbers are equal, pure water is neutral (not acidic or basic) and has an electrical conductivity of 5.5 microSiemen, μS m-1. For comparison, sea water's conductivity is about one million times higher, 5 S m-1.

An Arrhenius base, on the other hand, is a substance which increases the concentration of hydroxide ions when dissolved in water, hence decreasing the concentration of hydronium ions.

To qualify as an Arrhenius acid, upon the introduction to water, the chemical must either cause, directly or otherwise:
Conversely, to qualify as an Arrhenius base, upon the introduction to water, the chemical must either cause, directly or otherwise:
The definition is expressed in terms of an equilibrium expression:

acid + base ⇌ conjugate base + conjugate acid.

With an acid, HA, the equation can be written symbolically as:

HA + B ⇌ A- + HB+

The equilibrium sign, ⇌, is used because the reaction can occur in both forward and backward directions. The acid, HA, can lose a hydron to become its conjugate base, A-. The base, B, can accept a hydron to become its conjugate acid, HB+. Most acid-base reactions are fast so that the components of the reaction are usually in dynamic equilibrium with each other.

Brønsted-Lowry acids and bases

While the Arrhenius concept is useful for describing many reactions, it has limitations. In 1923, chemists Johannes Nicolaus Brønsted and Thomas Martin Lowry independently recognized that acid-base reactions involve the transfer of a hydron. A Brønsted-Lowry acid (or simply Brønsted acid) is a species that donates a hydron to a Brønsted-Lowry base. The Brønsted-Lowry acid-base theory has several advantages over the Arrhenius theory. Consider the following reactions of acetic acid (CH3COOH):

CH3COOH + H2O ⇌ CH3COO- + H3O+
CH3COOH + NH3 ⇌ CH3COO- + NH4+

Both theories easily describe the first reaction: CH3COOH acts as an Arrhenius acid because it acts as a source of H3O+ when dissolved in water, and it acts as a Brønsted acid by donating a hydron to water. In the second example CH3COOH undergoes the same transformation, in this case donating a hydron to ammonia (NH3), but it cannot be described using the Arrhenius definition of an acid because the reaction does not produce hydronium ions.

Lewis acids and bases

A third concept was proposed in 1923 by Gilbert N. Lewis which includes reactions with acid-base characteristics that do not involve a hydron transfer. A Lewis acid is a species that reacts with a Lewis base to form a Lewis adduct. The Lewis acid accepts a pair of electrons from another species; in other words, it is an electron pair acceptor. Brønsted acid-base reactions involve hydron transfer reactions while Lewis acid-base reactions involve electron pair transfers. All Brønsted acids are Lewis acids, but not all Lewis acids are Brønsted acids.

BF3 + F- ⇌ BF4-
NH3 + H+ ⇌ NH4+

In the first example BF3 is a Lewis acid since it accepts an electron pair from the fluoride ion. This reaction cannot be described in terms of the Brønsted theory because there is no hydron transfer. The second reaction can be described using either theory. A hydron is transferred from an unspecified Brønsted acid to ammonia, a Brønsted base; alternatively, ammonia acts as a Lewis base and transfers a lone pair of electrons to form a bond with a hydrogen ion.

Hard and Soft Acids and Bases, Pearson's HSAB

This theory proposes that soft acids react faster and form stronger bonds with soft bases, whereas hard acids react faster and form stronger bonds with hard bases, all other factors being equal. The classification in the original work was largely based on equilibrium constants for the reaction of two Lewis bases competing for a Lewis acid.

Hard acids and hard bases tend to have the following characteristics:
Examples of hard acids are: H+, light alkali ions (Li through K are considered to have small ionic radii), Ti4+, Cr3+, Cr6+, BF3. Examples of hard bases are: OH-, F-, Cl-, NH3, CH3COO-, CO32-. The affinity of hard acids and hard bases for each other is mainly ionic in nature.

Soft acids and soft bases tend to have the following characteristics:
Examples of soft acids are: CH3Hg+, Pt2+, Pd2+, Ag+, Au+, Hg2+, Hg22+, Cd2+, BH3. Examples of soft bases are: H-, R3P, SCN-, I-. The affinity of soft acids and bases for each other is mainly covalent in nature.

HSAB acids HSAB bases
HSAB acids and bases

This provides a qualitative approach to looking at the reactions of metal ions with various ligands since, from the diagram above, it is expected that whereas Al(III) and Ti(III) would prefer to react with O-species over S-species, the reverse would be predicted for Hg(II).

Lux-Flood acid-base definition

This acid-base theory was a revival of the oxygen theory of acids and bases, proposed by German chemist Hermann Lux in 1939 and further improved by Håkon Flood circa 1947. It is still used in modern geochemistry and for the electrochemistry of molten salts. This definition describes an acid as an oxide ion (O2-) acceptor and a base as an oxide ion donor. For example:

MgO (base) + CO2 (acid) ⇌ MgCO3
CaO (base) + SiO2 (acid) ⇌ CaSiO3
NO3- (base) + S2O72- (acid) ⇌ NO2+ + 2 SO42-

Usanovich acid-base definition

Mikhail Usanovich developed a general theory that does not restrict acidity to hydrogen-containing compounds, and his approach, published in 1938, was even more general than the Lewis theory. Usanovich's theory can be summarized as defining an acid as anything that accepts negative species, anions or electrons or donates positive ones, cations, and a base as the reverse. This definition could even be applied to the concept of redox reactions (oxidation-reduction) as a special case of acid-base reactions.

Some examples of Usanovich acid-base reactions include:
Na2O (base) + SO3 (acid) → 2Na+ + SO42- (species exchanged: anion O2- )
3(NH4)2S (base) + Sb2S5 (acid) → 6NH4+ + 2SbS43- (species exchanged: anion S2- )
2Na (base) + Cl2 (acid) → 2Na+ + 2Cl- (species exchanged: electron)

A comparison of the above definitions of Acids and Bases shows that the Usanovich concept encompasses all of the others but some feel that because of this it is too general to be useful.

Solvated H+ ions

The hydron (a completely free or "naked" hydrogen atomic nucleus) is far too reactive to exist in isolation and readily hydrates in aqueous solution. The simplest hydrated form of the hydrogen cation, the hydronium (hydroxonium) ion H3O+ (aq), is a key object of Arrhenius' definition of acid. Other "simple" hydrated forms include the Zundel cation H5O2+ which is formed from a hydron and two water molecules, and the Eigen cation H9O4+, formed from a hydronium ion and three water molecules. The hydron itself is crucial in the more general Brønsted-Lowry acid-base theory, which extends the concept of acid-base chemistry beyond aqueous solutions. Both of these complexes represent ideal structures in a more general hydrogen bonded network defect. A freezing-point depression study determined that the mean hydration ion in cold water is on average approximately H3O+(H2O)6: where each hydronium ion is solvated by 6 water molecules. Some hydration structures are quite large: the H3O+.20H2O magic ion number structure (called magic because of its increased stability with respect to hydration structures involving a comparable number of water molecules).

hydronium ion (H3O+)

Zundel cation (H5O2+)

Eigen cation (H9O4+)

extended hydronium ion (H3O+.20H2O)

H vibrations
simuulation by H. Rzepa

In 1806 Theodor Grotthuss proposed a theory of water conductivity. He envisioned the electrolytic reaction as a sort of "bucket line" where each oxygen atom simultaneously passes and receives a single hydrogen atom. It was an astonishing theory to propose at the time, since the water molecule was thought to be OH not H2O and the existence of ions was not fully understood. The theory became known as the Grotthuss mechanism. The transport mechanism is now thought to involve the inter-conversion between the Eigen and Zundel solvation structures, Eigen to Zundel to Eigen (E-Z-E).


Everything you wanted to know about water and more.

Water covers 71% of the Earth's surface and is vital for all known forms of life. On Earth, 96.5% of the planet's water is found in seas and oceans, 1.7% in groundwater, 1.7% in glaciers and the ice caps of Antarctica and Greenland, a small fraction in other large water bodies, and 0.001% in the air as vapour, clouds (formed from solid and liquid water particles suspended in air), and precipitation.

Only 2.5% of the Earth's water is freshwater, and 98.8% of that water is in ice and groundwater. Less than 0.3% of all freshwater is in rivers, lakes, and the atmosphere, and an even smaller amount of the Earth's freshwater (0.003%) is contained within biological bodies and manufactured products.

The major chemical and physical properties of water are:
Most known pure substances display simple behaviour when they are cooled, they shrink. Liquids contract as they are cooled because the molecules move slower and they are less able to overcome the attractive intermolecular forces drawing them closer to each other. Once the freezing temperature is reached, the substances solidify, causing them to contract even more because crystalline solids are usually tightly packed.

Water however water has the anomalous property of becoming less dense when it is cooled to its solid form, ice.

When liquid water is cooled, it initially contracts as expected, until a temperature of 3.98 °C is reached (~4 °C). After that, it expands slightly until it reaches the freezing point, and then when it freezes, it expands by approximately 9%.

Just above the freezing point, the water molecules begin to locally arrange into ice-like structures with an extended hydrogen bonded network. This creates some "openness" in the liquid water, accounting for the decrease in its density. This is in opposition to the usual tendency for cooling to increase the density. At 3.98 °C these opposing tendencies cancel out, producing the density maximum.

Since water expands to occupy a 9% greater volume in the form of ice and is less dense, it floats on liquid water, as in icebergs. Fortunately this happens, since in colder climates where water is susceptible to freezing, if it all turned solid during the winter, it would kill all the life within it.

The extended structure of the water molecule in liquid and solid form seen in the models below provides the explanation for the variation of density with temperature.

extended structure of liquid water

extended structure of solid ice


A solvent (from the Latin solvo-, "I loosen, untie, I solve") is a substance that dissolves a solute (a chemically different liquid, solid or gas), resulting in a solution. A solvent is usually a liquid but can be a solid or a gas. The maximum quantity of solute that can dissolve in a specific volume of solvent varies with temperature.

Although many inorganic reactions take place in aqueous solution, water is not always the most suitable solvent; some reagents react violently or decompose in water (e.g. the alkali metals) and non-polar molecules are often insoluble in water.

Solvents can be broadly classified into two categories: polar and non-polar. Generally, the relative permittivityr, formerly called the dielectric constant) of the solvent provides a rough measure of a solvent's polarity. This can be thought of as its ability to insulate charges from each other and acts as a reasonable predictor of the solvent's ability to dissolve common ionic compounds, such as salts. The strong polarity of water is indicated, by a relative permittivity of 88 at 0 °C compared to 1 by definition for a vacuum. Solvents with a relative permittivity of less than 15 are generally considered to be nonpolar.

Coulombic potential energy ∝ q1q2/(4 π ε0 εr r)

A value of 88 can be considered to be a 'high' value and from the expression for Coulombic electric potential, the force between two point charges (or two ions) in aqueous solution is considerably reduced compared with that in a vacuum. Thus a dilute aqueous solution of a salt is considered to contain well-separated, non-interacting ions.

dielectric constant dielectric constant effect - NaCl in water
relative permittivity (dielectric constant) and NaCl dissolved in water

The polarity, dipole moment, polarizability and hydrogen bonding of a solvent determines what type of compounds it is able to dissolve and with what other solvents or liquid compounds it is miscible. Generally, polar solvents dissolve polar compounds best and non-polar solvents dissolve non-polar compounds best: "like dissolves like". Strongly polar compounds like sugars (e.g., sucrose) or ionic compounds, like inorganic salts (e.g., table salt) dissolve only in very polar solvents like water, while strongly non-polar compounds like oils or waxes dissolve only in very non-polar organic solvents like hexane. Similarly, water and hexane (or vinegar and vegetable oil) are not miscible with each other and will quickly separate into two layers even after being shaken well.

Solvents with a relative static permittivity greater than 15 (i.e. polar or polarizable) can be further divided into protic and aprotic. Protic solvents solvate anions (negatively charged solutes) strongly via hydrogen bonding. Water is a protic solvent. Aprotic solvents such as acetone or dichloromethane tend to have large dipole moments (separation of partial positive and partial negative charges within the same molecule) and solvate positively charged species via their negative dipole.

Properties Table for some common solvents
Solvent Chemical formula Boiling point / °C Relative permittivity Density / g ml-1 Dipole moment / D
Non-polar solvents
Pentane C5H12 36  1.84 0.626 0.00
Hexane C5H14 69  1.88 0.655 0.00
Benzene C6H6 80  2.3 0.879 0.00
Toluene C6H5-CH3 111  2.38 0.867 0.36
Chloroform CHCl3 61  4.81 1.498 1.04
Dichloromethane CH2Cl2 40  9.1 1.3266 1.60
Polar aprotic solvents
Ethyl acetate AcO-Et 77  6.02 0.894 1.78
Acetone (CH3)2C=O 56  21 0.786 2.88
Dimethylformamide (DMF) (CH3)2NCH(=O) 153  38 0.944 3.82
Acetonitrile (MeCN) CH3-C≡N 82  37.5 0.786 3.92
Nitromethane CH3-NO2 100–103  35.87 1.1371 3.56
Propylene carbonate C4H6O3 240  64 1.205 4.9
Polar protic solvents
Formic acid H-C(=O)OH 101  58 1.21 1.41
n-Butanol CH3-CH2-CH2-CH2-OH 118  18 0.810 1.63
n-Propanol CH3-CH2-CH2-OH 97  20 0.803 1.68
Ethanol CH3-CH2-OH 79  24.55 0.789 1.69
Methanol CH3-OH 65  33 0.791 1.70
Acetic acid CH3-C(=O)OH 118  6.2 1.049 1.74
Water H-O-H 100  80 1.000 1.85

Acid and Base effects in non-aqueous solvents.

Levelling and differentiating solvents

When a strong acid is dissolved in water, it fully dissociates to form the hydronium ion (H3O+). For example:

HA + H2O → A- + H3O+ (where "HA" is a strong acid)

No acid can be stronger than H3O+ in H2O. Strong acids can be said to be "levelled" in water.

The same argument applies to bases. In water, OH- is the strongest base. Thus, even though sodium amide (NaNH2) is an exceptional base (pKa of NH3 ~ 33), in water it is "levelled" and is only as strong as sodium hydroxide.

In a differentiating solvent, acids dissociate to varying degrees and thus have different strengths. In a levelling solvent, acids become completely dissociated and are thus of the same strength. A weakly basic solvent has less tendency than a strongly basic one to accept a hydron. Similarly a weak acid has less tendency to donate hydrons than a strong acid.

All acids tend to become indistinguishable in strength when dissolved in strongly basic solvents, owing to the greater affinity of strong bases for hydrons, ("levelling").

A strong acid, such as perchloric acid, exhibits more strongly acidic properties than a weak acid, such as acetic acid, when dissolved in a weakly basic solvent, ("differentiation").

For acids, strong bases are levelling solvents, weak bases are differentiating solvents.

Another classification of solvents is on the basis of hydron interaction:
  1. Protophilic solvents: Solvents which have greater tendency to accept hydrons, i.e., water, alcohol, liquid ammonia, etc.
  2. Protogenic solvents: Solvents which have the tendency to produce hydrons, i.e., water, liquid hydrogen chloride, glacial acetic acid, etc.
  3. Amphiprotic solvents: Solvents which act both as protophilic or protogenic, e.g., water, ammonia, ethyl alcohol, etc.
  4. Aprotic solvents: Solvents which neither donate nor accept hydrons, e.g., benzene, carbon tetrachloride, carbon disulfide, etc.
HCl acts as an acid in H2O, a stronger acid in NH3, a weak acid in CH3COOH, neutral in benzene and a weak base in HF.

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Much of the information in these course notes has been sourced from Wikipedia under the Creative Commons License.
'Inorganic Chemistry' - C. Housecroft and A.G. Sharpe, Prentice Hall, 4th Ed., 2012, ISBN13: 978-0273742753, pps 24-27, 43-50, 172-176, 552-558, 299-301, 207-212
'Basic Inorganic Chemistry' - F.A. Cotton, G. Wilkinson and P.L. Gaus, John Wiley and Sons, Inc. 3rd Ed., 1994.
'Introduction to Modern Inorganic Chemistry' - K.M. Mackay, R.A. Mackay and W. Henderson, International Textbook Company, 5th Ed., 1996.

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