CHAPTER 1: Foundations of Chemistry

Chemistry is the branch of science concerned with matter—investigating the properties of different substances, exploring how they react and determining their composition. In this introductory chapter, key aspects of general chemistry are discussed which are relevant to volumetric analysis, assuming only a basic understanding of science and mathematics. On reading this chapter and attempting the questions which follow you should be able to:

• Use dimensional analysis to convert units for physical quantities.

• Predict formulae for simple ionic and covalent compounds and apply systematic naming rules.

• Construct simple expressions describing chemical equilibria and calculate the equilibrium constant for simple systems.

Chemistry is the study of matter—solids, liquids and gasses—all of which have mass and occupy volume. Until relatively recently, the physical properties of matter were described using a variety of units which made it difficult for scientists to compare their work. Then, in 1960, the international system of units was introduced¹ which describes seven base units formed from the European metric system from which all other units can be derived (Table 1.1).¹  There are a potentially limitless number of derived units; those commonly encountered are shown in Table 1.2. With the exception of the kilogram, all SI base units are defined in terms of a physical constant—for example, the speed of light in a vacuum (c ≈ 3×10⁸ m s⁻¹) is used to define the quantity one meter. The definition of a kilogram is based on the mass of a cylinder of platinum–iridium, which is stored at the International Bureau of Weights and Measures in Paris.

All physical quantities have two components: magnitude and dimension. For example, the quantity ‘six metres’ has the dimensions of length and a magnitude six-times that of a metre. The metre is a constant that defines the dimensions of the quantity for what would otherwise be an arbitrary length. The dimensions for the SI base units provide a means of deriving the SI unit for a particular quantity using dimensional analysis. For example, if we wish to derive the SI unit for density (mass per unit volume), we consider what SI base units describe that quantity. Mass is a SI base unit with dimensions M; however, volume is not, and so must be expressed in terms of its dimensions, which for a regular cube would be L×L×L, or L³. We can therefore describe density in terms of its dimensions:

This would give units of kg m⁻³, the SI units of density. Most textbooks and scientific journals insist on the use of SI units. However, a few traditional units still persist, especially atmospheres (atm) for pressure (SI unit is Pascals, Pa) and calories (cal) for energy (SI unit is Joules, J). SI units follow the standard prefix convention for decimal multipliers as shown in Table 1.3. These are a convenient way of describing very large or very small numbers in multiples of SI units and are used extensively in chemistry. Thus, the quantity 0.000001 m can be written as 1 µm (=1×10⁻⁶ m).

Another application of dimensional analysis is in the conversion of a measurement from one unit to another. To do this we use a conversion factor, which is simply a statement which relates one unit to another. For example, to convert the empirical measure pounds (lb) to kilograms (kg) we would use the equality 2.21 lb=1 kg and write it as a fraction; this is the conversion factor. Since there are two ways we could write the fraction we get two different conversion factors:

To convert a mass of 130 lb to kilograms the calculation would be:

In dimensional analysis units are treated like numbers—if a unit appears in the numerator of one term and the denominator of the other term, they cancel each other out. As any number which isn’t a fraction can be written as a fraction with one as the denominator, it follows that in order to make the lb units cancel, we will need to use a conversion factor with lb in the denominator:

As the lb units cancel, the unit which remains will be the unit the answer is given in.

Dimensional analysis is an incredibly useful technique in science as it greatly simplifies unit conversions as well as providing a means of determining the correct units for a quantity. In fact, this technique can be applied to all units, even those quantities that are not associated with typical units, like the number of tablets in a bottle or the number of lengths of wallpaper in a roll.

Matter is often described as being in one of three physical states: solid, liquid or gas.² Using water as an example, we can describe a solid (e.g. ice) as having a fixed volume and shape, a liquid as having definite volume but no fixed shape, and a gas (e.g. steam) as having neither fixed volume nor shape. Under the correct conditions, the states of matter are interconvertible by going through physical changes (Figure 1.1). The majority of matter around us consists of mixtures of pure substances which can be homogeneous (visibly indistinguishable parts) or heterogeneous (visibly distinguishable parts). A pure substance has constant composition and may be composed of elements or compounds.

Elements are the basic form of matter and cannot be broken down into simpler substances by chemical means (they can be broken down under other conditions). There are 92 naturally occurring elements found in the periodic table, with a further 25 artificially created through radioactive decay or use of particle accelerators. Compounds consist of two or more elements joined together in fixed proportions to form a new substance. The constituent elements are joined by chemical bonds, as in water for example—two hydrogen atoms joined to an oxygen atom by two covalent bonds. The individual constituents of a compound cannot be separated by physical means; to do this, a chemical change must occur. A mixture is composed of more than one component, but the individual components can be separated by physical means. Air is an important mixture of nitrogen, oxygen, carbon dioxide and trace amounts of other gases. These components can be physically separated by fractional distillation.

Elements are made up of a large number of microscopic entities known as atoms. The very small size of an atom can be appreciated when you consider that 12 g of carbon contains 6×10²³ atoms (known as Avogadro's number). Each element contains a specific type of atom and the properties of that atom dictate how the element will react. Atoms are composed of three subatomic particles—protons, neutrons and electrons—each of which have different physical properties (Table 1.4) and when combined give an atom its unique chemical reactivity. The number of protons in an element equals the atomic number (Z) of that element, and in a neutral atom this also equals the number of electrons. The nucleons (protons and neutrons) of an atom give the atom most of its mass. However, since an atom is too small to be weighed easily, we take the mass of 6×10²³ atoms of that element and compare this to the mass of the equivalent amount of carbon. The value obtained is known as the relative atomic mass (RAM), which is a dimensionless quantity listed in the periodic table (Figure 1.2).

The specific chemical properties of an element are largely dictated by the number of electrons. Since the number of electrons equals the number of protons in an atom, we can state that a specific element contains a fixed number of protons and electrons—for example, carbon always contains six protons and six electrons. However, the number of neutrons in an element can vary—for example, a small proportion of carbon atoms have seven or eight neutrons, rather than the more common six. These different forms of the same element are known as isotopes. An isotope of an element will have the same atomic number (i.e. number of protons and electrons), but a different relative atomic mass (different number of neutrons). We can identify the isotopes of an element using mass spectrometry—a technique which forcibly causes atoms to lose electrons, creating positively charged ions, which are separated by a magnetic field according to their mass-to-charge (m/z) ratio. Mass spectrometry can be used to deduce the proportions of isotopes in a sample of an element, or to study the properties of molecules (Box 1.1).

The arrangement of protons, neutrons and electrons in an atom was a focus for major scientific endeavour in the early 1900s. English physicist J. J. Thomson (1856–1940) was awarded the Nobel Prize in Physics for his discovery of electrons in 1906 and the development of the plum pudding model of atomic structure. However, it was Ernst Rutherford (1871–1937) who developed a theory of atomic structure in 1911 which is most recognisable to us today—a dense central nucleus containing protons and neutrons, surrounded by electrons moving at a relatively large distance from the nucleus. It was later proven that Rutherford's ‘nuclear atom’ was only partially correct as classical physics gave way to the new quantum theory, which will be briefly discussed later.

Atoms are described as being electrically neutral—that is, the proportion of negative charge equals that of the positive charge. However, if an atom gains or losses an electron, it will become electrically charged. Metal atoms and hydrogen form positive ions known as cations and non-metal atoms form negative ions called anions. The formation of ions is a consequence of the electronic structure of atoms. When we look at an element on the periodic table, for example sodium, we can deduce from its atomic number (11) and relative atomic mass (23) that it has 11 protons, 11 electrons and 12 neutrons. The protons and neutrons are accommodated within the nucleus, but what about the electrons? An early theory of atomic structure proposed by Niels Bohr (1885–1962) stated that electrons were positioned in a series of circular shells around the nucleus (Figure 1.4). Later, Erwin Schrödinger (1887–1961) proposed a different model, in which electrons were not found in neat, circular shells, but instead in three dimensional regions of space known as orbitals (these really represent the probability of finding an electron, but this is more advanced than we require in this book). Depending on the distance the electron is from the nucleus, the shape of the orbital could be a sphere, dumbbell or more complex form (Figure 1.5), with each orbital having a maximum capacity for electrons.

This view of electronic structure, which became known as the quantum-mechanical model, conveniently describes the formation of ions. For example, using the quantum-mechanical model, we can describe the electronic structure of a sodium atom in terms of its atomic orbitals:³

One of the fundamental concepts of modern atomic theory is that atoms are at their most stable when they have a full outer orbital of electrons. In sodium's case, the outer 3s-orbital has only one electron. Therefore, in order to gain stability, the sodium atom loses this outer electron, forming a sodium ion:

Chlorine also has an incomplete outer orbital and its electronic configuration can be written as:

In order for it to become electronically stable, it must gain an electron, forming a chloride ion:

If these two processes were to occur in close proximity to one another, the sodium ion would transfer its electron to chlorine, forming the compound sodium chloride, in a process known as ionic bonding. The formation of ionic compounds is based on the interaction between pairs of ions which is governed by Coulomb's law. An important implication of this law is that when an ionic compound is formed, the energy of the compound is lower than that of the individual ions—this provides greater stability and is the main driving force behind formation of all compounds (not just those involving ionic bonding).

Some elements don’t transfer electrons in order to gain stability, but instead share their outer electrons in what is described as a covalent bond, created through the formation of molecular orbitals. Some elements form covalent bonds with identical atoms and exist as diatomic molecules (in order to gain stability), such as oxygen (O₂), nitrogen (N₂) and chlorine (Cl₂). Although these substances contain two elements joined together by a chemical bond they are not compounds, as this requires two or more different elements. If a compound is formed between a non-metal and a metal (e.g. potassium and chlorine), it is called an ionic compound, because the type of bond involved is an ionic bond. Conversely, if a compound is formed from two non-metals (e.g. sulfur and oxygen), it is called a covalent compound, since covalent bonding is involved. Generally speaking, we should resist the temptation to speak of ionic compounds as molecules and reserve this noun for covalent compounds only.

The formation of a compound is described by a chemical equation, which may include the reaction of just elements, elements and compounds or just compounds. For example, when sulfur is burned in oxygen, we get sulfur dioxide: S+O₂ → SO₂. We say that ‘SO₂’ is the formula for sulfur dioxide. Often, especially in analytical chemistry, we are expected to include state symbols in chemical equations. These are particularly important if solid products are formed (precipitates) or if gases are evolved. For example:

In this system, we use the symbol (s) for solid, (l) for liquid, (g) for gas and (aq) for aqueous solution. In general, there are three main types of chemical formula—the empirical formula, the molecular formula and the structural formula.

• Empirical formulae describe the basic proportions of elements in a compound, but they do not necessarily show the exact amounts of elements present. For example, the empirical formula for glucose is CH₂O.

• Molecular formulae are a simple multiple of the empirical formula and they describe the exact amounts of elements present. For glucose, the molecular formula is C₆H₁₂O₆—six times the empirical formula.

• Structural formula of a compound shows the position and number of covalent bonds in a molecule, such as glucose (Figure 1.6).

The system for naming compounds is referred to as nomenclature and follows a series of internationally recognised rules established by IUPAC. The naming system for organic compounds is necessarily complex, but not directly relevant to our discussion of volumetric analysis, and so we will focus on the nomenclature of inorganic compounds. Often, we wish to name a compound based on its formula, which may be predicted from a chemical equation such as the reaction between sulfuric acid and iron chloride:

In this reaction, the iron cation carries a charge of +2 (Fe²⁺) and combines with the sulfate anion (SO$42−$) to form iron sulfate. However, some metals, such as iron, can form ions with variable charges, e.g. Fe²⁺ and Fe³⁺, and to avoid ambiguity the magnitude of the positive charge is given by a Roman numeral in parentheses immediately after the metal's name. In this case, iron(II) sulfate is the salt formed. Most of the elements with a variable charge are transition metals, whereas common metal ions do not have variable charges. Occasionally, an older method of distinguishing between two differently charged ions of a metal is used, which involves applying the suffix ‘–ous’ or ‘–ic’ to the metal's Latin name, e.g. Fe²⁺ is known as the ferro̲u̲s̲ ion while Fe³⁺ is the ferri̲c̲ ion. For the few non-metal cations commonly encountered, the suffix ‘–ium’ is used, as in ammoni̲u̲m̲ (NH$4+$) and hydroni̲u̲m̲ (H₃O⁺) ions. A list of the common cations is given in Table 1.5.

Ascribing names to anions follows a similar system. Monoatomic anions have names formed by dropping the ending of the element's name and adding ‘–ide’, for example O²⁻ is oxi̲d̲e̲ and N³⁻ is nitri̲d̲e̲. A few of the simple polyatomic anions also end in ‘–ide’, such as hydroxi̲d̲e̲ (OH⁻), cyani̲d̲e̲ (CN⁻) and peroxi̲d̲e̲ (O$22−$). Polyatomic anions which contain oxygen (oxyanions) end in ‘–ate’ or ‘–ite’; the most common oxyanion of an element takes the ‘–ate’ ending, while the ‘–ite’ ending is used for an oxyanion with the same charge but one less oxygen atom, e.g. NO$3−$ is known as nitra̲t̲e̲ and SO$42−$ as sulfa̲t̲e̲ whereas NO$2−$ is known as nitri̲t̲e̲ and SO$32−$ as sulfi̲t̲e̲. Prefixes are used when the oxyanions of an element extends to four members, such as the halogens. The prefix ‘per–’ indicates one more oxygen atom than the oxyanion ending in ‘–ate’; the prefix ‘hypo–’ indicates one less oxygen atom than the oxyanion ending in ‘–ite’, e.g. ClO$4−$ is the p̲e̲r̲chlora̲t̲e̲ ion, ClO$3−$ is the chlora̲t̲e̲ ion, ClO$2−$ is the chlori̲t̲e̲ ion and ClO⁻ is the hypochlori̲t̲e̲ ion. Anions formed by adding hydrogen (H⁺) to an oxyanion are named by adding the prefix ‘hydrogen’ or ‘dihydrogen’, e.g. the carbonate ion, CO$32−$, becomes h̲y̲d̲r̲o̲g̲e̲n̲carbonate, HCO$3−$ and the phosphate ion, PO$43−$, becomes the d̲i̲h̲y̲d̲r̲o̲g̲e̲n̲ phosphate ion, H₂PO$4−$. Common anions are listed in Table 1.6.

The nomenclature for covalent compounds is generally more straightforward. For a simple two-element covalent compound, the name of the element farthest to the left of the periodic table usually comes first. The name of the second element is given the suffix ‘–ide’. The number of atoms of an element is usually described by Greek prefixes (mono–, di–, tri–, tetra– etc.); thus, PCl₅ is called phosphorous p̲e̲n̲t̲a̲chlori̲d̲e̲.

Since the Big Bang, the Universe has contained a certain, fixed amount of energy. At first this energy was highly compressed into a relatively small region of space, but as the Universe expands, this energy spreads out. However, the overall amount of energy remains the same. This is described by the first law of thermodynamics:

This is a fundamental principle of the Universe and equally applies to deep space or to a chemistry laboratory on Earth. A second fundamental property of the Universe is that all things (atoms, molecules, people, planets, solar systems) have a tendency to become disordered (this is why the Universe expands). The amount of disorder can be measured by the thermodynamic property entropy (S), which is described by the second law of thermodynamics. If we want to go against this natural tendency to disorder, we must expend energy (think of how easily a kitchen can become untidy and of the effort required to straighten it out again).

These principles also apply to chemical reactions. Chemical reactions occur because of a tendency towards disorder (increase in entropy), which (usually) arises from a difference in energy between the reactants and the products (chemical bonds are broken in reactants and new bonds are formed in products). The difference in energy between the reactants and products is known as enthalpy change (ΔH); those reactions which take in more energy than they release are known as endothermic reactions, which have a positive enthalpy change (+ve ΔH), and those which release energy are known as exothermic reactions, which have a negative enthalpy change (−ve ΔH). For example, the reaction of ammonium nitrate with barium hydroxide is accompanied by a drop in temperature to about −20 °C:

The decrease in temperature implies that energy has been taken in from the surroundings to give the reaction the energy it needs to proceed; in other words, the reaction has gained extra energy, hence positive ΔH. Conversely, the highly energetic thermite reaction liberates sufficient heat energy to produce molten iron:

In this case, the increase in temperature implies that energy is released from the reaction to the surroundings; the reaction system has lost energy, hence negative ΔH.

We have already seen that chemical reactions happen because of a difference in energy between reactants and products. However, this does not explain why some reactions happen on their own while others require an external input of energy. Chemists use the term spontaneous or feasible to describe reactions which happen of their own accord. Although, in general, spontaneous reactions are exothermic, many endothermic reactions are spontaneous too; for example, the reaction between ammonium nitrate and barium hydroxide (ΔH=+62.3 kJ/mol) which we saw earlier, or dissolving ammonium nitrate in water (ΔH=+26.7 kJ/mol). The key to understanding why endothermic reactions are spontaneous is to notice that they involve a ‘spreading out’ in some way—solids reacting to form liquids and gases (ammonium nitrate and barium hydroxide) or solid dissolving to form solutions (dissolving ammonium nitrate in water). This, of course, means that entropy plays a role in deciding whether or not a reaction will be spontaneous or not. If the change in entropy (ΔS) is positive, then the reaction will be spontaneous; this is the second law of thermodynamics:

Taking enthalpy and entropy into account, this leads to four possible combinations which can be used to predict whether or not a reaction will be spontaneous (Figure 1.7).

For a chemical reaction to be guaranteed spontaneity the enthalpy change should be negative and entropy change should be positive. For the two cases where a reaction ‘might proceed’, we need an additional deciding factor, known as Gibbs energy, G, which is often thought of as the free energy available within a reaction. We see that the change in Gibbs energy (ΔG) is related to the change in enthalpy and change in entropy by the temperature of the reaction:

If a reaction is to be spontaneous, the change in Gibbs energy must be less than zero (ΔG<0),⁴ which would be the case when ΔH is negative and ΔS is positive. The opposite extreme, in which ΔG>0 (a non-spontaneous reaction), would have a positive ΔH and a negative ΔS. However, we are still left with the two ambiguous cases identified in Figure 1.7. For these two cases, the fourth parameter in the Gibbs equation, temperature, T, governs spontaneity. We see that when ΔH and ΔS are both negative, spontaneity is favoured by low temperatures (TΔS<ΔH), and when ΔH and ΔS are both positive, spontaneity is favoured by high temperatures (TΔS>ΔH).

The criterion of Gibbs energy being less than zero for a spontaneous process is not quite the complete picture. Consider the combustion of methane:

This reaction is exothermic (ΔH=−882.0 kJ/mol) and has ΔG=−580 kJ/mol and should therefore be spontaneous under our current definition. However, when methane reacts with oxygen, it does not instantly combust. Instead, an initial input of energy is required to start the reaction, after which it proceeds spontaneously. This initial input of energy is known as the activation energy (E_a) of the reaction (Figure 1.8 and 1.9). The input of energy could be heat (as in the case of the combustion of methane) or it could be another form of energy, such as light in the photolysis of water in photosynthesis. It is important to realise that the spontaneity of a reaction gives no indication of how fast that reaction will occur. Take the decomposition of nitrogen dioxide:

This is spontaneous but very slow at room temperature. However, if we were to heat a flask of nitrogen dioxide to 300 °C the decomposition reaction happens much faster. We say that the rate of reaction has increased.

Suppose, for the above reaction, we were able to measure the decrease in the concentration of nitrogen dioxide over a period of time. A graph of [NO₂] vs. time would have the form shown in Figure 1.10. If we were to draw a tangent to the curve and determine the gradient of this tangent, this would give us an estimation of the rate of reaction with respect to the consumption of nitrogen dioxide:

If we were to conduct a series of experiments with different initial concentrations of nitrogen dioxide, but under otherwise identical conditions, we would see that the rate of reaction is dependent on the concentration of nitrogen dioxide. For the decomposition of nitrogen dioxide we can write a rate law in which k is a proportionality constant, known as the rate constant, and n is the order of reaction:

The order of reaction can only be determined from experimental data and could be an integer or a fraction. In this case, n=2 and we say that this is a second-order reaction. The significance of this is that if the concentration of nitrogen dioxide is doubled, the rate of reaction will quadruple. In stating the rate law for this reaction we only include nitrogen dioxide as only the forward reaction is being studied under conditions which ensure that the reverse reaction does not affect the overall rate.

The chemical reactions described so far have been presented as proceeding from reactants to products. Such reactions are described as unidirectional and tend to involve major physical and/or chemical changes, e.g. the combination of two gases to form a liquid. However, in principle, all reactions are reversible under the right conditions and we see that the products can react to regenerate the reactants:

In such reactions there is a point at which the amounts of reactants and products appear to remain constant (Figure 1.11) and the reaction is said to be in equilibrium. This is a consequence of the rate of the forward reaction being equal to the rate of the reverse reaction:

It was the Norwegian chemists Cato Guldberg (1836–1902) and Peter Waage (1833–1900) who first made a serious study of reversible reactions which lead them propose the law of mass action. For the equilibrium:

the law of mass action is represented by the expression:

The square brackets represent the equilibrium concentration of the species and K is known as the equilibrium constant. It is a relatively simple procedure to determine the value of the equilibrium constant at a given temperature if the equilibrium concentrations are known. For reasons which are developed in Box 1.2, equilibrium constants are dimensionless.

In 1885, French chemist Henri Louis Le Châtelier (1850–1936) reported findings on the factors affecting the equilibrium between salts in solution. He stated that if a chemical system at equilibrium experiences a change in concentration, temperature or pressure, equilibrium will shift to counteract the change and establish a new equilibrium. The effect of temperature on the position of equilibrium depends on the enthalpy change of the reaction. Take the well-known reaction for the production of ammonia which is exothermic:

If energy is supplied to this reaction in the form of heat, the position of equilibrium moves to the left in order to maintain the position of equilibrium and decreases the equilibrium constant. Conversely, if an endothermic reaction, like the decomposition of calcium carbonate (Eqn. (1.20)), is subjected to external heat energy, the position of equilibrium moves to the right, favouring formation of products increasing the equilibrium constant.

The effects of changes in concentration (or partial pressure for gaseous reactions) follow a similar pattern. For example, in the reaction:

when hydroxide ions are added, the position of equilibrium shifts to favour the products, effectively absorbing the excess OH⁻ and increasing the equilibrium constant. However, if the concentration of OH⁻ was reduced by addition of acid (H₃O⁺), then the position of equilibrium would tend to the reactants’ side due to the formation of water, restoring equilibrium and decreasing the equilibrium constant. In a gaseous reaction such as the formation of ammonia, we replace the idea of concentration with partial pressure (which is really the gaseous equivalent of concentration) and we see that an increase in external pressure would cause the position of equilibrium to move towards the products as this side is under lower pressure (fewer moles of gas; pressure ∝ moles).

One of the major applications of equilibrium constants in volumetric analysis is to describe the extent to which a compound has dissociated in solution. For example, when methylamine dissolves in water an equilibrium is established which has an associated equilibrium constant:

We see from the value of the equilibrium constant (4.7×10⁻⁴) that the position of equilibrium lies heavily to the left-hand side, favouring the reactants, which implies that methylamine is poorly dissociated in water. In evaluating an expression such as Eqn. (1.23) we must be able to calculate the equilibrium concentration of the reactants/products from their initial concentrations. This is easily achieved using the ‘ICE method’ as demonstrated in Worked Examples 1.1 and 1.2.

Not all reactions occur in a single step. For example, the reaction of nitrogen with oxygen to give nitrogen dioxide occurs in two steps which have two separate equilibrium constants:

The overall formation of nitrogen dioxide can be shown to be the product of Eqns. (1.24) and (1.25) cancelling like terms algebraically:

If we were interested in the reverse process, the equilibrium constant would still have the same magnitude, but its sign is inverted:

Chemical equilibria and interpretation of equilibrium constants is a central theme in analytical chemistry. Some examples of common equilibria are shown in Table 1.7. The simplified, concentration-based approach to evaluating equilibrium constants adopted in chapter is acceptable for most purposes. However, readers should be aware that as a consequence of the ‘correct way’ to calculate equilibrium constants (the thermodynamic equilibrium constant), all equilibrium constants are affected by the ionic strength of the solution.

Elements; mixtures; compounds; physical changes; homogeneous; heterogeneous; Avogadro's number; atomic number; relative atomic mass; isotopes; mass spectrometry; cations; anions; ionic bond; covalent bond; ionic compound; covalent compound; empirical formula; molecular formulae; oxyanion; enthalpy change; exothermic; endothermic; entropy; Gibbs energy; activation energy; equilibrium.

• Measurements in science have been standardised using the international system of units and we can convert between units using dimensional analysis.

• The three states of matter are interchangeable under the correct conditions and are all composed of atoms which comprise three sub-atomic particles (protons, neutrons and electrons).

• When an atom undergoes a gain or loss of electrons, charged species known as ions are formed. Positive ions, formed through loss of electrons, are known as cations; negative ions, formed through gain of electrons, are known as anions.

• When ions form in close proximity to each other, an ionic bond is formed, through transfer of electrons; this occurs between metals and non-metals.

• For non-metals to gain stability, they often undergo covalent bonding, through a sharing of electrons.

• The formation of ionic or covalent compounds is governed by the laws of thermodynamics and must meet certain criteria in order to proceed (usually a decrease in enthalpy and an increase in entropy).

• Some reactions are reversible under standard conditions; these are known as equilibria.

1. C. E. Housecroft and E. C. Constable, Chemistry: An Introduction to Organic, Inorganic and Physical Chemistry, Prentice Hall (Pearson Education Ltd), London, 4^th edn, 2010.

2. J. Keeler and P. Wothers, Why Chemical Reactions Happen, Oxford University Press, Oxford, 1^st edn, 2003.

3. J. Gribbin, Erwin Schrödinger and the Quantum Revolution, Black Swan, London, 2013.

1. Using dimensional analysis, carryout the following conversions:

   1. 500 g to mg

   2. 4 L to μL

   3. 2 ft to m (1 ft=0.3 m)

   4. 3 tones to kg

   5. 29.5 g to oz (1 g=0.035 oz)

   6. 10.9 Bq to Ci (37 GBq=1 Ci)

2. A laboratory analyst reported a patient's serum cholesterol as 186 mg/dL. Convert this concentration to g/L. Given that 1 mol of cholesterol is equivalent to 386.85 g, how many moles per litre are present in the patient's blood?

3. Provide names for the following ionic compounds:

   1. Na₂O

   2. CrCl₂

   3. Fe(NO₃)₂

   4. NH₄Cl

   5. Sn(HPO₄)₂

   6. NaH₂PO₄

4. Provide formulae for the following compounds:

   1. Phosphorous tribromide

   2. Dinitrogen oxide

   3. Carbon tetrachloride

   4. Sulfur hexafluoride

   5. Selenium dioxide

   6. Potassium nitrate

5. The formation of nitrosyl chloride at 25 °C proceeds as 2NO(g)+Cl₂(g)⇌2NOCl(g). Given that the partial pressures at equilibrium of the participating species were p(NOCl)=1.2 atm, p(NO)=5.0×10⁻² atm and p(Cl₂)=3.0×10⁻¹ atm, evaluate K for the reaction.