Electrochemical Science and Technology

Chapter 2

Chemistry

In Chapter 1 we introduced those aspects of electricity that have close relevance to electrochemistry. In the present chapter our subject is those fundamental aspects of physical chemistry on which much of electrochemistry is based.

Chemical Reactions: changes in oxidation state

In this book we need not go deeply into the subject of valency - how atoms bond together to form chemical compounds - but the term oxidation state (or oxidation number201) is relevant both to chemistry and electrochemistry. As a working definition applied to a metallic element, it refers to the number of positive charges on the bare ion, or the number of chloride atoms bonded to each atom of the element in its chloride, or to twice the number of oxygen atoms per atom of the element in its oxide. Thus, aluminum is in oxidation state +3 in Al3+, in AlCl3, and in Al2O3. Less obviously it is also in oxidation state +3 in AlOOH and in AlF−4. In fact, aluminum is rarely in an oxidation state other than +3, except in its elemental form when its oxidation state is 0. Other metals, however, wantonly adopt a variety of oxidation states; iron, for example, is found in states202 0, +2, +3, and +4. In such cases it is common to add a roman numeral to specify the oxidation state. Thus “copper(II) sulfate” implies that the copper in this salt is in oxidation state +2.

The main focus of chemistry, and of electrochemistry, is on reactions, in which one form of matter, the reactants or substrates, are converted into different substances, the products. A stoichiometric equation203, or chemical equation, of which

2:1

is an example204, provides a shorthand way of representing a reaction205. A stoichiometric equation must be “balanced”; that is, equal numbers of all atoms must appear on each side of the → symbol. Moreover, the charge on each side must be equal.

Though many chemical reactions do not involve any change in oxidation state, many others do. When one element undergoes a change in oxidation state during a chemical reaction, another element necessarily changes its oxidation state too. In reaction 2:1, for example, the elements mercury Hg and hydrogen H both change their oxidation states. When, later in this book, we address electrochemical reactions, you will find that they invariably involve changes in oxidation state, and that usually it is a single element that changes its oxidation state.

Gibbs Energy: the property that drives chemical reactions

Energy can exist in many forms. All nonthermal forms of energy may be converted, often rather easily, into an equivalent quantity of heat. If a reaction generates heat

2:2

the reactants evidently contained more energy than do the products. Energy associated with chemicals is called enthalpy H. The change in enthalpy206 accompanying reaction 2:2, ΔH = Hproducts - Hreactants, is negative. Most, but not all, chemical reactions that proceed spontaneously have negative ΔH values, and liberate heat.

That most chemical reactions liberate heat is a manifestation of a general law of nature: processes that lead to a lowering of nonthermal energy are favored. Another rule is: processes that lead to an increase in disorder are favored. The chemical property that reflects the change in disorder accompanying a reaction is the entropy change ΔS. Depending on the temperature T, either the change in H or the change in S is the more important influence on the reaction. The Gibbs energy207 G takes both factors into account appropriately by defining206

2:3

Just as a boulder can tumble downhill but not uphill, chemical changes can occur if G decreases, but not if it increases. G is the “chemical energy” that governs the feasibility of chemical reactions. Physical chemists have accurately measured the standard Gibbs energy of very many chemicals and a list will be found on page 390; those of the six substances in reaction 2:1 are tabulated as G° values below. To give this property its full name and fully embellished symbol, the tabulated values are the molar Gibbs free energies of formation at 25.00°C of each substance in its standard state, . The “of formation” in this name means “during the process of formation from its elements in their standard states”, which is why G° is zero for Hg and H2. Because the Gibbs energies of individual ions cannot be measured, one ion – the hydronium ion H3O+ - is chosen as a standard and assigned the same G° value as water208. From tabulated values of G°, one can calculate the change in Gibbs energy accompanying any reaction206,209. Thus, for reaction 2:1, the value calculated for the change in Gibbs energy is

2:4

No reaction that has a positive ΔG° will occur chemically under standard conditions. Processes with negative ΔG°, such as reaction 2:1, are said to be feasible210 and may occur.

Thermodynamicists use the term “standard state”. By this they mean not only that the substance should be in the physical state usually encountered in the laboratory211 - for example H2O as liquid water, not ice - but also that it be in a prescribed condition described as unit activity. Precisely what “activity” means is discussed in the following section.

The statement that no reaction with a positive ΔG° will occur chemically “under standard conditions” means “with all of the reactants and products present in their standard states”. Under those conditions and with ΔG° > 0, the reverse reaction will inevitably be feasible. Except for the unlikely event that ΔG° = 0, either the forward reaction or the reverse reaction will always be feasible for any conceivable process. Of course, only to be feasible is not a guarantee that the reaction will, in fact, occur. Moreover, even if a feasible reaction does occur, it will often fail to go to completion; that is, it may cease before all the reactant is consumed.

Associated with ΔG° is the equilibrium constant K for a reaction. A negative value of ΔG° implies an equilibrium constant of greater than unity. In fact, the important relationship

2:5

provides a quantitative link between the two properties212,213. Here R is the gas constant.

2:6

Note that RT = 2.4790 kJ mol−1 at the standard temperature T° = 298.15K.

The statement above - that no reaction will occur unless ΔG° < 0 - requires the reactants and products to be in their standard states. For states other than standard, the requirement is that Δ<G < 0, the distinction between Δ<G° and ΔG hinging on the activities of the products and reactants, a subject addressed in the next section. A chemical reaction ceases when the change in Gibbs energy becomes zero and equilibrium prevails.

2:7

A caveat is that the process be purely chemical. If other kinds of work can be brought into play to foster the reaction, then the requirement is that

2:8

whereas

2:9

Here W is the work214 performed by some external agency when the Reactants → Products reaction takes place. By supplying external work, you can make that boulder travel uphill! It is the facility to couple electrical work into a chemical reaction that makes electrochemistry into apowerful synthetic tool, creating a possibility to drive reactions that would otherwise be unfeasible. Examples of electrosynthesis, as the generation of chemicals with electrochemical assistance is called, will be found in Chapter 4. Other examples of external work being coupled to chemical processes include metabolically powered physiological “pumps” (Chapter 9), photosynthesis, and some gravitationally powered processes.

Activity: restlessness in chemical species

The concept of activity is useful in chemistry and especially in electrochemistry. Before encountering a definition of the term, it is valuable to acquire a qualitative appreciation of what activity implies. In daily life, the terms “unsettled” and “restless” are used to describe discontented persons who are eager to leave their present...