Botany online 1996-2004. No further update, only historical document of botanical science!

## Some Basic Terms of Thermodynamics

All living things require a continuous throughput of energy. Their metabolism ultimately transforms the energy to heat, which is dissipated to the environment. A large portion of the cell's biochemical apparatus is therefore devoted to the acquisition and utilization of energy.

Thermodynamics (Greek: therme, heat + dynamis, power) is the science that describes the relationships between the different forms of energy. In its simplest sense could it be said to deal with material systems filling an exactly defined space and communicating with their surroundings. A knowledge of thermodynamics allows to determine whether a physical process is possible or not.

In thermodynamics is the part of the universe that is of interest, such as an organism, defined as a system. The rest of the universe is regarded as the surroundings. Depending on whether or not a system can exchange energy with the surroundings is it said to be open or closed. All living things are open systems.

The first law of thermodynamics states that the total energy of the universe is always conserved. Energy can neither be created nor destroyed. Expressed mathematically:

delta E = EB - EA = Q - W

EA represents the energy present at the beginning of a process, EB that at its end; Q is the amount of heat absorbed by the system from the surroundings and W the work done by the system on the surroundings.

The formula states that changes of a system's (or a reaction's) energy content are only dependent on the initial and final state of the system, while the path by which the final state is reached can be neglected. It does consequently give no explanation about the way and the quality of the transformation. Processes during which the system releases heat, are known as exothermic processes and are by convention assigned a negative Q, while those, in which a system gains heat are termed endothermic ( Q is positive).

The second law of thermodynamics expresses the phenomenon that the universe tends towards maximum disorder, or, in other words: the direction of all spontaneous processes is such as to increase the entropy of a system plus its surroundings ( delta S is positive). It introduces the quantity S, the entropy to describe the state of a system. The entropy is a measure for a system's degree of disorder. It increases with increasing disorder.For a system at equilibrium is the entropy of the system plus its surroundings maximal and delta S is zero.

The fact that the entropy of a system may decrease during partial processes is not inconsistent with this law. It is normal as long as the entropy of the surroundings increase in at least the same amount.

This slightly abstract law is maybe best explained with the example of the phenomenon life with all its aspects like growth, reproduction and evolution. Everybody knows that cells, cell assemblies and organisms are complex structures with processes much more complex than those taking place in the inanimate nature. Every organism represents an open system, i.e. it has continuously to take up energy from its surroundings to keep up its degree of order and the integrity of its structures. All its processes are irreversible. Organisms are thus always in a state of flow (a steady state), never at a stable equilibrium. Moreover is it generally known that most of this energy is made available by photosynthesis, which again is dependent on sun energy. The energy transformation (matter to energy) taking place at the sun's surface causes a large positive delta S. A small part of it is invested into the generation and perseverance of structures at the earth and the delta S of the sun is diminished only by this insignificant portion, but the overall entropy of sun plus organisms on earth still increases.

In 1878 introduced J.W.GIBBS a formula that brought the first and second law into connection. It introduces the term free energy, abbreviated G in the honour of GIBBS. It describes the type of energy available from a reaction for the performance of work. The free energy can among other things also be used by cells. It is defined by the relationship

delta G = delta H - T delta S

delta G is thus a measure for the change of a system's free energy in which a reaction takes place at constant pressure (P) and the absolute temperature (T). delta H describes the change in the system's heat content and delta S again is the change of entropy. The change in a system's heat content can also be described as follows:

delta H = delta E + P delta V

Since changes of the volume (delta V) can be neglected in biochemical reactions, because they take usually place in solutions, equals

and thus is

delta G = delta E - T delta S

This means that delta G is dependent both on the change in a systems' energy level (as a consequence, for example, of a chemical reaction) and on the entropy.

The quantity delta G (kcal/mol or kJ/mol) is easily worked with and the following statements can be deduced: The sign of delta G shows whether a process occurs spontaneously or not. Only processes with a negative delta G, i.e. such, in which delta G is reduced are thermodynamically possible.

Processes for which delta G is negative, are 'energy-releasing' or exergonic. Conversely, for any process moving away from equilibrium is delta G positive. Such reactions are 'energy-consuming' or endergonic. They take place only when coupled to a strongly exergonic process. The cell has to do work to render the process exergonic overall. Such coupling mechanisms are the key to the understanding of many processes of biosynthesis, where the break-down of energy-rich compounds (like ATP) provides the energy for endergonic processes.

The system is at equilibrium, if delta G = 0. A negative delta G alone does not mean that a reaction can start by itself, since not only a negative delta G, but also activation energy is needed. A catalyst may diminish the activation energy needed, but the rest has to be supplied.

delta G describes the starting state of the reactants but not the way in which transformation occurs. It is thus without interest whether a reaction is catalyzed or not or whether it takes place in one or several steps. An example will explain this: the oxidation of glucose produces delta G = -686 kcal/mol ( 2881 kJ/mol). Whether glucose is oxidized in one step or in several steps, as in a cell, is unimportant, the amount of delta G produced is always the same.

## Changes in Free Energy Occurring in Chemical Reactions and The Meaning of Equilibrium Constants

For the general reaction scheme

A + B < > C + D

is the actual free energy change given by

delta G = delta G0 + RT ln [C][D] / [A][B]

where the terms in brackets refer to the actual concentrations at the time of the reaction, R is the gas constant and T the absolute temperature. delta G0 is the standard free energy change and refers to conditions such that all reactants and products are present at a concentration of 1 Mol.

This means that delta G0 can be calculated, if the concentration of the reactants (in Mol) is known. In biochemistry is the pH by convention taken to be 7. In equilibrium (delta G = 0) would thus

0 = delta G0 + RT [C][D] / [A][B]

or

delta G0 = - RT ln [C][D] / [A][B]

In chemistry is the equilibrium constant k defined as

k = [C][D] / [A][B]

This means that

delta G0 = - RT ln k

or

delta G0 = - 2,303 RT log k

delta G0 and k have consequently a simple relationship. An equilibrium constant of 10, for example, would correspond to a change in free energy of

-1,36 kcal/mol (= - 5,71 kJ/mol) (bei 25 şC).

There is a clear difference between delta G0 and deltaG. delta G0 is the constant of a certain reaction that takes place at a given temperature and a certain pH. delta G is variable and depends on the concentrations of the respective substrates and products. Even if a positive delta G0 is calculated under standard conditions can a negative delta G be achieved by the choice of suitable starting concentrations.

The conditions obtained in cells are likely do be very different from standard conditions. The values accessible for delta G0 are thus not to be used uncritically as guides to what happens in cells. It is actually very difficult to obtain realistic delta G values, since neither the concentration of the reactants nor that of the products is known and since any biochemical reaction is a part in a network of reactions partially competing, partially complementing each other.

© Peter v. Sengbusch - b-online@botanik.uni-hamburg.de