The role of entropy, free energy in assessing thermodynamic spontaneity

Thermodynamic spontaneity—whether a reaction can go—can be measured by changes in either of two parameters: entropy or free energy. These concepts are abstract and can be somewhat difficult to understand.

Entropy- It is represented by the symbol S. For any system, the change in entropy, ΔS, represents a change in the degree of randomness or disorder of the components of the system. For example, the combustion of paper involves an increase in entropy because the carbon, oxygen, and hydrogen atoms of cellulose are much more randomly distributed in space once they are converted to carbon dioxide and water. Entropy also increases as ice melts or as a volatile solvent, such as gasoline, is allowed to evaporate.

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Entropy change as a measure of thermodynamic spontaneity. How can the second law of thermodynamics help predict what changes will occur in a cell? There is a very important link between spontaneous events and entropy changes because, whenever a process occurs in nature, the randomness or disorder of the universe (that is, the entropy of the universe) invariably increases. This is one of two alternative ways to state the second law of thermodynamics. According to this formulation, all processes or reactions that occur spontaneously result in an increase in the total entropy of the universe. Or, in other words, the value of ΔSuniverse is positive for every real process or reaction.

These have to be kept in mind; however, that this formulation of the second law pertains to the universe as a whole and may not apply to the specific system under consideration. Every real process, without exception, must be accompanied by an increase in the entropy of the universe, but for a given system, the entropy may increase, decrease, or stay the same as the result of a specific process. For example, the combustion of paper is clearly spontaneous and is accompanied by an increase in the system entropy. On the other hand, the freezing of water at -0.1 degrees Celsius is also a spontaneous event, yet it involves a decrease in the system entropy. This makes sense when you consider the greater ordering of water molecules in ice crystals. Thus, while the change in entropy of the universe is a valid measure of the spontaneity of a process, the change in entropy of the system is not.

To express the second law in terms of entropy change is therefore of limited value in predicting the spontaneity of biological processes because it would require keeping track of changes that occur not only within the system but also in its surroundings. Far more convenient would be a parameter that would enable the prediction of the spontaneity of reactions from a consideration of the system alone.

Free Energy. As it might guess, a measure of spontaneity for the system alone does, in fact, exist. It is called free energy and is represented by the symbol G, after Willard Gibbs, who first developed the concept. Because of its predictive value and its ease of calculation, the free energy function is one of the most useful thermodynamic concepts in biology. One could even make the case that our entire discussion of thermodynamics so far has really been a way of getting us to free energy, because it is here that the usefulness of thermodynamics for cell biologists becomes apparent.

Like most other thermodynamic functions, free energy is defined only in terms of mathematical relationships. But for biological systems at constant pressure, volume, and temperature, the free energy change is related to the changes in enthalpy and entropy by the formula change.

ΔH = ΔG + TΔS

or

ΔG = ΔH – TΔS

where ΔH is the change in enthalpy, ΔG is the change in free energy, ΔS is the change in entropy, and T is the temperature of the system in degrees Kelvin (K = °C + 273).

Notice that ΔG is the algebraic sum of two terms, ΔH and – TΔS. Like ΔH, ΔS for a specific reaction or process will be either positive (increase in entropy) or negative (decrease in entropy). Because of the minus sign, the term – TΔS will be negative if entropy increases or positive if entropy decreases.

Given that the values for ΔH and – TΔS can be either positive or negative, the value of ΔG for a given reaction will depend on the signs and numerical values of the ΔH and – TΔS terms. The terms will be additive if they both have the same sign, whether positive or negative. Thus, a reaction that is exothermic (i.e., ΔH is negative) and results in an increase in entropy (i.e., ΔS is positive and -TΔS is negative) has a ΔG value that is the sum of two negative terms and is therefore more negative than either term. However, if the ΔH and -TΔS terms differ in sign, the ΔG value will have the sign of the larger, but its value will be the numerical difference between the two terms. Thus, a reaction that is endothermic (i.e., ΔH is positive) and results in an increase in entropy (i.e., ΔS is positive and -TΔS is negative) will have a ΔG value that is either positive or negative, depending on the numerical values of ΔH and – TΔS.

Free energy changes as a measure of thermodynamic spontaneity. Free energy is an exceptionally useful concept as a readily measurable indicator of spontaneity. As we shall see shortly, ΔG for a reaction can be readily calculated from the equilibrium constant for the reaction and from easily measurable system variables, such as the concentrations of reactants and products. Once determined, ΔG provides exactly what we have been looking for: A measure of the spontaneity of a reaction based solely on the properties of the system in which the reaction is occurring.

Specifically, every spontaneous reaction is characterised by a decrease in the free energy of the system (ΔGsystem < 0) just as surely as it is characterised by an increase in the entropy of the universe (ΔSuniverse > 0). This is true because with the temperature and pressure held constant, ΔG for the system is related to ΔS for the universe in a simple but inverse way. This gives us a second, equally valid way of expressing the second law: All processes or reactions that occur spontaneously result in a decrease in the free energy content of the system. In other words, the value of ΔG is negative for every real process or reaction.

Such processes or reactions are called exergonic, which means energy-yielding. Note carefully that the reference is specifically to the change in free energy and not to the changes either in enthalpy or in the entropy of the system; these values may be negative, positive, or zero for a given reaction and are therefore not valid measures of thermodynamic spontaneity. Conversely, any process or reaction that would result in an increase in the free energy of the system is called endergonic (energy-requiring) and cannot proceed under the conditions for which ΔG was calculated.

The meaning of spontaneity. Before considering how it can actually calculate AG and use it as a measure of thermodynamic spontaneity, we need to look more closely at what is—and what is not—meant by the term spontaneous. As noted earlier, spontaneity tells us only that a reaction can go; it says nothing at all about whether it will go. A reaction can have a negative ΔG value and yet not actually proceed to any measurable extent at all. The cellulose of paper obviously burns spontaneously once ignited, consistent with a highly negative ΔG value of -686 kcal/mol of glucose units. Yet in the absence of a match, paper is reasonably stable and might require hundreds of years to oxidise. Thus, ΔG can really tell us only whether a reaction or process is thermodynamically feasible—whether it has the potential for occurring. Whether an exergonic reaction will in fact proceed depends not only on its favorable (negative) ΔG, but also on the availability of a mechanism or pathway to get from the initial state to the final state. Usually, an initial input of activation energy is required as well, such as the heat energy from the match that was used to ignite the piece of paper.

Thermodynamic spontaneity is therefore a necessary but insufficient criterion for determining whether a reaction will actually occur. It will explore the subject of reaction rates in the context of enzyme-catalyzed reactions. For the moment, need only note that when designating a reaction as thermodynamically spontaneous, it simply means that it is an energetically feasible event that will liberate free energy if and when it actually takes place.

The author is an associate professor (retd.) and former head of the department of botany at Ananda Mohan College.

Regards,