Laws of Thermodynamics in Bioenergetics (With Diagram)

Thermodynamics is the study of energy changes, that is, the conversion of energy from one form into an­other. Such changes obey the first two laws of thermo­dynamics.

The First Law of Thermodynamics:

The first law is concerned with the conversion of en­ergy within a “system,” where a system is defined as a body (e.g., a cell or an organism) and its surround­ings.

This law, which applies to both biological and non-biological systems, states the following: Energy cannot be created or destroyed but can be converted from one form into another: during such a conversion, the total amount of the energy of the system remains constant.

This law applies to all levels of organization in the liv­ing world; it applies to organisms, cells, organelles, and to the individual chemical reactions that char­acterize metabolism. In practice, it is difficult to measure the energy possessed by cells (i.e., to limit the “system” to an individual cell), because energy may escape into the environment surrounding the cell during the measurement.

Similarly, energy may be ac­quired by the cell from its environment; for example, a photosynthesizing cell absorbs energy from its envi­ronment in the form of light. A cell’s acquisition of en­ergy from its environment (or its loss to the environment) should not be confused with the destruc­tion or creation of energy, which according to the first law of thermodynamics does not occur.

From a biological viewpoint, the first law of thermo­dynamics indicates that at any given moment a cell possesses a specific quantity of energy.

This energy takes several forms; it includes:

(1) Potential energy (e.g., the energy of the bonds that link atoms together in a molecule or the pressure-volume relationships within the cell as a whole or within membrane- enclosed intracellular components);

(2) Electrical en­ergy (e.g., the distribution of different amounts of electrical charge across cellular membranes); and

(3) Thermal energy (e.g., the temperature-dependent constant and random motions of molecules and at­oms).

According to the first law, these forms of energy may be inter-converted; for example, some of the cell’s potential energy can be converted into electrical or thermal energy, but the cell cannot create or destroy energy. When a cell breaks down a polysaccharide to ultimately form CO₂ and H₂O, some of the potential energy present in the carbohydrate is conserved as potential energy by phosphorylating ADP, thereby forming ATP.

The ATP so produced represents a new energy source (and also one that is of greater immedi­ate utility for the cell). However, not all of the energy of the original carbohydrate is conserved as potential energy; some of it becomes thermal energy and is transferred to the surroundings as heat. It is impor­tant to recognize that none of the energy is destroyed and it should be possible to account for all of the en­ergy originally present in the polysaccharide in other forms within the system (i.e., in the ATP that is pro­duced and in the heat that is released).

The Second Law of Thermodynamics:

The first law of thermodynamics tells us that the total energy of an isolated system consisting of a cell (or or­ganism) and its surroundings is the same before and after a series of events or chemical reactions has taken place. What the first law does not tell us is the direction in which the reactions proceed.

This prob­lem can be illustrated using a simple example. Sup­pose we place a small cube of ice in a liter of hot water, seal the combination in an insulated container (e.g., a vacuum bottle), and allow the system (i.e., the ice and the water) to reach an equilibrium.

In such a system, we would not be surprised to find that the ice melts and that this is accompanied by a decrease in the tem­perature of the water. When we later examine the sys­tem, we find that we are left only with water (no ice) and that the water is at a reduced temperature.

The flow of heat, which is thermal energy, from the hot wa­ter to thrice thereby causing the ice to melt is sponta­neous and the energy that is “lost” by the water is “gained” by the melting ice so that the total energy of the system remains the same.

We certainly would not expect ice to form spontaneously in a sealed system that contains warm water, even though such an eventu­ality is not prohibited by the first law. Consequently, the important lessons to be learned from this illustra­tion are that energy changes have direction and may be spontaneous.

To anticipate the spontaneity of a reaction and pre­dict its direction, one must take into account a func­tion called entropy. Entropy is a measure of the de­gree of randomness or disorder of a system, the entropy increasing with increasing disorder. Accord­ingly, the second law of thermodynamics states: In all processes involving energy changes within a system, the entropy of the system increases until an equilibrium is attained.

In the illustration that was presented above, the highly ordered distribution of energy (i.e., large amounts of energy in the hot water and smaller amounts of energy in the ice) was lost as the ice melted to form water. In the resulting warm water, the energy was more randomly and uniformly distrib­uted among the water molecules.

The units of entropy are J/mole (or cal/mole), indi­cating that entropy is measured in terms of the amount of substance present. When equal numbers of moles of a solid, liquid, and gas are compared at the same temperature, the solid has less entropy than the liquid and the liquid has less entropy than the gas (the gaseous state is the state of greatest disorder).

En­tropy can be thought of as the energy of a system that is of no value for performing work (i.e., it is not “use­ful” energy). For example, the catabolism of sucrose or other sugars by a cell is accompanied by the forma­tion of energy-rich ATP.

Although superficially it may appear as though useful energy has increased in the form of the ATP gained by the cell, the total amount of useful energy has actually decreased and the amount of unavailable energy increased. It is true that some of the potential energy of the sugar has been converted to potential energy in the form of ATP, but some has also been converted to thermal energy, which tends to raise the temperature of the cell and therefore its en­tropy.

Suggestions that cells can decrease entropy by carrying out photosynthesis are misleading. Although it is true that during photosynthesis cells convert mol­ecules with very little potential energy (CO₂ and H₂O) into larger molecules with considerably more poten­tial energy (sugars) and that there is an accompanying decrease in the entropy of the cell, energy in the form of light was absorbed from the cell’s environment.

Be­cause the light energy consumed during photosynthe­sis is a part of the whole system (i.e., the cell and its surroundings), it is clear that there has actually been an overall decrease in useful energy and an increase in entropy (see Fig. 9-4).

The entropy change during a reaction may be quite small. For example, when sucrose undergoes hydroly­sis to form the sugars glucose and fructose, much of the potential energy of the original sucrose is present in the resulting glucose and fructose molecules. Changes in entropy are extremely difficult to calcu­late, but the difficulty can be circumvented by employ­ing two other thermodynamic functions: enthalpy or heat content (denoted H) and free energy (denoted G).

The change in a system’s enthalpy (∆H) is a measure of the total change in energy that has taken place, whereas the change in free energy (∆G) is the change in the amount of energy available to do work. Changes in entropy (∆S), enthalpy, and free energy are related by the equation in which T is the absolute temperature of the system.

∆G = ∆H-T∆S …(9-1)

The change in free energy can also be defined as the total amount of free energy in the products of a reac­tion minus the total amount of free energy in the reactants, that is,

∆G = G (products) – G(reactants) …(9-2)

A reaction that has a negative ∆G value (i.e., the sum of the free energy of the products is less than that of the reactants) will occur spontaneously, a reaction for which the ∆G is zero is at equilibrium; and a reaction that has a positive AG value will not occur spontane­ously and proceeds only when energy is supplied from some outside source.

∆G, ∆G⁰, and ∆G⁰‘ Values

The hydrolysis of sucrose

Sucrose + H₂O → glucose + fructose

has a negative AG value, and therefore when sucrose is added to water, there is the spontaneous conversion of some of the sucrose molecules to glucose and fruc­tose. However, the reverse reaction

glucose + fructose →sucrose + H₂O

has an equal but positive ∆G value and therefore does not occur without an input of energy. Hence, special attention must be paid to the direction in which the reaction is written (i.e., the direction of the arrow) and the sign of the ∆G value. If 5 moles of sucrose are mixed with water, the formation of glucose and fruc­tose will take place spontaneously and the ∆G may be determined; this value is, of course, greater than if 4 or 2 miles of sucrose are used.

Thus, ∆G values are dependent on the amounts and concentrations of reac­tants and products. More uniform standards of refer­ence that have been established by convention are the standard free energy changes, ∆G⁰ and ∆G⁰‘ values. ∆G⁰ represents the change in free energy that takes place when the reactants and products are maintained at 1.0 molar concentrations (strictly speaking, 1.0 molar) during the course of the reaction and the reaction proceeds under standard conditions of temperature (25°C) and pressure (1 atmosphere) and at pH 0.0.

The ∆G⁰‘ value is a much more practical term for use with biological systems in which reactions take place in an aqueous environment and at a pH that usually is either equal or close to 7.0. The ∆G⁰‘ value is defined as the standard free energy change that takes place at pH 7.0 when the reactants and products are main­tained at 1.0 molar concentration (Table 9-2).

The changes in standard free energy are indepen­dent of the route that leads from the initial reactants to the final products. For example, glucose can be con­verted to carbon dioxide and water either by combus­tion in the presence of oxygen or through the actions of cellular enzymes.

Changes in standard free energy are the same, regardless of the method that is used; thus, the value of the standard free energy change provides no information about the reaction sequence by which the change has taken place. By the same to­ken, the values obtained for changes in standard free energy tell us nothing about the rate at which the changes have taken place.

The ∆G⁰‘ can be calculated from the equilibrium constant, K’_eq, of a reaction using the relationship

∆G⁰‘=-RT InK’_eq (9-3)

= – 2.303 R T log₁₀ K’_eq (9-4)

Where R is the gas constant (8.314 J/mole/degree), T is the absolute temperature (in degrees Kelvin), -and K’_eq is the equilibrium constant. Table 9-3 lists a num­ber of ∆G⁰‘ values for common reactions.

For the reaction

A+B→C+D

The equilibrium constant is defined as

K’_eq = [C][D] at equilibrium (9-5)

Where [A] and [J3] are the concentrations of the reac­tants and [C] and [D] are the concentrations of the products. If the equilibrium constant is 1.0, then the ∆G⁰‘ value equals zero. If the equilibrium constant is greater than 1.0, then the ∆G⁰‘ value is negative (e.g., -11.41 kJ/mole for a K’_eq value of 100), and the reac­tion is said to be exergonic (i.e., “energy releasing”) because it proceeds spontaneously in the direction written when starting with unimolar concentrations of reactants and products.

When the K’_eq value is less than 1.0, the ∆G⁰‘ value is positive (e.g., 5.71 kJ/mole for a K’_eq of 0.1), and the reaction is said to be endergonic (i.e., “energy consuming”) because it does not proceed spontaneously in the direction written when starting with unimolar concentrations of reactants and products.

Calculations of AG⁰‘ values are usually based on ex­perimental measurements of isolated reactions, that is, with reactions that take place independently of other reactions and that are not associated with cells. ∆G⁰ and ∆G⁰‘ values do not provide information about the free energy changes of reactions as they might take place in cells or under conditions in which the concentrations of reactants and prod acts, pH, etc., may change. This may be dramatically illustrated by considering the following example. At pH 7.0 and 25°C, the equilibrium constant for the reaction dihydroxyacetone phosphate → glyceraldehyde-3-phosphate is 0.0475. Therefore, using equation 9-3,

∆G⁰‘ = – 2.303 RT log ₁₀ K’_eq

= – 2.303 (8.314 J/mole/degree) (298) log₁₀ (0.0475)

= + 7.55 kJ/mole

The positive value indicates that this reaction does not proceed spontaneously in the direction written. How­ever, in cells, this reaction is but one of a series of re­actions in a metabolic pathway called glycolysis. Other reactions of glycolysis that occur prior to this one and that have negative ∆G⁰‘ values produce additional substrate (i.e., dihydroxyacetone phosphate) and reactions with negative ∆G⁰‘ values that occur after this step remove the product glyceraldehyde-3-phosphate.

As a result, the reaction proceeds in the direction written under the conditions specified above, even though the ∆G⁰‘ value is positive. This example illustrates the important point that the ∆G⁰‘ value for a specific biological reaction cannot be used to predict reliably whether or not that particular reaction is actually taking place within the cell.