Chemical reactions can be divided into two types, depending on whether energy is absorbed or released in the process. In an exergonic (“energy-releasing”) reaction, the products contain less energy than the reactants. Exergonic reactions take place spontaneously. The liberated energy is usually released as heat (the energy of molecular motion) and generally results in a rise in temperature, as in the oxidation (burning) of wood. In an endergonic (“energy-absorbing”) reaction, the products contain more energy than the reactants, and energy is absorbed during the reaction. If there is no external source of energy to drive an endergonic reaction, it cannot take place. Endergonic reactions are responsible for the ability of the instant cold packs often used to treat injuries to rapidly cool below room temperature. Crushing the pack mixes the reactants, initiating the reaction.

A fundamentally important concept in understanding if a reaction is exergonic or endergonic, and therefore if it occurs spontaneously or not, is free energy (G), or Gibbs free energy, named after J. W. Gibbs. Gibbs, who received the first PhD in engineering in America in 1863, showed that “all systems change in such a way that free energy [G] is minimized.” In other words, a chemical reaction occurs spontaneously when the free energy of the products is lower than the free energy of the reactants. In the case of a chemical reaction, reactants ⇌ products, the free-energy change, ΔG, is given by

ΔG = G_products – G_reactants

The relation of ΔG to the direction of any chemical reaction can be summarized in three statements:

By convention, the standard free-energy change of a reaction (ΔG°′) is the value of the change in free energy at 298 K (25 °C), 1 atm pressure, pH 7.0 (as in pure water), and initial concentrations of 1 M for all reactants and products except protons, which are kept at 10^–7 M (pH 7.0). Most biological reactions differ from these standard conditions, particularly in the concentrations of reactants, which are normally less than 1 M.

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The free energy of a chemical system can be defined as G = H – TS, where H is the bond energy, or enthalpy, of the system; T is its temperature in degrees Kelvin (K); and S is the entropy, a measure of its randomness or disorder. According to the second law of thermodynamics, the natural tendency of any isolated system is to become more disordered—that is, for entropy to increase. A reaction can occur spontaneously only if the combined effects of changes in enthalpy and entropy lead to a lower ΔG. That is, if temperature remains constant, a reaction proceeds spontaneously only if the free-energy change, ΔG, in the following equation is negative:

ΔG = ΔH – TΔS (2-6)

In an exothermic (“heat-releasing”) chemical reaction, ΔH is negative. In an endothermic (“heat-absorbing”) reaction, ΔH is positive. The combined effects of the changes in the enthalpy and entropy determine if the ΔG for a reaction is positive or negative, and thus if the reaction occurs spontaneously. An exothermic reaction (ΔH < 0), in which entropy increases (ΔS > 0), occurs spontaneously (ΔG < 0). An endothermic reaction (ΔH > 0) will occur spontaneously if ΔS increases enough so that the TΔS term can overcome the positive ΔH.

Many biological reactions lead to an increase in order and thus a decrease in entropy (ΔS < 0). An obvious example is the reaction that links amino acids to form a protein. A solution of protein molecules has a lower entropy than does a solution of the same amino acids unlinked because the free movement of any amino acid is more restricted (greater order) when it is bound into a long chain than when it is not. Thus, when cells synthesize polymers such as proteins from their constituent monomers, the polymerizing reaction will be spontaneous only if the cells can efficiently transfer energy to both generate the bonds that hold the monomers together and overcome the loss in entropy that accompanies polymerization. Often cells accomplish this feat by “coupling” such synthetic, entropy-lowering reactions with independent reactions that have a very highly negative ΔG, such as the hydrolysis of nucleoside triphosphates (see below). In this way, cells can convert sources of energy in their environment into the highly organized structures and metabolic pathways that are essential for life.

The actual change in free energy during a reaction is influenced by temperature, pressure, and the initial concentrations of reactants and products, so it usually differs from the standard free-energy change ΔG°′. Most biological reactions—like others that take place in aqueous solutions—are also affected by the pH of the solution. We can estimate free-energy changes for temperatures and initial concentrations that differ from the standard conditions by using the equation

where R is the gas constant of 1.987 cal/(degree·mol), T is the temperature (in degrees Kelvin), and Q is the initial ratio of products to reactants. For a reaction A + B ⇌ C, in which two molecules combine to form a third, Q in Equation 2-7 equals [C]/[A][B]. In this case, an increase in the initial concentration of either [A] or [B] will result in a larger negative value for ΔG and thus drive the reaction toward spontaneous formation of C.

Regardless of the ΔG°′ of a particular biochemical reaction, it will proceed spontaneously within cells only if ΔG is negative given the intracellular concentrations of reactants and products. For example, the conversion of glyceraldehyde 3-phosphate (G3P) to dihydroxyacetone phosphate (DHAP), two intermediates in the breakdown of glucose,

G3P ⇌ DHAP

has a ΔG°′ of –1840 cal/mol. If the initial concentrations of G3P and DHAP are equal, then ΔG = ΔG°′ because RT ln = 0; in this situation, the reversible reaction G3P ⇌ DHAP will proceed spontaneously in the direction of DHAP formation until equilibrium is reached. However, if the initial [DHAP] is 0.1 M and the initial [G3P] is 0.001 M, with other conditions standard, then Q in Equation 2-7 equals 0.1/0.001 = 100, giving a ΔG of +887 cal/mol. Under these conditions, the reaction will proceed in the direction of formation of G3P.

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The ΔG of a reaction is independent of the reaction rate. Indeed, under normal physiological conditions, few, if any, of the biochemical reactions needed to sustain life would occur without some mechanism for increasing reaction rates. As we describe below and in more detail in Chapter 3, the rates of reactions in biological systems are usually determined by the activity of enzymes, the protein catalysts that accelerate the formation of products from reactants without altering the value of ΔG.