Biochemistry - The Chemical Reactions of Living Cells, Volume 1 - D. Metzler 1980

Energetics of Biochemical Reactions
Thermodynamics
The Second Law of Thermodynamics

The Second Law of Thermodynamics can be stated in various ways, but in standard mathematical terms it asserts that in the "universe" (or in a closed system)

Class="center">∆S (system + its surroundings) = 0 for reversible processes,

∆S > 0 for real (irreversible) processes.

Sometimes the second law is expressed differently: the Entropy of the universe is constantly increasing.

The second law defines both S and the thermodynamic Temperature scale simultaneously:

dS_reversible = q/T,       (3-5)

where q is an infinitesimally small amount of heat absorbed. For a reversible phase transition, such as the melting of ice at constant pressure and temperature, the entropy change of H₂O is exactly equal to ∆H/T [Equation (3-6)]. Entropy is measured in joules per 1 K or in calories per 1 K.

∆S_{P,T,reversible} = Q/T = ∆H/T.       (3 6)

In the latter case, the abbreviation E.U. (entropy units) is often used. Since the melting of ice is a reversible process, the second law dictates that the entropy of the surroundings decreases by the exact same amount that the entropy of the Water increases. Note that for water at 0 °C, TAS is numerically equal to the heat of fusion,

6.008 kJ∙mol^-1. Thus, the increase in the entropy of ice during its melting at 0 °C is 6.008∙10³ J / 273.16 K = 22.0 J∙deg^-1.

The definition of thermodynamic temperature [Equation (3-7); see textbooks on thermodynamics for more details] also follows from Equation (3-5):

T(K) = (dE/dS)_v = (dH/dS)_p.       (3-7)

Entropy can be precisely described mathematically through the degree of disorder of a system

S = k InΩ.       (3-8)

Here, k is the Boltzmann constant (Table 3-1), and Ω is the number of microscopic states (different particle arrangements) of the system corresponding to a given macroscopic state—that is, a state with a specific temperature, pressure, and number of molecules. Ω increases with an increase in volume or temperature, as well as when a substance transitions from a solid to a liquid and subsequently to a gaseous state. Equation (3-8) is not an equation of classical thermodynamics, which deals solely with macroscopic systems, i.e., large collections of molecules. However, by employing the Methods of statistical thermodynamics [9], it can be used to determine the entropy of gases quite accurately.

A biochemical example that can be directly related to Equation (3-8) is the Racemization of Amino Acids. A solution of an L-amino acid can be readily converted into a racemic mixture, where 50% of The amino acid is in the D-form and 50% in the L-form, using a specific enzyme called racemase; this process is accompanied by neither the absorption nor the release of heat. Thus, ∆Н = 0, and the only changing parameter of the system is entropy. Let us denote Ω of the pure isomer as Ω'. Taking into account that each of the N molecules of 1 mole of the racemate can exist in one of two configurations, we can write for the racemic mixture

Ω = 2NΩ'.       (3-9)

Based on Equation (3-8), we obtain

∆S = k (ln 2^N + ln Ω') — k ln Ω' = Nk ln 2 = R ln 2=

      = 5.76 J∙mol^-1.            (3-10)