Review Exercises

# Thermodynamics

SECTIONS
 1 Introduction 2 The First Law 3 The Second Law 4 Gibbs Free Energy 5 G, H, S 6 Spontaneity 7 Relating G, H, S 8 Equilibrium 9 Review

## UNDERSTANDING THERMODYNAMIC RELATIONSHIPS

Let’s look at how DH (enthalpy change or heat of reaction) and DS (entropy change of a reaction) fit together with DG to explain the behavior of a chemical reaction. Consider the thermodynamic equation:

 DG = DH – TDS

It is clear that the value of DG (positive or negative) depends on the values of DH and DS as well as the temperature of the reaction. Another way to think about it is that the DG, or maximum potential usable energy of the reaction, is distributed between the two terms, DH and TDS. The DH (enthalpy) term represents energy that can be measured as the evolution or absorption of heat during the course of the reaction. The TDS (entropy) term indicates energy associated with the change of entropy, or disorder, of the system during the course of the reaction. This is the energy that increases the random motion or orientation of molecules involved in the reaction and is thus lost to the system, because it cannot be utilized productively.

 Enthalpy, and Entropy Enthalpy (DH) positive (+) Heat absorbed negative (–) Heat released Entropy (DS) positive (+) Increase in disorder negative (–) Decrease in disorder

 DG = DH – TDS Maximum usable potential energy of a reaction Heat energy Energy gained or lost due to changes in thermal and positional disorder of molecules

### Understanding spontaneity in terms of enthalpy and entropy

There is only so much potential energy associated with a chemical reaction, and any energy that is involved in increasing entropy cannot be made to do useful work. Let’s look at a concrete example. The hydrolysis of ATP, a common biochemical reaction in our bodies, provides energy for physiological processes:

 ATP ADP + Pi   DG = –30.5 kJ/mol at 25°C

Measurements of enthalpy show that DH for this reaction is only – 16.7 kJ/mol at 25°C. In other words, although the Gibbs Free Energy of the reaction is –30.5 kJ/mol, meaning it has the potential to release 30.5 kJ/mol of usable energy when hydrolyzed, only 16.7 kJ/mol of heat energy was actually released. What happened to the other 13.8 kJ/mol of energy? Look once again at Willard Gibbs’ equation and plug in the values for DG and DH:

 DG = DH – TDS –30.5 kJ/mol = –16.7 kJ/mol – TDS –13.8 kJ/mol = – TDS TDS = 13.8 kJ/mol

The rest of the energy is accounted for by the TDS term. The TDS term is positive, indicating an increase in the entropy of the system. This energy that increases the entropy of the system cannot be recovered to do useful work.

Thus, in the Gibbs equation, the enthalpy and entropy terms are in competition with each other. Experiment with the following interactive element to gain a better understanding of the interplay between enthalpy and entropy. Notice that the temperature of a reaction is also a factor in the entropic term of the equation. Move the sliders to experiment with different thermodynamic scenarios.

### Example 5: Protein folding

Polypeptide chains fold spontaneously into defined patterns to make functional proteins. This process involves the polypeptide chain going from a disordered, random structure to a highly ordered one. How is this not a violation of the Second Law of Thermodynamics?

The ordering of the protein from a free-swinging peptide chain involves a variety of physical forces, some that favor the unfolded peptide chain, and some that favor the neatly folded protein. When assessing entropic contributions to Gibbs Free Energy for the purpose of determining spontaneity, you must not look only at the system, but also at the surroundings. It is true that the entropy of the protein decreases when it is folded because the chain is arranged in a more orderly fashion. However, there are other entropic considerations in the surroundings of the protein. In an unfolded protein, all of the hydrophobic portions of the polypeptide are exposed to the aqueous environment, and the water molecules order themselves around the hydrophobic residues in ordered structures called hydration spheres. As a protein is folded, these hydrophobic residues initially exposed to the aqueous environment are buried in the interior of the protein, hidden away from contact with water molecules, and the entropy of the water molecules increases as the need for hydration spheres diminishes, in effect overcoming the entropy decrease for the protein alone. In other words, while the entropy of the system (the protein) decreases, the entropy of the surroundings increases to a greater degree, leading to an overall increase in entropy for the universe.

The folding of a protein also provides an example of the "DH" and "–TDS" terms competing with one another to determine the DG of the folding process. As described above, the change in entropy of the protein as it folds is negative, so the "–TDS" term is positive. However, in addition to entropic effects there are enthalpic contributions to protein folding. These include hydrogen bonding, ionic salt bridges, and Van der Waals forces. An input of thermal (heat) energy is required to disrupt these forces, and conversely when these interactions form during protein folding they release heat (the DH is negative). When all of these entropic and enthalpic contributions are weighed, the enthalpy term wins out over the entropy term. Therefore the free energy of protein folding is negative, and protein folding is a spontaneous process.