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

## GIBBS FREE ENERGY, ENTHALPY, AND ENTROPY

In the previous two sections, we learned that there are laws of thermodynamics that govern physical processes, including chemical reactions, and that a quantity called the Gibbs Free Energy of Reaction (DG) can tell us if a reaction is thermodynamically favorable, or likely to happen naturally without energy input. In this section, we will learn more about the DG's dependence on two quantities, enthalpy (H) and entropy (S).

### Entropy: The disorder of a system

Entropy, as was noted in the introduction, is a measure of the disorder of a system. We all understand disorder in terms of a messy sock drawer, but what does disorder mean in a chemical sense? Remember that any substance comprises a collection of molecules. This collection of molecules can have positional disorder and thermal disorder. Positional disorder refers to the arrangement of the molecules in space (like the arrangement of socks in the sock drawer). Substances that have all their molecules or atoms neatly arranged in orderly rows (such arrangements are found in crystals) have less positional disorder than substances made up of molecules that move around freely (such as those found in a liquid or gas). Thermal disorder refers to the distribution of available energy among all the particles. Thermal disorder is tied to the temperature of a substance, since molecules are more energetic at higher temperatures.

To understand this, think of an ice cube. Ice is simply water that has frozen, and each H2O molecule is neatly arranged in a crystal whose structure is dictated by the constraints of hydrogen bonding. In ice, the position of each H2O molecule is highly ordered.

If that ice cube is placed in a hot pan, the H2O molecules are heated and the ice melts to water, which subsequently boils and turns to steam. The neat crystal structure of the ice thus disappears, replaced by the random, energetic motion of steam wafting out of the pan. While ice is characterized by low positional and thermal disorder of the water molecules, steam is characterized by high positional and thermal disorder. Entropy is denoted by the symbol S, and the change of entropy of a system is written as DS. The conversion of ice to water and then steam has a positive value of DS.

### Enthalpy: The “heat of reaction”

Enthalpy is another thermodynamic property that we need to understand. Enthalpy is denoted by the symbol H, and is a measure of the internal energy of a system. In the course of a reaction, the change in internal energy between reactants and products, or DH, can be measured by the heat absorbed or released during the course of a reaction (One caveat: this holds true as long as the reaction is performed under constant pressure, which is generally the case in biological systems). Because the enthalpy can be measured as heat, DH is often called the heat of reaction. Reactions that consume enthalpy (have a positive DH) are said to be endothermic (heat consuming), while reactions that release enthalpy (have a negative DH) are said to be exothermic (heat releasing). Given how you feel jogging on a hot summer’s day, what can you say about the enthalpy of the metabolic processes that are put into gear inside your body during exercise?

 ENTHALPY Sign of DH Description Term used Positive (+) DH Consumes heat energy Endothermic Negative (–) DH Releases heat energy Exothermic

Those instant heat or ice packs that are often found in first-aid kits take advantage of exothermic or endothermic chemical processes. These packs have to be “activated” by crushing internal containers, which allows the chemicals to mix, generally causing dry chemicals to dissolve in water. Both of these kinds of packs rely on chemicals that either release heat or draw it out of their surroundings when they come into contact with water.

 ENTHALPY EXAMPLES: HOT AND COLD PACKS Endothermic process Cold Pack NH4NO3(s) + H2O + heat NH4NO3(aq) Exothermic process Hot Pack CaCl2(s) + H2O CaCl2(aq) + heat

Notice that for the cold pack reaction, heat from the surroundings is being absorbed in the reaction. So when you apply a cold pack to an injury, heat is drawn away from the the tissue the cold pack is in contact with as the ammonium nitrate dissolves into solution. In the case of the hot pack, calcium chloride going into solution releases heat to the tissue you apply it to, such as an aching back.

### Relation of entropy and enthalpy to Gibbs free energy

Now that we understand DH and DS, we can better understand the relationship of these quantities to Gibbs Free Energy Change, or DG, formulated by the thermodynamicist Willard Gibbs over 100 years ago:

 DG = DH – TDS

The T in the formula stands for the temperature at which the reaction occurs. It is important to remember that the temperature is measured in degrees Kelvin, which as you may remember are on the same scale as degrees Celsius, but start at absolute zero. Since absolute zero (zero degrees Kelvin) is approximately –273°C, the conversion formula for Celsius to Kelvin is

 K = °C + 273

Notice how DG for a reaction depends on both the enthalpy change (DH) and entropy change (DS) of the reaction. Furthermore, the temperature of the reaction (T) is important for calculating DG. In the next section, we will consider how all these factors can help us understand biochemical reactions.

### Example 4: Free energy of a phase change

Calculate the DG for the freezing of water at 0°C. (The DH = 6 kJ/mol, and the DS is 22 J mol–1 K–1.)