We have discussed enthalpy as one form of energy, namely heat. Entropy is a different type of energy: disorder. While it sounds strange at first, seeing disorder or randomness as a form of energy is not too difficult. Think of a garden: if left alone, disorder takes over: weeds grow in the planting beds, flowers die, leaves fall, and plants grow out of control. Keeping the garden in order requires energy in the form of maintenance, so you can think of a nice, orderly garden as having high energy and low entropy. Later, the energy declines as thinks go out of control. Eventually, a situation of more-or-less complete disorder will be reached, and the energy decline will stop. One can think of states of matter in terms of randomness as well. Solids, since they are highly structured, have low entropies. Liquids have much higher entropies, and gases have the highest entropies of all. In addition, the faster molecules are moving, the more entropy they having, since fast-moving particles are more chaotic than slow-moving particles.
This situation applies to the entire universe as well. Things naturally seem to favor a condition of high randomness over more ordered states. This is due to the laws of probability: for any given system, there are many, many more disordered states than ordered states. Think of a jigsaw puzzle: there is only one completely ordered state, the solved puzzle, but there are many disordered states, when the pieces are scattered about. This theory constitutes the Second Law of Thermodynamics, which simply states that the disorder of the universe is always increasing. Consider the garden example: you can go out and weed the garden, which makes it more ordered, but the energy of your efforts will be released as heat, which makes the rest of the universe less ordered. The total change in disorder is always positive.
Like enthalpy, entropy can be measured. We assume that a crystal at absolute zero is in a perfect state of order, since the crystal is highly structured and nothing is moving. Using this as a basis of comparison, scientists postulated the Third Law of Thermodynamics: if the entropy of every element in a crystalline state is zero at 0 K, every substance has a finite and measurable entropy. Entropy values are represented by the symbol S, and entropy values for many substances can be found in our "Reference" section, under the Thermodynamics link. Higher values represent a state of higher disorder. A superscript "o" indicates that the value is for standard conditions (25 °C, 1 atm).
As with enthalpy, the entropy change of a reaction can be found by subtracting the enthalpies of the reactants from the enthalpies of the products, as shown below:
ΔS° = Σ S°(products) - Σ S°(reactants)
If nature favors a state of high entropy, the total entropy change, ΔS, should be positive in a favorable reaction, since randomness has increased. In general, the following reaction types have high ΔS values:
- Conversion of a solid to a liquid or a liquid to a gas
- Conversion of simple molecules to a more complex molecule (in larger molecules, individual atoms have more possible positions in space, thus more entropy)
- Weakening of ionic forces (ionic attractions lead to structured states, including crystal lattices)
- Dissolving substances (mixing two types of matter together increases disorder)
- Dissolved gases escaping from the solvent (in spite of above, because gases have such high entropies)
However, in our discussion of entropy change and favorability, we have not considered the effect of heat release or absorption on the surroundings. For some reactions, this doesn't matter: if heat is released (good) and disorder increases (good), the reaction is always favorable. Similarly, if heat is absorbed (bad) and entropy decreases (bad), the reaction will never occur. But if one value is "good" and one is "bad," does the reaction occur? For instance, boiling water generates a gas, which has much high entropy than the liquid, but heat input is required, which decreases the entropy of the rest of the universe. In some reactions, these two values are in conflict. Is there a way to predict which value predominates: the entropy change or the enthalpy change? Yes: through a third thermodynamic value, Gibbs free energy.