Kaplan MCAT General Chemistry Review

These examples have a common denominator: In all of them, energy of some form or another is going from being localized or concentrated to being spread out or dispersed. The thermal energy in the hot tea is spreading out to the cooler air that surrounds it. The thermal energy in the warmer air is spreading out to the cooler frozen drink. The chemical energy in the bonds of elemental iron and oxygen is released and dispersed as a result of the formation of the more stable (lower-energy) bonds of iron oxide (rust). The potential energy of the building is released and dispersed in the form of light, sound, and heat (motional energy) of the ground and air as the building crumbles and falls. The motional energy of the pressurized air is released to the surrounding atmosphere as the balloon deflates. The chemical energy of all the molecules and atoms in living flesh is released into the environment during the process of death and decay.

This is the second law of thermodynamics: Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. Pay attention to this: The usual way of thinking about entropy as “disorder” must not be taken too literally, a trap that many students fall into. Be very careful in thinking about entropy as disorder. The old analogy between a messy (disordered) room and entropy is arguably deficient and may not only hinder understanding but actually increase confusion.

Entropy, then, according to statistical mechanics, is the measure of the spontaneous dispersal of energy at a specific temperature: how much energy is spread out, or how widely spread out energy becomes, in a process. The equation for calculating the change in entropy is

where S is the change in entropy, Q_rev is the heat that is gained or lost in a reversible process (a process that proceeds with infinitesimal changes in the system), and T is the temperature in Kelvin. The units of entropy are usually kJ/mol • K.When energy is distributed into a system at a given temperature, its entropy increases. When energy is distributed out of a system at a given temperature, its entropy decreases.

Notice that the second law states that energy will spontaneously disperse; it does not say that energy can never be localized or concentrated. However, the concentration of energy will rarely, if ever, happen spontaneously in a closed system (there is an exceedingly small but measurable chance that it could, but this is beyond the scope of the MCAT). Work usually must be done to concentrate energy. For example, refrigerators move thermal energy against a temperature gradient (that is, they cause heat to be transferred from “cool” to “warm”), thereby “concentrating” energy outside of the system in the surroundings. Nevertheless, refrigerators consume a lot of energy (they do a lot of work) to accomplish this movement of energy against the temperature gradient.

Figure 6.1

The second law has been described as “time’s arrow,” because there is a unidirectional limitation on the movement of energy by which we recognize “before and after” or “new and old.” For example, you would instantly recognize whether a video recording of an explosion was running forward or backward. This is what is meant by the phrase “time’s arrow.” Another way of understanding this is to say that energy in a closed system will spontaneously spread out and entropy will increase if it is not hindered from doing so. Remember that a system can be variably defined to include ultimately the entire universe; in fact, the second law ultimately claims that the entropy of the universe is increasing. That is to say, energy concentrations at any and all locations in the universe are in the process of becoming distributed and spread out.

S_{uni verse} = S_system + S _surroundings > 0

Entropy is a state function, so a change in entropy from one equilibrium state to another is pathway-independent and only depends upon the difference in entropies of the final and initial states:

S = S_final-S_initial

The standard entropy change for a reaction, S°_rxn, is calculated using the standard entropies of reactants and products:

S°_rxn = ΣS°_products - ΣS°_reactants

Gibbs Free Energy