MCAT General Chemistry Review - Alexander Stone Macnow, MD 2019-2020

Thermochemistry
Entropy

LEARNING GOALS

After Chapter 7.5, you will be able to:

· Order the phases of matter from lowest to highest entropy

· Define entropy in terms of its relation to energy distribution and disorder

· Predict the direction of change in entropy within a given reaction

Many students are perplexed by the concept of entropy. Enthalpy makes intuitive sense, especially when the energy change from reactants to products is large, fast, and dramatic (as in combustion reactions involving explosions). Entropy seems to be less intuitive—except that it isn’t. Consider, for example, how “normal” each of the following seems: hot tea cools down, frozen drinks melt, iron rusts, buildings crumble, balloons deflate, living things die and decay, and so on.

Key Concept

Entropy changes that accompany phase changes can be easily estimated, at least qualitatively. For example, freezing is accompanied by a decrease in entropy, as the relatively disordered liquid becomes a well-ordered solid. Meanwhile, boiling is accompanied by a large increase in entropy, as the liquid becomes a much more disordered gas. For any substance, sublimation will be the phase transition with the greatest increase in entropy.

These examples have a common denominator: in each of them, energy of some form 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 as the building crumbles and falls. The 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.

The second law of thermodynamics states that 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 deficient and may not only hinder understanding but actually increase confusion.

Entropy 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:

Equation 7.7

where ΔS is the change in entropy, Q_rev is the heat that is gained or lost in a reversible process, and T is the temperature in kelvin. The units of entropy are usually 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 happen spontaneously in a closed system. Work usually must be done to concentrate energy. For example, refrigerators work against the direction of spontaneous heat flow (that is, they counteract the flow of heat from the “warm” exterior of the refrigerator to the “cool” interior), thereby “concentrating” energy outside of the system in the surroundings. As a result, refrigerators consume a lot of energy to accomplish this movement of energy against the temperature gradient.

Figure 7.10. Entropy in the kitchen

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, as shown in Figure 7.10. For example, you would instantly recognize whether a video recording of an explosion was running forward or backward. 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 the entire universe; in fact, the second law ultimately claims that the entropy of the universe is increasing.

ΔS_universe = ΔS_system + ΔS_surroundings > 0

Equation 7.8

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. Further, the standard entropy change for a reaction, ΔS^°_rxn, can be calculated using the standard entropies of the reactants and products—much like enthalpy:

ΔS^°_rxn = Σ ΔS^°_f,products − Σ ΔS^°_f,reactants

Equation 7.9

MCAT Concept Check 7.5:

Before you move on, assess your understanding of the material with these questions.

1. Rank the phases of matter from lowest to highest entropy.

2. Describe entropy in terms of energy dispersal and disorder.

3. Do the following situations result in an increase or decrease in entropy?