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20.1: Entropy

Difficulty Level: At Grade Created by: CK-12

Lesson Objectives

• Identify the two driving forces behind all chemical reactions and physical processes.
• Describe entropy, and be able to predict whether the entropy change for a reaction is increasing or decreasing.
• Calculate the standard entropy change for a reaction from the standard entropies of all substances in the reaction.

Lesson Vocabulary

• entropy

Recalling Prior Knowledge

• What is the difference between an endothermic and an exothermic reaction?
• How is chemical stability related to energy?

In the chapter Thermochemistry, you learned that chemical reactions either absorb or release energy as they occur. The change in energy is one factor that allows chemists to predict whether a certain reaction will occur. In this lesson, you will learn about a second driving force for chemical reactions called entropy.

Enthalpy as a Driving Force

The vast majority of naturally occurring reactions are exothermic. In an exothermic reaction, the reactants have a relatively high quantity of energy compared to the products. As the reaction proceeds, energy is released into the surroundings. Low energy can be thought of as providing a greater degree of stability to a chemical system. Since the energy of the system decreases during an exothermic reaction, the products of the system are more stable than the reactants. We can say that an exothermic reaction is an energetically favorable reaction.

If the drive toward lower energy were the only consideration for whether a reaction is able to occur, we would expect that endothermic reactions could never occur spontaneously. In an endothermic reaction, energy is absorbed during the reaction, and the products thus have a larger quantity of energy than the reactants. This means that the products are less stable than the reactants. Therefore, the reaction would not occur without some outside influence such as persistent heating. However, endothermic reactions do occur spontaneously, or naturally. There must be another driving force besides enthalpy change which helps promote a spontaneous chemical reaction.

Entropy as a Driving Force

A very simple endothermic process is that of a melting ice cube. Energy is transferred from the room to the ice cube, causing it to change from the solid to the liquid state.

H2O(s) + 6.01 kJ → H2O(l)

The solid state of water, ice, is highly ordered because its molecules are fixed in place. The melting process frees the water molecules from their hydrogen-bonded network and allows them a greater degree of movement. Water is more disordered than ice. The change from the solid to liquid state of any substance corresponds to an increase in the disorder of the system.

There is a tendency in nature for systems to proceed toward a state of greater disorder or randomness. Entropy is a measure of the degree of randomness or disorder of a system. Entropy is an easy concept to understand when thinking about everyday situations. When the pieces of a jigsaw puzzle are dumped from the box, the pieces naturally hit the table in a very random state. In order to put the puzzle together, a great deal of work must be done in order to overcome the natural entropy of the pieces. The entropy of a room that has been recently cleaned and organized is low. As time goes by, it likely will become more disordered, and thus its entropy will increase (Figure below). The natural tendency of a system is for its entropy to increase.

The messy room on the right has more entropy than the highly ordered room on the left. The drive toward an increase in entropy is the natural direction for all processes.

Chemical reactions also tend to proceed in such a way as to increase the total entropy of the system. How can you tell if a certain reaction shows an increase or a decrease in entropy? The states of the reactants and products provide certain clues. The general cases below illustrate entropy at the molecular level.

1. For a given substance, the entropy of the liquid state is greater than the entropy of the solid state. Likewise, the entropy of the gas is greater than the entropy of the liquid. Therefore, entropy increases in processes in which solid or liquid reactants form gaseous products. Entropy also increases when solid reactants form liquid products.
2. Entropy increases when a substance is broken up into multiple parts. The process of dissolving increases entropy because the solute particles become separated from one another when a solution is formed.
3. Entropy increases as temperature increases. An increase in temperature means that the particles of the substance have greater kinetic energy. The faster moving particles have more disorder than particles that are moving more slowly at a lower temperature.
4. Entropy generally increases in reactions in which the total number of product molecules is greater than the total number of reactant molecules. An exception to this rule is when nongaseous products are formed from gaseous reactants.

The examples below will serve to illustrate how the entropy change in a reaction can be predicted.

Cl2(g) → Cl2(l)
The entropy is decreasing because a gas is becoming a liquid.
CaCO3(s) → CaO(s) + CO2(g)
The entropy is increasing because a gas is being produced, and the number of molecules is increasing.
N2(g) + 3H2(g) → 2NH3(g)
The entropy is decreasing because four total reactant molecules are forming two total product molecules. All are gases.
AgNO3(aq) + NaCl(aq) → NaNO3(aq) + AgCl(s)
The entropy is decreasing because a solid is formed from aqueous reactants.
H2(g) + Cl2(g) → 2HCl(g)
The entropy change is unknown (but likely not zero) because there are equal numbers of molecules on both sides of the equation, and all are gases.

Standard Entropy

All molecular motion ceases at absolute zero (0 K). Therefore, the entropy of a pure crystalline substance at absolute zero is defined to be equal to zero. As the temperature of the substance increases, its entropy increases because of an increase in molecular motion. The absolute or standard entropy of substances can be measured. The symbol for entropy is S, and the standard entropy of a substance is given by the symbol S°, indicating that the standard entropy is determined under standard conditions. The units for entropy are J/K•mol. Standard entropies for a few substances are shown below (Table below).

Standard Entropy Values at 25°C
Substance S° (J/K•mol)
H2(g) 131.0
O2(g) 205.0
H2O(l) 69.9
H2O(g) 188.7
C(graphite) 5.69
C(diamond) 2.4

The standard entropy change (ΔS°) for a reaction can be calculated from the absolute entropies of the various reaction components, analogous to the way that the enthalpy change of a reaction can be calculated from standard heat of formation values.

ΔS° = ∑nS°(products) - ∑nS°(reactants)

The standard entropy change is equal to the sum of all the standard entropies of the products minus the sum of all the standard entropies of the reactants. The symbol “n” signifies that each entropy must first be multiplied by its coefficient in the balanced equation.

For example, the entropy change for the vaporization of water can be found as follows:

ΔS° = S°(H2O(g)) - S°(H2O(l))
ΔS° = 188.7 J/K•mol - 69.9 J/K•mol = 118.8 J/K•mol

The entropy change for the vaporization of water is positive because the gas state has higher entropy than the liquid state.

The entropy change for the formation of liquid water from gaseous hydrogen and oxygen can also be calculated using this equation.

2H2(g) + O2(g) → 2H2O(l)
ΔS° = 2(69.9) - [2(131.0) + 1(205.0)] = -327 J/K•mol

The entropy change for this reaction is highly negative because three gaseous molecules are being converted into two liquid molecules. According to the drive toward higher entropy, the formation of water from hydrogen and oxygen is an unfavorable reaction. However, the reaction is also highly exothermic, and the drive toward a decrease in energy allows the reaction to occur.

Lesson Summary

• The tendency for a reaction or process to result in a lowering of the energy of the system is one of the primary driving forces in chemistry. The majority of naturally occurring reactions are exothermic because the products are lower in energy.
• Entropy is a measure of the disorder of a system. The tendency for a reaction or process to result in an increase in the entropy of the system is another fundamental driving force. The entropy change for a reaction can often be predicted based on the physical states of the substances involved and on the total numbers of reactant and product molecules.
• The standard entropy of a reaction can be calculated from the standard entropies of the reactants and products. A positive entropy change is more favorable than a negative entropy change, but changes in both enthalpy and entropy need to be considered to determine whether a reaction will occur spontaneously.

Lesson Review Questions

Reviewing Concepts

1. In a certain reaction, the energy of the reactants is less than the energy of the products. Is the reaction endothermic or exothermic? Do you have enough information to say whether it is favorable or unfavorable?
2. What are the two driving forces for all chemical reactions and physical processes?
3. What is entropy and how does it relate to the spontaneity of a reaction?
4. How does an increase in temperature affect the entropy of a system?
5. Which system has the greater entropy in each of the following?
1. solid sodium chloride or a sodium chloride solution
2. bromine liquid or bromine vapor
3. 25 g of water at 80°C or 25 g of water at 50°C
4. liquid mercury or solid mercury
6. How does the entropy of a system change for each of the following processes?
1. A solid melts.
2. A liquid freezes.
3. A liquid boils.
4. A vapor condenses to a liquid.
5. Sugar dissolves in water.
6. A solid sublimes.
7. According to the table above (Table above), which allotrope of carbon, graphite, or diamond, contains more disorder within its structure?
8. Xenon gas has a larger absolute entropy than neon gas when both are at the same temperature and pressure. Why is this true?

Problems

1. Predict the sign of ΔS for each of the following reactions. Explain your reasoning.
1. 4Na(s) + O2(g) → 2Na2O(s)
2. Zn(s) + 2H+(aq) → Zn2+(aq) + H2(g)
3. 2C2H6(g) + 7O2(g) → 4CO2(g) + 6H2O(g)
4. H2(g) + F2(g) → 2HF(g)
2. Use the standard entropies listed below to calculate the standard entropy change (ΔS°) for each of the reactions in problem number 6.
1. Na(s) = 51.05 J/K•mol; O2(g) = 205.0 J/K•mol; Na2O(s) = 72.8 J/K•mol
2. Zn(s) = 41.6 J/K•mol; H+(aq) = 0; Zn2+(aq) = 106.5 J/K•mol; H2(g) = 131.0 J/K•mol
3. C2H6(g) = 229.5 J/K•mol; O2(g) = 205.0 J/K•mol; CO2(g) = 213.6 J/K•mol; H2O(g) = 188.7 J/K•mol
4. H2(g) = 131.0 J/K•mol; F2(g) = 203.3 J/K•mol; HF(g) = 173.5 J/K•mol

Points to Consider

The drives toward lower enthalpy and greater entropy determine whether a chemical reaction is likely to occur under a given set of conditions.

• How can enthalpy and entropy changes be combined into one quantity?
• If a reaction is not spontaneous under one set of conditions, is it possible that it will be spontaneous under some other set of conditions?

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