13.6: Entropy and Chemical Reactions
- Page ID
- 476641
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- Describe the relationship between enthalpy, entropy, and spontaneity.
When the pieces of a jigsaw puzzle are dumped from the box, the pieces naturally hit the table in a very random pattern. In order to put the puzzle together, a great deal of work must be done to overcome the natural disorder of the pieces. The pieces need to be turned right-side up, then sorted by color or edge (some people like to put the border together first). Finally comes the challenge of finding the exact spot of each piece of the puzzle, in order to obtain the finished picture.
Entropy
As was discussed earlier in this text, natural processes tend towards increasing entropy.
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 molecular state of the reactants and products provide certain clues. The general cases below illustrate entropy at the molecular level.
- 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.
- Entropy increases when a substance is broken up into multiple parts. The process of dissolution increases entropy because the solute particles become separated from one another when a solution is formed.
- 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 slowly at a lower temperature.
- 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 a gas is produced from nongaseous reactants.
These examples serve to illustrate how the entropy change in a reaction can be predicted:
\(\ce{Cl_2} \left( g \right) \rightarrow \ce{Cl_2} \left( l \right)\)
The entropy is decreasing because a gas is becoming a liquid.
\(\ce{CaCO_3} \left( s \right) \rightarrow \ce{CaO} \left( s \right) + \ce{CO_2} \left( g \right)\)
The entropy is increasing because a gas is being produced and the number of molecules is increasing.
\(\ce{N_2} \left( g \right) + 3 \ce{H_2} \left( g \right) \rightarrow 2 \ce{NH_3} \left( g \right)\)
The entropy is decreasing because four total reactant molecules are forming two total product molecules. All are gases.
\(\ce{AgNO_3} \left( aq \right) + \ce{NaCl} \left( aq \right) \rightarrow \ce{NaNO_3} \left( aq \right) + \ce{AgCl} \left( s \right)\)
The entropy is decreasing because a solid is formed from aqueous reactants.
\(\ce{H_2} \left( g \right) + \ce{Cl_2} \left( g \right) \rightarrow 2 \ce{HCl} \left( g \right)\)
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 \(\left( 0 \: \text{K} \right)\). 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 \(S^\text{o}\), indicating that the standard entropy is determined under standard conditions. The units for entropy are \(\text{J/K} \cdot \text{mol}\). Standard entropies for a few substances are shown in the table below.
| Table \(\PageIndex{1}\): Standard Entropy Values at \(25^\text{o} \text{C}\) | |
|---|---|
| Substance | \(S^\text{o} \left( \text{J/K} \cdot \text{mol} \right)\) |
| \(\ce{H_2} \left( g \right)\) | 131.0 |
| \(\ce{O_2} \left( g \right)\) | 205.0 |
| \(\ce{H_2O} \left( l \right)\) | 69.9 |
| \(\ce{H_2O} \left( g \right)\) | 188.7 |
| \(\ce{C} \: \left( \text{graphite} \right)\) | 5.69 |
| \(\ce{C} \: \left( \text{diamond} \right)\) | 2.4 |
We will not perform calculations using entropy in this class, but we will see how having a numerical value for it will be important for other decisions about the energy associated with chemical reactions.
Spontaneous Reactions
Reactions are favorable when they result in a decrease in enthalpy and an increase in entropy of the system. When both of these conditions are met, the reaction occurs naturally. A spontaneous reaction is a reaction that favors the formation of products at the conditions under which the reaction is occurring. A roaring bonfire is an example of a spontaneous reaction, since it is exothermic (there is a decrease in the energy of the system as energy is released to the surroundings as heat). The products of a fire are composed partly of gases such as carbon dioxide and water vapor. The entropy of the system increases during a combustion reaction. The combination of energy decrease and entropy increase dictates that combustion reactions are spontaneous reactions.
A nonspontaneous reaction is a reaction that does not favor the formation of products at the given set of conditions. In order for a reaction to be nonspontaneous, it must be endothermic, accompanied by a decrease in entropy, or both. Our atmosphere is composed primarily of a mixture of nitrogen and oxygen gases. One could write an equation showing these gases undergoing a chemical reaction to form nitrogen monoxide:
\[\ce{N_2} \left( g \right) + \ce{O_2} \left( g \right) \rightarrow 2 \ce{NO} \left( g \right)\nonumber \]
Fortunately, this reaction is nonspontaneous at normal temperatures and pressures. It is a highly endothermic reaction with a slightly positive entropy change \(\left( \Delta S \right)\). Nitrogen monoxide is capable of being produced at very high temperatures and has been observed to form as a result of lightning strikes.
One must be careful not to confuse the term spontaneous with the notion that a reaction occurs rapidly. A spontaneous reaction is one in which product formation is favored, even if the reaction is extremely slow. A piece of paper will not suddenly burst into flames, although its combustion is a spontaneous reaction. What is missing is the required activation energy to get the reaction started. If the paper were to be heated to a high enough temperature, it would begin to burn, at which point the reaction would proceed spontaneously until completion.
In a reversible reaction, one reaction direction may be favored over the other. Carbonic acid is present in carbonated beverages. It decomposes spontaneously to carbon dioxide and water, according to the following reaction.
\[\ce{H_2CO_3} \left( aq \right) \rightleftharpoons \ce{CO_2} \left( g \right) + \ce{H_2O} \left( l \right)\nonumber \]
If you were to start with pure carbonic acid in water and allow the system to come to equilibrium, more than \(99\%\) of the carbonic acid would be converted into carbon dioxide and water. The forward reaction is spontaneous because the products of the forward reaction are favored at equilibrium. In the reverse reaction, carbon dioxide and water are the reactants, and carbonic acid is the product. When carbon dioxide is bubbled into water, less than \(1\%\) is converted to carbonic acid when the reaction reaches equilibrium. The reverse reaction, as written above, is not spontaneous.
Free Energy
Many chemical reactions and physical processes release energy that can be used to do other things. When the fuel in a car is burned, some of the released energy is used to power the vehicle. Free energy is energy that is available to do work. Spontaneous reactions release free energy as they proceed. Recall that the determining factors for spontaneity of a reaction are the enthalpy and entropy changes that occur for the system. The free energy change of a reaction is a mathematical combination of the enthalpy change and the entropy change.
\[\Delta G^\text{o} = \Delta H^\text{o} - T \Delta S^\text{o}\nonumber \]
The symbol for free energy is \(G\), in honor of American scientist Josiah Gibbs (1839-1903), who made many contributions to thermodynamics. The change in Gibbs free energy is equal to the change in enthalpy minus the mathematical product of the change in entropy, multiplied by the Kelvin temperature. Each thermodynamic quantity in the equation is for substances in their standard states. The usual units for \(\Delta H\) are \(\text{kJ/mol}\), while \(\Delta S\) is often reported in \(\text{J/K} \cdot \text{mol}\). It is necessary to change the units for \(\Delta S\) to \(\text{kJ/K} \cdot \text{mol}\), so that the calculation of \(\Delta G\) is in \(\text{kJ/mol}\).
A spontaneous reaction is one that releases free energy, and so the sign of \(\Delta G\) must be negative. Since \(\Delta H\) and \(\Delta S\) can be either positive or negative, depending on the characteristics of the particular reaction, there are four different general outcomes for \(\Delta G\), and these are outlined in the table below.
| Table \(\PageIndex{1}\): Enthalpy, Entropy, and Free Energy Changes | ||
|---|---|---|
| \(\Delta H\) | \(\Delta S\) | \(\Delta G\) |
| - value (exothermic) | + value (disordering) | always negative |
| + value (endothermic) | + value (disordering) | negative at higher temperatures |
| - value (exothermic) | - value (ordering) | negative at lower temperatures |
| + value (endothermic) | - value (ordering) | never negative |
Keep in mind that the temperature in the Gibbs free energy equation is the Kelvin temperature and so can only be positive. When \(\Delta H\) is negative and \(\Delta S\) is positive, the sign of \(\Delta G\) will always be negative, and the reaction will be spontaneous at all temperatures. This corresponds to both driving forces being in favor of product formation. When \(\Delta H\) is positive and \(\Delta S\) is negative, the sign of \(\Delta G\) will always be positive, and the reaction can never be spontaneous. This corresponds to both driving forces working against product formation.
When one driving force favors the reaction, but the other does not, it is the temperature that determines the sign of \(\Delta G\). Consider first an endothermic reaction (positive \(\Delta H\)) that also displays an increase in entropy (positive \(\Delta S\)). It is the entropy term that favors the reaction. Therefore, as the temperature increases, the \(T \Delta S\) term in the Gibbs free energy equation will begin to predominate and \(\Delta G\) will become negative. A common example of a process that falls into this category is the melting of ice. At a relatively low temperature (below \(273 \: \text{K}\)), the melting is not spontaneous because the positive \(\Delta H\) term "outweighs" the \(T \Delta S\) term. When the temperature rises above \(273 \: \text{K}\), the process becomes spontaneous because the larger \(T\) value has tipped the sign of \(\Delta G\) over to being negative.
When the reaction is exothermic (negative \(\Delta H\)) but undergoes a decrease in entropy (negative \(\Delta S\)), it is the enthalpy term that favors the reaction. In this case, a spontaneous reaction is dependent upon the \(T \Delta S\) term being small relative to the \(\Delta H\) term, so that \(\Delta G\) is negative. The freezing of water is an example of this type of process. It is spontaneous only at a relatively low temperature. Above \(273 \: \text{K}\), the larger \(T \Delta S\) value causes the sign of \(\Delta G\) to be positive, and freezing does not occur.
Section Summary
- Situations involving entropy changes are described.
- Entropy can be measured and tabulated.
- Relationships between enthalpy, entropy, and free energy are described.
Glossary
- spontaneous reaction
- A reaction that favors the formation of products at the conditions under which the reaction is occurring.
- nonspontaneous reaction
- A reaction that does not favor the formation of products at the given set of conditions.
- free energy
- Energy that is available to do work.