Thermochemistry Gibbs Free Energy, Entropy, and Spontaneity

Thermochemistry

Gibbs Free Energy, Entropy, and Spontaneity

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•How can a fire start on its own?

Sometimes a fire can occur without an external source of ignition, such as a match or an electrical spark. Spontaneous combustion is the term used to describe these fires.


Free Energy andSpontaneous Reactions

Free Energy and Spontaneous Reactions

•What are two characteristics of spontaneous reactions?



•Some of the energy released in a chemical reaction can be harnessed to do work, such as pushing the pistons in an internal-combustion engine. • The energy that is available to do work is

called free energy.



Spontaneous Versus Nonspontaneous Reactions•You can write a balanced equation for a chemical reaction, but the reaction may not actually take place.

CO2(g) C(s) + O2(g)

• Experience tells you that this reaction does not tend to occur.

• Carbon and oxygen react to form carbon dioxide, not the reverse.



Spontaneous Versus Nonspontaneous Reactions•The world of balanced chemical equations is really divided into two groups.

• One group contains equations representing reactions that actually occur.

• The other contains equations representing reactions that do not tend to occur, or at least not efficiently.



•A spontaneous reaction occurs naturally and favors the formation of products at the stated conditions.

Spontaneous Versus Nonspontaneous Reactions



•Spontaneous reactions produce large amounts of products and release free energy.

Fireworks displays are the result of highly favored spontaneous reactions.




•A chemical reaction that does not favor the formation of products at the stated conditions is called a nonspontaneous reaction.

• Such reactions produce little, if any, product.




•In nearly all reversible reactions, one reaction is favored over the other.

Reversible Reactions



Reversible Reactions•Consider the decomposition of carbonic acid in water.

H2CO3(aq) CO2(g) + H2O(l)<1% >99%




• The forward reaction is spontaneous and releases free energy.

H2CO3(aq) CO2(g) + H2O(l)<1% >99%




• The forward reaction is spontaneous and releases free energy.

• The combination of carbon dioxide and water to form carbonic acid is a nonspontaneous reaction.

H2CO3(aq) CO2(g) + H2O(l)<1% >99%



•When solutions of cadmium nitrate and sodium sulfide are mixed, the products are aqueous sodium nitrate and solid yellow cadmium sulfide.

• A precipitate of cadmium sulfide forms spontaneously.

• The reverse reaction is nonspontaneous.

Cd(NO3)2(aq) + Na2S(aq) CdS(s) + 2NaNO3(aq)

Reversible Reactions



The Rate of Spontaneous Reactions•The terms spontaneous and nonspontaneous do not refer to the rate of a reaction.• Some spontaneous reactions are so slow

that they appear to be nonspontaneous.



•Changing the conditions of a chemical reaction can affect whether a reaction will occur.

• A reaction that is nonspontaneous in one set of conditions may be spontaneous in other conditions.



•Photosynthesis is a multistep reaction that takes place in plant leaves.• Outside of plants, carbon dioxide and water do not

normally combine to produce sugar and oxygen.

• This complex process could not happen without the energy supplied by sunlight and plant pigments such as chlorophyll.



Coupled Reactions•Sometimes a nonspontaneous reaction can be made to occur if it is coupled to a spontaneous reaction.



Coupled Reactions•Sometimes a nonspontaneous reaction can be made to occur if it is coupled to a spontaneous reaction.• One reaction releases energy that is used

by the other reaction.

• Coupled reactions are common in the complex biological processes that take place in living organisms.


•Decomposition reactions that occur inside a pile of oily rags or a damp stack of hay cause heat to build up. If the heat cannot escape, the temperature within the pile or stack will rise. How can a rise in temperature cause a fire to start on its own?


•Decomposition reactions that occur inside a pile of oily rags or a damp stack of hay cause heat to build up. If the heat cannot escape, the temperature within the pile or stack will rise. How can a rise in temperature cause a fire to start on its own?

The combustion reaction is a nonspontaneous reaction that can be made to occur when it is coupled to the spontaneous decomposition reaction. The decomposition reaction releases energy that is used by the combustion reaction.


•Which of the following is ALWAYS true of spontaneous reactions?A. They produce heat and are not reversible at

the stated conditions.

B. They release free energy and favor the formation of products at the stated conditions.

C. They are coupled with a nonspontaneous reaction and are easily reversible at the stated conditions.


•Which of the following is ALWAYS true of spontaneous reactions?

A. They produce heat and are not reversible at the stated conditions.

B. They release free energy and favor the formation of products at the stated conditions.

C. They are coupled with a nonspontaneous reaction and are easily reversible at the stated conditions.


Entropy

Entropy

What part does entropy play in a reaction?


Entropy

You might expect that only exothermic reactions are spontaneous. Some processes, however, are spontaneous even though they absorb heat.


Entropy

You might expect that only exothermic reactions are spontaneous. Some processes, however, are spontaneous even though they absorb heat.• Consider what happens as ice melts.

• As it changes from a solid to a liquid, 1 mol of ice at 25oC absorbs 6.0 kJ of heat from its surroundings.

• If you consider only enthalpy changes, it is difficult to explain why the ice melts.


Entropy

Some factor other than the enthalpy change must help determine whether a physical or chemical process is spontaneous.


Entropy

Some factor other than the enthalpy change must help determine whether a physical or chemical process is spontaneous.

• The other factor is related to order.


Entropy

Entropy is a measure of the disorder of a system.

• The law of disorder states that the natural tendency is for systems to move in the direction of increasing disorder or randomness.


Entropy

•A dog walker with several dogs could represent relative order and disorder.

All of the dogs are on leashes and are strolling orderly along the path.

The dogs are no longer wearing leashes and are running freely.

This situation represents disorder.


Entropy

Reactions in which entropy increases as reactants form products tend to be favored.

Entropy can affect the direction of a reaction.


Entropy

•For a given substance, the entropy of the gas is greater than the entropy of the liquid or the solid. Thus, entropy increases in reactions in which solid reactants form liquid or gaseous products.


Entropy

•Entropy increases when a substance is divided into parts.

• For instance, entropy increases when an ionic compound dissolves in water.


Entropy

•Entropy tends to increase in chemical reactions in which the total number of product molecules is greater than the total number of reactant molecules.


Entropy

•Entropy tends to increase when the temperature increases. As the temperature rises, the molecules move faster and faster, which increases the disorder.


•Which of the following would have an increase in the entropy of the reaction system?

A.2NH4NO3(s) 2N2(g) + 4H2O(l) +O2(g)

B.2H2(g) + O2(g) 2H2O(l)

C.C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(l)

D.2Fe(s) + O2(g) + 2H2O(l) 2Fe(OH)2(s)


•Which of the following would have an increase in the entropy of the reaction system?

A.2NH4NO3(s) 2N2(g) + 4H2O(l) +O2(g)

B.2H2(g) + O2(g) 2H2O(l)

C.C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(l)

D.2Fe(s) + O2(g) + 2H2O(l) 2Fe(OH)2(s)


Enthalpy and Entropy


What two factors determine whether a reaction is spontaneous?



The size and direction of enthalpy changes and entropy changes together determine whether a reaction is spontaneous.



•Consider an exothermic reaction in which entropy increases.

• The reaction will be spontaneous because both factors are favorable.



• A decrease in entropy is offset by a large release of heat.

• An increase in enthalpy is offset by an increase in entropy.

A reaction can be spontaneous if:



•The table below summarizes the effect of enthalpy and entropy changes on the spontaneity of reactions.

How Enthalpy Changes and Entropy ChangesAffect Reaction Spontaneity

Enthalpy change Entropy change Is the reaction spontaneous?

Decreases (exothermic)

Increases (more disorder in products than in reactants)

Yes

Increases (endothermic)

IncreasesOnly if unfavorable enthalpy change is offset by favorable entropy change

Decreases (exothermic)

Decreases (less disorder in products than in reactants)

Only if unfavorable entropy change is offset by favorable enthalpy change

Increases (endothermic)

Decreases No


•Would the following exothermic reaction be spontaneous? Explain why or why not.

2KClO3(s) 2KCl(s) +3O2(g)


•Would the following exothermic reaction be spontaneous? Explain why or why not.

2KClO3(s) 2KCl(s) +3O2(g)

Two molecules of solid are transformed into 2 molecules of solid and 3 molecules of gas, so entropy is increased in the reaction. A reaction that is exothermic with an increase in entropy will be spontaneous.


Free Energy Change

Free Energy Change

How is the value of ΔG related to the spontaneity of a reaction?


•Free energy is often expressed as Gibbs free energy.

Free Energy Change

• This term is named for Josiah Gibbs, the scientist who defined this thermodynamic property.

• The symbol for Gibbs free energy is G.

• Free energy can either be released or absorbed during a physical or chemical process.


ΔG = ΔH – TΔS

•The equation below is used to calculate the change in Gibbs free energy (ΔG).

Free Energy Change

• ΔS is the change in entropy.

• ΔH is the change in enthalpy.

• T is the temperature in Kelvins.


Free Energy Change

When the value of ΔG is negative, the process is spontaneous. When the value is positive, the process is nonspontaneous.


•The entropy change for the following reaction at 298 K is 3.0 J/mol·K, and the enthalpy change is –394 kJ/mol.

C(s) + O2(g) CO2(g)

Calculate the Gibbs free energy change and determine whether the reaction will occur spontaneously.


•The entropy change for the following reaction at 298 K is 3.0 J/mol·K, and the enthalpy change is –394 kJ/mol.

C(s) + O2(g) CO2(g)

Calculate the Gibbs free energy change and determine whether the reaction will occur spontaneously. ΔG = –394 kJ/mol – (298 K 0.0030 kJ/mol·K)

ΔG = –395 kJ/mol

The reaction is spontaneous.


Key Concepts

•Spontaneous reactions produce large amounts of products and release free energy.

Reactions in which entropy increases as reactants form products tend to be favored.

The size and direction of enthalpy changes and entropy changes together determine whether a reaction is spontaneous.

When the value of ΔG is negative, a process is spontaneous. When the value is positive, a process is nonspontaneous.


Key Equation

ΔG = ΔH – TΔS


Glossary Terms

• free energy: the energy available to do work

• spontaneous reaction: a reaction that favors the formation of products at the specified conditions; spontaneity depends on enthalpy and entropy changes

• nonspontaneous reaction: a reaction that does not favor the formation of products at the specified conditions


Glossary Terms

• entropy: a measure of the disorder of a system; systems tend to go from a state of order (low entropy) to a state of maximum disorder (high entropy)

• law of disorder: it is a natural tendency of systems to move in the direction of maximum chaos or disorder


• Chemical Reactions, Matter, and Energy

BIG IDEABIG IDEA

Changes in enthalpy and entropy can be used to explain why some reactions occur naturally and others do not.

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Thermochemistry Gibbs Free Energy, Entropy, and Spontaneity