Chemical Thermodynamics

Chapter 18

Thermodynamics

• Spontaneous Processes

• Entropy and Second Law of Thermodynamics

• Entropy Changes

• Gibbs Free Energy

• Free Energy and Temperature

• Free Energy and Equilibrium

Spontaneous Processes

A process that does occur under a specific set of conditions is called a spontaneous process.

A process that does not occur under a specific set of conditions is called nonspontaneous.

Spontaneous Processes

A process that results in a decrease in the energy of a system often is spontaneous:

The sign of ΔH alone is insufficient to predict spontaneity in every circumstance:

CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔH° = ‒890.4 kJ/mol

H2O(l) H2O(s) T > 0°C; ΔH° = ‒6.01 kJ/mol

Entropy

To predict spontaneity, both the enthalpy and entropy must be known.

Entropy (S) of a system is a measure of how spread out or how dispersed the system’s energy is.

Entropy

Spontaneity is favored by an increase in entropy.

k is the Boltzmann constant (1.38 x 10–23 J/K)

W is the number of different arrangements

S = k ln W

The number of arrangements possible is given by:

X is the number of cells in a volume

N is the number of molecules

W = X N

Entropy

Entropy

There are three possible states for this system:

1) One molecule on each side (eight possible arrangements) 2) Both molecules on the left (four possible arrangements) 3) Both molecules on the right (four possible arrangements)

The most probable state has the largest number of arrangements.

Entropy Changes in a System

The change in entropy for a system is the difference in entropy of the final state and the entropy of the initial state.

Alternatively:

ΔSsys = Sfinal – Sinitial

Practice Problem

Determine the change in entropy (ΔSsys) for the expansion of 0.10 mole of an ideal gas from 2.0 L to 3.0 L at constant temperature.

Entropy Changes in a System

The standard entropy is the absolute entropy of a substance at 1 atm.

Temperature is not part of the standard state definition and must be specified.

Entropy Changes in a System

There are several important trends in entropy:

§ S°liquid > S°solid

§ S°gas > S°liquid

§ S° increases with molar mass

§ S° increases with molecular complexity

§ S° increases with the mobility of a phase (for an element with two or more allotropes)

Entropy Changes in a System

In addition to translational motion, molecules exhibit vibrations and rotations.

Entropy Changes in a System

For a chemical reaction

aA + bB → cC + dD

Alternatively,

ΔS°rxn = [cS°(C) + dS°(D)] – [aS°(A) + bS°(B)]

ΔS°rxn = ΣnS°(products) – ΣmS°(reactants)

Practice Problems

Calculate the standard entropy change for the following reactions at 25°C.

2CO2(g) → 2CO(g) + O2(g)

Entropy Changes in a System

Several processes that lead to an increase in entropy are:

§ Melting

§ Vaporization or sublimation

§ Temperature increase

§ Reaction resulting in a greater number of gas molecules

Entropy Changes in a System

The process of dissolving a substance can lead to either an increase or a decrease in entropy, depending on the nature of the solute.

Molecular solutes (i.e. sugar): entropy increases

Ionic compounds: entropy could decrease or increase

Entropy Changes in a System

Determine the sign of ΔS for the following:

1) crystallization of sucrose from a supersaturated solution.

2) cooling water vapor from 150°C to 110°C.

3) Sublimation of dry ice.

Entropy Changes in the Universe

Correctly predicting the spontaneity of a process requires us to consider entropy changes in both the system and the surroundings.

An ice cube spontaneously melts in a room at 25°C.

A cup of hot water spontaneously cools to room temperature.

The entropy of both the system AND surroundings are important!

Perspective Components ΔS

System ice positive

Surroundings everything else negative

Perspective Components ΔS

System hot water negative

Surroundings everything else positive

Entropy Changes in the Universe

The change in entropy of the surroundings is directly proportional to the enthalpy of the system.

The second law of thermodynamics states that for a process to be spontaneous, ΔSuniverse must be positive.

ΔSuniverse = ΔSsys + ΔSsurr

Entropy Changes in the Universe

The second law of thermodynamics states that for a process to be spontaneous, ΔSuniverse must be positive.

ΔSuniverse > 0 for a spontaneous process

ΔSuniverse < 0 for a nonspontaneous process

ΔSuniverse = 0 for an equilibrium process

ΔSuniverse = ΔSsys + ΔSsurr

Practice Problems

Consider the synthesis of ammonia at 25°C:

N2(g) + 3H2(g) → 2NH3(g)

ΔS°sys = –199 J/K·mol

ΔH°sys = –92.6 kJ/mol

Is this process spontaneous or non spontaneous?

Practice Problem

Is the following reaction spontaneous, non-spontaneous, or at equilibrium when T = 10.4°C?

N2O4(g) → 2NO2(g)

ΔS°sys = 176.6 J/K·mol; ΔH°sys = 58.04 kJ/mol

Entropy Changes in the Universe

The third law of thermodynamics states that the entropy of a perfect crystalline substance is zero at absolute zero.

Entropy increases in a substance as temperature increases from absolute zero.

Predicting Spontaneity

Measurements on the surroundings are seldom made, limiting the use of the second law of thermodynamics.

Gibbs free energy (G) or simply free energy can be used to express spontaneity more directly.

The change in free energy for a system is:

G = H – TS

ΔG = ΔH – TΔS

Predicting Spontaneity

Using the Gibbs free energy, it is possible to make predictions on spontaneity.

ΔG < 0 The reaction is spontaneous in the forward direction.

ΔG > 0 The reaction is nonspontaneous in the forward direction.

ΔG = 0 The system is at equilibrium

ΔG = ΔH – TΔS

Predicting Spontaneity

The standard free energy of reaction (ΔG°rxn) is free-energy change for a reaction when it occurs under standard-state conditions.

The following conditions define the standard states of pure substances and solutions are:

§ Gases 1 atm pressure

§ Liquids pure liquid

§ Solids pure solid

§ Elements the most stable allotropic form at 1 atm and 25°C

§ Solutions 1 molar concentration

Entropy Changes in a System

For a chemical reaction

aA + bB → cC + dD

Alternatively,

ΔG°f for any element in its most stable allotropic form at 1 atm is defined as zero.

ΔG°rxn = [cΔG°f (C) + dΔG°f (D)] – [aΔG°f (A) + bΔG°f (B)]

ΔG°rxn = ΣnΔG°f (products) – ΣmΔG°f (reactants)

Practice Problems

Calculate the standard free-energy for the following reaction at 25°C:

2C2H6(g) + 7O2(g) → 4CO2(g) + 6H2O(l)

Free Energy and Chemical Equilibrium

It is the sign of ΔG (not ΔG°) that determines spontaneity.

The relationship between ΔG and ΔG° is:

R is the gas constant (8.314 J/K·mol).

T is the kelvin temperature.

Q is the reaction quotient.

ΔG = ΔG° + RT lnQ

Consider the following equilibrium:

H2(g) + I2(g)  ⇌  2HI(g)

ΔG° at 25°C = 2.60 kJ/mol

ΔG depends on the partial pressures of each chemical species.

If PH2 = 2.0 atm; PI2

= 2.0 atm; and PHI = 3.0 atm:

Then:

Free Energy and Chemical Equilibrium

The spontaneity can be manipulated by changing the partial pressures of the reaction components:

H2(g) + I2(g)  ⇌  2HI(g)

ΔG° at 25°C = 2.60 kJ/mol

If PH2 = 2.0 atm; PI2

= 2.0 atm; and PHI = 1.0 atm:

Then:

Free Energy and Chemical Equilibrium

At equilibrium, ΔG = 0 and Q = K:

0 = ΔG° + RT ln K

Free Energy and Chemical Equilibrium

ΔG° = –RT ln K

At equilibrium, ΔG = 0 and Q = K:

0 = ΔG° + RT ln K

Free Energy and Chemical Equilibrium

ΔG° = –RT ln K

At equilibrium, ΔG = 0 and Q = K:

0 = ΔG° + RT ln K

Free Energy and Chemical Equilibrium

ΔG° = –RT ln K

Calculate the equilibrium constant, Kp, for the following reaction at 25°C.

2O3(g) ⇌  3O2(g)

ΔG° = –326.8 kJ/mol

Practice Problems

Thermodynamics of Living Systems

Many biological reactions have positive ΔG° value, making the reaction nonspontaneous.

None spontaneous reactions can be coupled with spontaneous reactions in order to drive a process forward:

alanine + glycine → alanylglycine Δ G° = 29 kJ/mol

ATP + H2O → ADP + H3PO4 ΔG° = –31 kJ/mol

ATP + H2O + alanine + glycine → ADP + H3PO4 + alanylglycine

ΔG° = 29 kJ/mol + –31 kJ/mol = –2 kJ/mol

Thermodynamics of Living Systems

Many biological reactions have positive ΔG° value, making the reaction nonspontaneous.

Objective

• Understand the meaning of spontaneous and nonspontaneous processes

• Know what the second and third law of thermodynamic are

• Be able to predict the sign of ∆S for physical and chemical processes

• Be able to calculate the standard entropy for a system

• Know what Gibbs free energy is and how to calculate it from the enthalpy change and entropy change at a given temperature

• Know how to use Gibbs free energy to predict whether reactions are spontaneous

• Be able to calculate ∆G and ∆Gº

• Know how ∆Gº and equilibrium constant are related and be able to solve these types of problems