Thermodynamics: Spontaneous Processes, Entropy, and Free Energy
Chapter 18 Thermodynamics - · PDF fileThermodynamics • Spontaneous Processes •...
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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