chapter 19 principles of chemical reactivity: entropy and free energy

Jeffrey MackCalifornia State University,

Sacramento

Chapter 19

Principles of Chemical Reactivity: Entropy and Free Energy

Chemical Kinetics provides us with information about the rate of reaction and how the reaction proceeds.

Chemical Thermodynamics provides us with information about equilibrium and whether or not a reaction is Spontaneous.

Entropy & Free Energy

Chemical Thermodynamics provides us with information about equilibrium and whether or not a reaction is Spontaneous.

Spontaneous changes occur only in the direction that leads to equilibrium.Systems never change spontaneously in a direction that takes them farther from equilibrium.

Example: Heat TransferHeat (thermal energy) always flows spontaneously from a

hot object to a cold object. The process occurs until thermal equilibrium is achieved,

that is when both objects are at the same temperature.

Entropy & Free Energy

Additional Examples:• Solvation of a Soluble salt: NH4NO3(s) dissolves

spontaneously even the process is endothermic (H > 0)

• Expansion of a gas and Diffusion. Gasses mix to form homogeneous mixtures spontaneously.

• Certain Phase Changes: Ice melts spontaneously above 0oC. Water evaporates even though the enthalpy of vaporization is endothermic.

• Certain Chemical Reactions: Na(s) reacts vigorously when dropped in water. Iron rusts when exposed to the atmosphere.

Spontaneous Process

But many spontaneous reactions or processes are endothermic or even have ∆H 0.

NH4NO3(s) + heat NH4NO3(aq)∆H = 0

Spontaneous Process

A Review of Concepts of Thermodynamics• First law of thermodynamics: The law of conservation

of energy; energy cannot be created or destroyed. • State Function: Quantity in which its determination is

path independent.• U = q + w: The change in internal energy of a system

is a function of heat and work done on or by the system.• H: Heat transferred at constant pressure.• Exothermic Process: H < 0• Endothermic Process: H > 0

Thermodynamics

Enthalpy alone does not predict spontaneity:Some processes are energetically favored (rH < 0) but not spontaneous. Equilibrium alone cannot determine spontaneity:Some processes are favored based on Equilibrium (K >> 1) yet they are non-spontaneous. There must be another factor that plays a role in determination of spontaneity!

Thermodynamics

Diamond is thermodynamically favored to convert to graphite, but not kinetically favored.

Paper burns once the reaction is initiates. The process is product-favored & kinetically favored.

Thermodynamics & Kinetics

Reactants

ProductsK

Thermodynamics

Factors that Affect Spontaneity (Thermodynamic favorability):

1. Enthalpy: Comparison of bond energy (H)2. Entropy: Randomness vs. Order of a system

(S)In general, enthalpy is more important than entropy.

• In a spontaneous processes the energy of the final state is more dispersed.

• The system moves to a higher state of disorder.

• The thermodynamic quantity associated with disorder and energy dispersal is called ENTROPY, S.

• The 2nd law of thermodynamics states that a spontaneous process results in an increase in the entropy of the universe. S > 0

Reaction of K and water

Dispersal of Energy: Entropy

Observation of a spontaneous process shows that it is associated with a dispersal of energy.

Energy Dispersal

The change in entropy for a spontaneous process is given by:

Where qrev is the heat gained or lost by the system during the process and T is the absolute temperature.A reversible process can be returned to its original state. (chemical equilibrium), an irreversible process cannot.Example: The breaking of a coffee mug into many pieces is an irreversible process.

To begin, particle 1 has 2 units of energy and 2-4 have none.

Particle 1 can transfer one unit of energy to particle 2, then the other to 3 or 4.

Particle 2 can initially have two units of energy.

Particle 2 transfer one unit to particles 4 or 3. (2 to 1 has already been counted.)

Particle 4 can initially have two units of energy.

Particle 4 transfer one unit to particle 3. (4 to 1 & 4 to 2 have already been counted.)

Particle 3 can start with two units of energy. Energy transfers between particle 3 were previously counted.

Each unique combination that results in a dispersion of energy is called a microstate. There are 10 microstates in this system. The greater the number of microstates, the greater the entropy of the system.

As the size of the container increases, the number of microstates accessible to the system increases. Therefore the entropy of the system increases.

• The entropy of liquid water is greater than the entropy of solid water (ice) at 0˚ C.

• Energy is more dispersed in liquid water than in solid water due to the lack of an ordered network as in the solid state.

So (J/K•mol)

H2O(liq) 69.95

H2O(gas) 188.8

Energy dispersal

S (solids) < S (liquids) < S (gases)

Entropy & States of Matter

S˚(Br2 liq) < S˚(Br2 gas) S˚(H2O sol) < S˚(H2O liq)

Entropy & States of Matter

Entropy and Microstates:As the number of microstates increases, so does the entropy of the system.

S = klnW

k = Boltzman’s constant (1.381 1023 J/K)

W = the number of microstates

Entropy and Microstates:The change in entropy associated with a process is a function of the number of final and initial microstates of the system.

If Wfinal > Winital, S > 0If Wfinal < Winital, S < 0

Entropy, Entropy Change, & Energy Dispersal: A Summary

When a solute dissolves in a solvent the process is spontaneous owing to the increase in entropy. Matter (and energy) are more dispersed. The number of microstates is increased.

The entropy of a substance increases with temperature.

Molecular motions of heptane, C7H16

Molecular motions of heptane at different temps.

Entropy Measurements & Values

An Increase in molecular complexity generally leads to increase in S.

Entropies of ionic solids depend on coulombic attractions.

S° (J/K•mol)

MgO 26.9

NaF 51.5

Mg2+ & O2- Na+ & F-

Defined by Ludwig Boltzmann, the third law states that a perfect crystal at 0 K has zero entropy; that is, S =0. The entropy of an element or compound under any other temperature and pressure is the entropy gained by converting the substance from 0 K to those conditions. To determine the value of S, it is necessary to measure the energy transferred as heat under reversible conditions for the conversion from 0 K to the defined conditions and then to use Equation 19.1

Because it is necessary to add energy as heat to raise the temperature, all substances have positive entropy values at temperatures above 0 K.

Standard Molar Entropies

The standard molar entropy, S°, of a substance is the entropy gained by converting 1 mol of it from a perfect crystal at 0 K to standard state conditions (1 bar, 1m for a solution) at the specified temperature.

Standard Molar Entropies

For a phase change,

where q = heat transferred in the phase change

Entropy Changes for Phase Changes

S increases slightly with T

S increases a large amount with phase changes

Entropy & Temperature

Standard molar entropy values can be used to calculate the change in entropy that occurs in various processes under standard conditions.The standard entropy change for a reaction (rS°) can be found in the same manner as rH° were:

Where n & m are the stoichiometric balancing coefficients.This calculation is valid only under reversible conditions.

S n S (products) m S (reactants)

Determining Entropy Changes in Physical & Chemical Processes

Problem:Consider the reaction of hydrogen and oxygen to form liquid water.What is the standard molar entropy for the reaction?

rS n S (products) m S (reactants)

2H (g) O (g) 2H O(l)

J J J JS 2 69.95 2 130.7 205.1 326.6K K K K

The enthalpy change is negative (net decrease in dispersion) due to the change in number of moles: 3 reduced to 2

The second law of thermodynamics states:..

S°universe = ∆S°system + ∆S°surroundings

Any change in entropy for the system plus the entropy change for the surroundings must equal the overall change in entropy for the universe.A process is considered to be spontaneous under standard conditions if S°(universe) is greater than zero.

2nd Law of Thermodynamics

The solution process for NH4NO3 (s) in water is an entropy driven process.

∆S°universe =

∆S°system + ∆S°surroundings

Calculating S°Surroundings:

system surroundingssystem surroundings

q qS S

at constant pressure, qsystem = rH°system

q qS S

at constant pressure, qsystem = rH°system

q qS S

surroundings r system

r systemsurroundings

Therefore : q H

Hand S

Problem:Calculate the entropy change for the surroundings for the reaction: 2H2(g) + O2(g) 2H2O(l)

The enthalpy change for the reaction is calculated using standard molar enthalpies of formation:

surroundings

10 K571.7kJ1kJ JS 1917 K298.15K

As calculated previously:

S°universe = 327 J/K + 1917 J/K =1590. J/K

surroundingsJS 1917 K

systemJS 327 K

S°universe = 327 J/K + 1917 J/K = 1590. J/K

The entropy of the universe increases ( > 0) therefore the process is spontaneous at standard state conditions.The process is spontaneous due to the entropy change in the surroundings, not the system.

Spontaneous or Not?

The method used so far to determine whether a process is spontaneous required evaluation of two quantities, S°(system) and S°(surroundings).J. Willard Gibbs asserted that that the maximum non-PV work available to the system must be a function of Enthalpy and Entropy:

G = H – TS

G = Gibbs Free energy of the system, H = system enthalpy and S = the entropy of the system.

J. Willard Gibbs1839-1903

Gibbs Free Energy, G

Since it is impossible to measure individual values of enthalpy, we often express free energy in terms of the changes of thermodynamic quantities.

(G = H – TS)At constant temperature:

G° = Gibbs Free energy change of the system, H° = enthalpy change and S° = the entropy change at SS conditions.

G H T S

If the reaction is exothermic (H < 0)And the change in entropy is positive (H > 0) at a given temperature, then S < 0.We then can assert that if G < 0 that the reaction is spontaneous as well as product favored!Spontaneity is a function of energy and dispersion!

G H T S

H S G Reaction

+ Product Favored

+ + Reactant Favored

? Temperature dependant

+ + ? Temperature dependant

G H T S

Since rG° is related to S°universe, it follows that:• If rG° < 0: The process is spontaneous in the

direction written under standard conditions.• If rG° = 0: The process is at equilibrium under

standard conditions and K=1• If rG° > 0: The process is non-spontaneous in

the direction written under standard conditions.• Conclusion: A reaction proceeds spontaneously

toward the minimum in free energy, which corresponds to equilibrium.

rGo & Equilibrium

Product Favored Reactions, ∆G° negative, K > 1

Q < K: Heading to equilibrium G < 0Q = K: At equilibrium G = 0Q > K: Heading away from equilibrium G > 0

∆G, ∆G°, Q, & K

• Product-favored• 2 NO2 N2O4

• ∆rG° = – 4.8 kJ• State with both reactants

and products present is more stable than complete conversion.

• K > 1, more products than reactants.

∆G, ∆G°, Q, & K

Reactant Favored Reactions, ∆G° positive, K < 1

Q < K: Heading to equilibrium G < 0

Q = K: At equilibrium G = 0

Q > K: Heading away from equilibrium G > 0

∆G, ∆G°, Q, & K

• Reactant-favored• N2O4 2 NO2

∆rG° = +4.8 kJ• State with both

reactants and products present is more stable than complete conversion.

• K < 1, more reactants than products

∆G, ∆G°, Q, & K

rG° represents the free energy change for a process at standard state conditions. (Equilibrium)What if this is not the case?Under nonstandard conditions:

Where R is thegas law constantand Q =

r rG G RTln(Q)

∆G, ∆G°, Q, & K

At equilibrium, we know that rG = 0 and Q = K

Therefore:

So knowing one quantity yields the other.

G G RTln(Q)

0 G RTln(K)

G RTln(K)

∆G, ∆G°, Q, & K

Problem:rG° for the formation of ammonia at SS conditions is 16.37 kJ/mol. What is the value of Kp at this temperature and pressure? (1 mol, 20 °C and 1 atm)

∆G, ∆G°, Q, & K

3 1H (g) N (g) NH (g)2 2

G RTln(K )

∆G, ∆G°, Q, & K

G RTln(K )

Gln(K)RT

kJ 10 J16.37G mol 1 kJK exp exp 740.JRT 8.314 298 Kmol K

∆G, ∆G°, Q, & K

G RTln(K )

Gln(K)RT

kJ 10 J16.37G mol 1 kJK exp exp 740.JRT 8.314 298 Kmol K

K >> 1, product favored as

predicted by G

∆G, ∆G°, Q, & K

The relation of ∆rG, ∆rG°, Q, K, reaction spontaneity, and product- or reactant favorability.

Summary

C (graphite) + 2H2(g) CH4(g)

rH° (kJ/mol) 0 0 74.9

S° (J/K) +56 +130.7 + 186.3

Calculating & Using Free Energy Standard Free Energy of Formation

H n H (products) m H (reactants)

rH° (kJ/mol) 0 0 74.9

S° (J/K) +56 +130.7 + 186.3

r rJH 74.9 kJ S 80.7 K

rHo (kJ/mol) 0 0 74.9

So (J/K) +56 +130.7 + 186.3

JH 74.9 kJ S 80.7 K

G H T S

J 1 kJG 74.9 kJ 298 K 80.7K 10 J

kJG 50.9 mol

rG° is negative at 298 K, so the reaction is predicted to be spontaneous under standard conditions at this temperature. It is also predicted to be product-favored at equilibrium.

Under reversible conditions, both enthalpy and entropy are state functions. It follows that the Gibbs free energy must also be.Therefore we can write that:

G H T S

r f fG n G (products) m G (reactants)

Note that ∆fG° for an element = 0

Free Energies of Formation

Using the fG° found in appendix L of your text, calculate rG° for the following reaction:

4NH3(g) + 7O2(g) → 4NO2(g) + 6H2O(g)

r f 2 f 2 f 2G 4 G NO (g) 6 G H O(g) 4 G NO (g) 0

4NH3(g) + 7O2(g) → 4NO2(g) + 6H2O(g)

rG° = –1101.14 kJ/mol (product-favored

r f 2 f 2 f 2

G 4 G NO (g) 6 G H O(g) 4 G NO (g) 0

G 4 mol (51.23 kJ/mol) 6 mol ( 228.59 kJ/mol) 4 mol ( 16.37 kJ /mol)

Is the dissolution of ammonium nitrate product-favored?

If so, is it enthalpy- or entropy-driven?

NH4NO3(s) + heat NH4NO3(aq)

Calculating ∆rG°

• By definition: G = H − TS

• Indicating that free energy is a function of temperature.

• rG° will therefore change with temperature.• A consequence of this temperature

dependence is that, in certain instances, reactions can be product-favored at equilibrium at one temperature and reactant-favored at another.

Free Energy & Temperature

When a reaction has

rH° < 0

rS° > 0

at all temperatures rG° is negative.

(Product favored)

When a reaction has

rH° > 0

rS° > 0

at high temperatures rG° is negative.

(Product favored)

When a reaction has

rH° < 0

rS° < 0

at low temperatures rG° is negative.

(Product favored)

At what temperature will a reaction that is non-spontaneous turn over to a reaction that is? (rG changes from + to )

Example: The reaction,

Has the following thermodynamic values.∆rH° = +470.5 kJ

∆rS° = +560.3 J/K

∆rG° = +301.3 kJ

Reaction is reactant-favored at 298 K

2 3 22Fe O (s) 3C(s) 4Fe(s) 3CO (g)

Free Energy & TemperatureAt what temperature will a reaction that is non-spontaneous turn over to a reaction that is? (rG changes from + to )

When rG 0, the reaction begins to become spontaneous.

2 3 22Fe O (s) 3C(s) 4Fe(s) 3CO (g)

When rG 0, the reaction begins to become spontaneous.

2 3 22Fe O (s) 3C(s) 4Fe(s) 3CO (g)

G H T S 0HTS

∆rH° = +467.9 kJ

∆rS° = +560.3 J/K 3

10 J467.9 kJH 1 kJT 839.7 KJS 560.3K

2 3 22Fe O (s) 3C(s) 4Fe(s) 3CO (g)

chapter 19 principles of chemical reactivity: entropy and free energy

energy energy

spontaneous processes

spontaneous changes

spontaneous reactions

chemical thermodynamics

spontaneous processpage

free energy chapter

endothermic h

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