CHEM 14 Thermodynamics, Kinetics, Equilibrium

Spontaneity

• Spontaneous change

– A process that occurs in a system left to itself; no outside intervention is

necessary to sustain the process

– E.g.

• Nonspontaneous change

– A process that will not occur unless some external action is continuously applied.

4 Fe(s) + 3 O2(g) 2 Fe2O3(s)

Spontaneity

• A ball rolls down a hill but never spontaneously rolls back up the hill.

• A gas fills its container uniformly; it never spontaneously collects at one end of the

container.

• Heat flows from a hotter body to a colder one, but the reverse never happens

spontaneously.

• Paper burns spontaneously in an exothermic reaction to form CO2(g) and H2O(l) but

paper is not formed when CO2(g) and H2O(l) are heated together.

What happens to the potential

energy of the system in each of

these examples?

Entropy

• BUT! There are also spontaneous reactions that are endothermic:

• Solid-to-liquid phase transition

H2O(s) H2O(l) ΔH° = 6.01 kJ

• Dissolution of NH4NO3 and NaCl in water (remember these?)

• Exothermicity does not guarantee the spontaneity of a reaction.

What factor is being considered when predicting the spontaneity of a

reaction??

ENTROPY!

Entropy

• What is ENTROPY?

– A state of randomness or disorder of a system.

– All things in the universe progress from a low entropy to high entropy

Entropy

• ENTROPY is a thermodynamic function that describes

the number of arrangements that are available to a

system existing at a given state. It is closely

associated with probability.

• Nature proceeds spontaneously to states having

higher probabilities of existing.

• Consider the possible arrangements of 4 gas

molecules in a 2-bulbed container (Figure 1).

• Microstate – a particular configuration of particles that

leads to a specific arrangement.Figure 1. Possible arrangements

of 4 gas molecules in a 2-bulbed

container.

Entropy

Figure 1. Possible arrangements

of 4 gas molecules in a 2-bulbed

container. Figure 2. All possible microstates of 4 gas molecules in a 2-bulbed container.

Entropy

• One important conclusion: The probability of occurrence of a particular

arrangement (state) depends on the number of ways or configurations

(microstates) that lead to that arrangement.

Entropy

• Positional Probability

– Probability that depends on the number of configurations in space (positional

microstates)

– Can also be seen in different states of matter

– This was also seen in the formation of solutions.

Entropy

For each pair, choose which has the higher entropy:

A. Solid CO2 and gaseous CO2

B. N2 gas at 1 atm and N2 gas at 1.0 x 10-2 atm

Predict the sign of ΔS for each of the following processes:

A. Solid sugar is added to water to form a solution

B. Iodine vapor condenses on a cold surface to form crystals

Second Law of Thermodynamics

• In any spontaneous process, the entropy of the universe increases.

• The total energy of the universe remains constant but its entropy is

increasing.

• Mathematically,

ΔSuniverse = ΔSsystem + ΔSsurroundings

ΔSuniverse > 0 the entropy of the universe increases and

the process is spontaneous in the direction

written

ΔSuniverse < 0 the process is spontaneous in the opposite

direction

ΔSuniverse = 0 the process has no tendency to occur and

the system is at equilibrium

Entropy and Temperature

• Consider the vaporization of 1 mole of H2O(l)

– What is the system in this case?

– What is the sign of ΔSsystem?

– What is the sign of ΔSsurroundings?

– What is the sign of ΔSuniverse?

• At 1 atm and temperatures above 100°C, water

spontaneously changes from liquid to gas. At 1 atm

and temperatures below 100°C, the reverse process

(condensation) is spontaneous.

• TEMPERATURE HAS AN EFFECT!

Entropy and Temperature

• Entropy changes in the surroundings are primarily determined by heat flow.

• The effect of this heat flow is dependent on the temperature.

• 2 characteristics of ΔSsurroundings:

– The sign of ΔSsurroundings depends on the direction of heat flow

– The magnitude of ΔSsurroundings depends on the temperature

– The minus sign in the formula is important!

Entropy and Temperature

In the metallurgy of antimony, one way to recover the pure metal is

through the use of iron to reduce antimony in sulfide ores:

Sb2S3(s) + 3 Fe(s) 2 Sb(s) + 3 FeS(s) ΔH = -125 kJ

Calculate ΔSsurr for these reaction at 25°C.

Note that ΔSsurr is positive.

Entropy of the System

• Consider the fusion of 1 mole of ice with ΔH = 6.01 kJ/mole at 25°C

ΔH

TΔSsys =

ΔSsys =6 010 J

298 K

= 22.0 J/K

ΔSsys = –6 010 J

310 K

= -19.4 J/K

ΔSuniv = ΔSsys + ΔSsurr

ΔSuniv = 22.0 J/K + -19.4 J/K

= 2.6 J/K

Entropy of the System

• A system is represented by the following reaction:

aA + bB cC + dD

• The standard entropy of reaction is given by

• Or, in general

Calculate ΔS° at 25°C for the reaction

2 NiS(s) + 3 O2(g) 2 SO2(g) + 2NiO(s)

given the following standard entropy values:

Entropy of the System

• If a reaction leads to more gas molecules, what is the sign of ΔS°?

• If a reaction leads to less gas molecules, what is the sign of ΔS°?

• If a reaction involves no net change in the number of gas molecules, what is

the sign of ΔS°?

Phase Transitions

• At the temperature at which a phase transition occurs, the system is at

equilibrium and ΔG = 0.

The molar heats of fusion and vaporization of benzene are 10.9 kJ/mol

and 31.0 kJ/mol, respectively. Calculate the entropy changes for the solid

to liquid and liquid to vapor transitions for benzene. At 1 atm, benzene

melts at 5.5°C and boils at 80.1°C.

ΔSfusion = 39.1 J K-1 mol-1

ΔSvap = 87.8 J K-1 mol-1

Third Law of Thermodynamics

• Thermodynamics commonly considers the change (Δ) in functions of a

system since some of them cannot be measured absolutely.

• ABSOLUTE ENTROPY VALUES, however, can be assigned.

• The entropy of a perfect crystalline substance is zero at the absolute zero of

temperature.

• As the temperature increases, the freedom of motion also increases and the

entropy of the substance above 0 K is greater than zero.

ΔS = Sfinal – Sinitial

• If the absolute zero is taken as the initial state, then ΔS can readily be

computed.

Gibb’s Free Energy

• The second law of thermodynamics states that in a spontaneous reaction, ΔSuniv > 0. ΔSsys and ΔSsurr have to be evaluated. ΔSsurr is a quantity difficult to measure. A different thermodynamic function must be used to create a criterion for spontaneity for a system.

• This thermodynamic function is called Gibb’s free energy, or simply free energy, defined by G = H – TS.

• The change in free energy in going from one state to another (constant T) is

ΔG = ΔH – TΔS

• Two functions can be used in predicting the spontaneity of processes: entropy (for all processes) and free energy (for processes at constant T and P).

Josiah Willard Gibbs

Gibb’s Free Energy

• Free energy is the energy available to do work. If ΔG is negative, the system released usable energy.

Gibb’s Free Energy

STANDARD FREE ENERGY CHANGES (ΔG°)

• The standard free energy change of a reaction is the free energy change for

a reaction when it occurs under standard state conditions, when reactants in

their standard states are converted to products in their standard states.

• Just like ΔH°, ΔG° absolute values cannot be measured and a reference

point must be used.

Gibb’s Free Energy

Consider the reaction

2 SO2(g) + O2(g) 2 SO3(g)

carried out at 25°C and 1 atm. Calculate ΔH°, ΔS°, and ΔG° using the

following data:

ΔH° = -198 kJ

ΔS° = -187 J/K

ΔG° = -142 kJ

Gibb’s Free Energy

ΔG° = -1378 kJ

Gibb’s Free Energy

ΔG° = -3 kJ

• Summary of thermodynamic quantities

Chemical Kinetics

• Thermodynamics tells the tendency of a process to take place. It cannot tell

how fast a reaction takes place.

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

• The above reaction has a high tendency to occur but the two gas reactants

can coexist and never react to form liquid water at 25°C.

• To completely describe a reaction, stoichiometry and thermodynamics are

not enough.

• The rates of reactions and the factors affecting these add to a complete

description of different reactions taking place (or not) around us.

• This is the concern of CHEMICAL KINETICS.

Chemical Kinetics

• Consider the following decomposition reaction:

2 NO2(g) 2 NO(g) + O2(g)

• Reaction rate – change in concentration of

reactant or product per unit time

Chemical Kinetics

• Change can be positive (an increase in

the concentration of the products) or

negative (a decrease in the

concentration of reactants).

• For convenience, rate is defined to be a

positive quantity.

Chemical Kinetics

• Rate is negative since the concentration of NO2 decreased. But rate was

defined to be positive so the rate is expressed as

• Note that the average rate for 50-second intervals

is not constant but decreases with time.

Chemical Kinetics

• The rate at a specific point in time is the

instantaneous rate. This is the slope of the

tangent to the curve at that point.

• At t = 100 seconds,

Chemical Kinetics

• The rate of the reaction can also be defined in terms of the products. Always

remember that the stoichiometry must be considered in describing the

relative rates of the reactants and products.

2 NO2(g) 2 NO(g) + O2(g)

• Relate the rate of production of NO to the rate of consumption of NO2.

• Relate the rate of production of NO to the rate of production of O2.

• At t = 250 seconds,

Chemical Kinetics

• As a summary:

• For a general reaction:

the rate is given by

Chemical Kinetics

a. How is the rate at which ozone disappears related to the rate at which

oxygen appears in the reaction 2 O3(g) 3 O2(g)?

b. If the rate at which O2 appears is 6.0 x 10-5 M at a particular instant, at

what rate is O3 disappearing at the same time?

Rate Law

• Expresses the relationship of the rate of a reaction to the rate constant and

the concentrations of the reactants raised to some powers.

• For the general reaction

the rate law is given as

Rate = k[A]x[B]y

k ≡ proportionality constant

x, y ≡ order of reactant

• The overall order of a reaction is given by the sum of the orders of

reactants, i.e., for the general rate law above

overall order = x + y

• The concentrations of the products do not appear in the rate law.

• The values of x and y must be determined by experiment.

Method of Initial Rates

• Initial rate – the instantaneous rate determined just after the reaction begins

(just after t = 0). The idea is to determine the instantaneous rate before the

initial concentrations of the reactants have significantly changed.

• Consider the following reaction carried out in three different experiments:

• The rate law for the reaction is Rate = k[NH4+]n[NO2

-]m. The values of n and

m are dependent on the initial concentrations of NH4+ and NO2

-,

respectively.

Method of Initial Rates

• For experiments 1 and 2, the concentration of NH4+ is constant but the concentration

of NO2- varies. This means that the change on the initial rate is due only to the

change in the concentration of NO2-.

Thus, m = 1.

Method of Initial Rates

• In order to determine the value of n, experiments 2 and 3 are used.

Thus, n = 1.

• What is the order of the reaction with respect to NH4+?

• What is the order of the reaction with respect to NO2-?

• What is the overall order of the reaction?

• The value of the rate constant, k, can be evaluated by plugging in values from any of

the three experiments into the rate law.

• What is the value of k in this example?

Method of Initial Rates

Reaction Mechanisms

• Chemical kinetics also focus on how reactions occur.

• A reaction mechanism is a proposed series of steps by which a reaction

occurs. It is different from a balanced equation in that the latter does not tell

us how a reaction occurs.

• Consider the reaction between nitrogen dioxide and carbon monoxide:

• The following is a proposed mechanism for the above reaction:

Reaction Mechanisms

k1 and k2 are rate constants for the individual reactions called elementary

steps.

• Molecularity – refers to the number of species that must collide to bring

about the reaction

• Elementary step – a reaction whose rate can be written from its molecularity

• What can be said about the molecularity of a reaction and its overall order?

Reaction Mechanisms

• Adding the two elementary steps gives the overall reaction given above.

• The proposed mechanism must agree with the experimentally-determined

rate law.

• Which can be determined first for a reaction: the mechanism or the rate

law?

Collision Theory

• Central idea: molecules must collide to react and after collision, there must

be a redistribution of energy that puts enough energy into some bonds to

break them (effective collision).

• Activation energy (Ea) – the minimum energy above the average kinetic

energy that molecules must bring to their collisions for a reaction to occur.

Collision Theory

• Factors affecting reaction rates:

1. Nature of reactants

– Highly reactive substances have high energy

Collision Theory

• Factors affecting reaction rates:

2. Concentration of reactants

Collision Theory

• Factors affecting reaction rates:

3. Temperature

Collision Theory

• Factors affecting reaction rates:

3. Temperature

Arrhenius proposed the following equation:

Number of collisions with Ea = (total collisions)e-Ea/RT

Ea is the activation energy; R is the gas constant in J mol-1 K-1; T is the temperature

in K.

• The fraction of effective collision increases exponentially with temperature

• This expression gives the number of total effective collisions

• Experiment, however, has shown that the observed reaction rate is somewhat

less than the rate of effective collisions. Why is this so??

The answer lies in molecular orientations.

Collision Theory

• Factors affecting reaction rates:

• The collision must involve enough energy to produce the reaction.

• The relative orientation of the reactants must allow the formation of any new

bonds necessary to produce the products.

Collision Theory

• Factors affecting reaction rates:

4. Particle size and surface area

Collision Theory

• Factors affecting reaction rates:

5. Presence of Catalyst

• A catalyst is a substance that speeds up a reaction without being consumed

itself. It provides an alternative pathway with a lower activation energy.

Collision Theory

• Factors affecting reaction rates:

• Catalysts are defined according to their state:

• Heterogeneous Catalysts – Catalyst differs in state

from the reactants. Commonly, the catalyst is a solid and

the reactants can be gas, liquid or aqueous. Catalysis

takes place via adsorption.

• Homogeneous Catalysts – Catalyst has the same state

as the reactants.

Transition State Theory

• The transition state is an unstable transitory combination of reactant

molecules that occur at a potential energy maximum.

• The transition state is characterized by partially broken and partially formed

bonds in the activated complex. The activated complex is a nonisolable

species.

Chemical Equilibrium

• Chemical equilibrium is described as a dynamic state where the

concentrations of the reactants and products remain constant with time.

Equilibrium Constant

• For a general reaction

the law of mass action which describes the equilibrium condition is given by

the equilibrium constant:

Write the equilibrium expression for the following reaction:

Equilibrium Constant

Equilibrium Constant

• For a general reaction

If the reaction is reversed, the new equilibrium expression is

If the original reaction is multiplied by a factor n to give

the equilibrium expression becomes

Equilibrium Constant

• There are an infinite number of ways to combine equilibrium concentrations

of reactants and products that will give the same equilibrium constant. Each

set of equilibrium concentrations is called an equilibrium position.

Equilibrium Constant

• If K > 1, the reaction system will consist mostly of products; the equilibrium

lies to the right.

• If K < 1, the reaction system will consist mostly of reactants and the

equilibrium lies to the left of the written equation.

• K and the time required to reach equilibrium are not related.

– The time required depends on the reaction rate which is dependent on the

activation energy.

– K depends on thermodynamic factors such as the difference in energy of

reactants and products.

Reaction Quotient, Q

• The reaction quotient, Q, is used in determining if the system is at

equilibrium and if not, to which direction it will shift to achieve equilibrium.

• Q is obtained by applying the law of mass action using concentrations at

states other than the equilibrium state of the system.

• It has the same formula as the equilibrium constant, K.

Reaction Quotient, Q

• Using the reaction quotient:

Calculating for Equilibrium

Concentrations

• Sometimes, the initial values of the reactants and products are given

instead of equilibrium concentrations. In these cases, an ICE table is very

helpful in computing for equilibrium concentrations.

A.

B.

Le Chatelier’s Principle

• There are factors that affect the position of a chemical

equilibrium. The effects of these factors (changes in

concentration, temperature and pressure) on a system

at equilibrium can be qualitatively predicted by using Le

Chatelier’s principle.

• If a change is imposed on a system at equilibrium, the

position of the equilibrium will shift in a direction that

tends to reduce that change. Henry Louis Le Chatelier

Le Chatelier’s Principle

1. Effect of Change in Concentration

• If a component (reactant or product) is added to a reaction system at

equilibrium (at constant T and P or constant T and V), the equilibrium

position will shift in the direction that lowers the concentration of that

component.

• If a component (reactant or product) is removed from a reaction system

at equilibrium (at constant T and P or constant T and V), the equilibrium

position will shift in the direction that increases the concentration of

that component.

Le Chatelier’s Principle

2. Effect of Change in Pressure

• There are 3 ways to change the pressure of a system:

a. Add or remove a gaseous reactant or product

b. Add an inert gas (one not involved in the reaction)

c. Change the volume of the container

• The addition of an inert gas increases the total pressure and changes

the partial pressures or concentrations of the reactants or products but

the equilibrium constant remains the same.

• When the volume of the container holding a gaseous system is

reduced, the system responds by reducing its own volume. This is done

by decreasing the total number of gaseous molecules in the system.

Le Chatelier’s Principle

2. Effect of Change in Pressure

Le Chatelier’s Principle

3. Effect of Change in Temperature

• The effect of the previous two factors is changing the equilibrium position

(equilibrium concentrations) but not the value of K.

• K depends on temperature

Le Chatelier’s Principle

3. Effect of Change in Temperature

• Treat energy as a reactant (endothermic process) or as a product (exothermic

process), and predict the direction of shift in the same way as when an actual

reactant or product is added or removed.

• A temperature increase favors an endothermic reaction, and a temperature

decrease favors an exothermic reaction.

Le Chatelier’s Principle

4. Effect of Catalyst

• Adding a catalyst to a reaction mixture that is not yet at equilibrium will simply cause

the mixture to reach equilibrium sooner.

• Kinetics and thermodynamics are independent of each other.

Equilibrium Constant

Free Energy and Chemical Equilibrium

• Under conditions that are not standard state, the following equation holds:

ΔG = ΔG° + RT lnQ

R = 8.314 J mol-1 K-1

T is in Kelvin

Q is the reaction quotient

• At equilibrium, ΔG = 0 and Q = K, where K is the equilibrium constant. The

following equation applies for a reaction system at equilibrium:

ΔG° = - RT lnK

• The larger the value of K, the more negative ΔG° is and the more

spontaneous the process.

Free Energy and Chemical Equilibrium

Acid-Base Equilibria

• Acid-Base Properties of Water

• Water is an amphoteric substance. It is a weak electrolyte and is a poor

conductor of electricity. However, it undergoes dissociation to a small extent:

H2O(l) ↔ H+(aq) + OH-

(aq)

2 H2O(l) ↔ H3O+

(aq) + OH-(aq)

• Which are the conjugate acid-base pairs?

• Autoionization of water

• The equilibrium constant expression for the autoionization of water is given by

• The concentration of water in aqueous solutions is considered constant.

Kw = [H+][OH-]

• Kw is the ion-product constant of water at a specific temperature. At 25°C, Kw

has a value of 1.0 x 10-14.

Kc =[H+][OH-]

[H2O]

Kc [H2O] = [H+][OH-]

Acid-Base Equilibria

Calculate the concentration of H+ in (a) a solution in which [OH-] is 0.010 M; (b) a

solution in which [OH-] is 1.8 x 10-9 M. (Unless otherwise stated, the temperature is

25°C.)

(a) Kw = [H+][OH-] (b) Kw = [H+][OH-]

H+ = 1.0 x 10-12 M H+ = 5.6 x 10-6 M

Is this solution acidic or basic? Is this solution acidic or basic?

What is the pH and pOH of each of the solutions given above?

Recall: pH = -log [H+], pOH = -log [OH-]

Kw 1.0 x 10-14

[OH-] 0.010H+ = =

Kw 1.0 x 10-14

[OH-] 1.8 x 10-9H+ = =

Acid-Base Equilibria

• Relative strengths of acids and bases

• A strong acid completely transfers its

protons while its conjugate base has

negligible tendency to be protonated.

• A weak acid only partially dissociates and its

conjugate base is a weak base.

• A substance with negligible acidity (e.g.

CH4) has a conjugate base that is very

strong.

Acid-Base Equilibria

• Strong acids and strong bases

HCl(aq) ↔ H+(aq) + Cl-(aq)

Kc = [H+][Cl-]

[HCl]

• Since HCl is a strong acid and dissociates almost completely in the solution,

[HCl] is almost zero. Therefore,

HCl(aq) H+(aq) + Cl-(aq)

Kc = [H+][Cl-] ≈ ∞

[HCl]

• [H+] = [Cl-] = initial concentration of HCl before dissociation took place

• The above trend goes for strong bases.

(a) Calculate the pH of 0.10 M HNO3

(b) Calculate the pH of 1.0 x 10-10 M HCl

(c) Calculate the pH of 0.0011 M Ca(OH)2

Acid-Base Equilibria

• Weak acids

• Consider the ionization of a weak acid in water:

• Ka is the acid dissociation constant at a specific temperature.

• Just like in molecular equilibrium, an ICE table is used in solving acid-base

equilibrium problems.

Acid-Base Equilibria

• Weak acids

• The following approximation can be used since Ka is very small:

Acid-Base Equilibria

• Weak acids

• When can we do the approximation? The approximation is valid if the result is

5% of the initial concentration.

The pH of a 0.10 M solution of formic acid (HCOOH) is 2.39. What is the Ka of the

acid? (1.8 x 10-4)

Acid-Base Equilibria

• Percent ionization

• Another measure of acid strength is percent ionization which has the formula:

• The extent of dissociation of a weak acid depends on

the initial concentration of the acid.

Acid-Base Equilibria

• Weak bases and Base dissociation constant

What is the pH of a 0.26 M methylamine solution (Kb = 4.4 x 10-4)?

What is the value of Ka for the conjugate acid of methylamine?

• Acid-base properties of Salts

• A salt is one of the products of an acid-base reaction (aside from water).

• The cation of a salt is from a base and its anion is from an acid.

• Salt hydrolysis refers to the reaction of a cation or an anion of a salt, or both, with water.

• Salts can be neutral, acidic, or basic depending on the strength of the acid and base that reacted to form the salt.

• The conjugate base has a Kb value at a specific temperature. What is the value of Kb for acetate anion?

Acid-Base Equilibria

• Acid-base properties of Salts

• If a strong acid and a strong base react, the resulting salt is neutral.

• If a strong acid and a weak base react, the resulting salt is acidic.

• If a weak acid and a strong base react, the resulting salt is basic.

• If a weak acid and a weak base react, the pH of the resulting solution depends

on the Kb of the conjugate base and Ka of the conjugate acid.

Acid-Base Equilibria

• Acid-base properties of Salts

Tell whether the following salts are neutral, acidic or basic:

(a) LiClO4

(b) Na3PO4

(c) NH4CN

Calculate the pH of a 0.24 M sodium formate solution (HCOONa).

Ka for HCOOH = 1.7 x 10-4

Calculate the pH of a 0.10 M NH4Cl solution. The Kb value for NH3 = 1.8 x 10-5.

Buffers

• A buffer solution is a solution consisting of (1) a weak acid or base and (2) its salt;

both must be present. A buffer solution has the ability to resist changes in pH upon

addition of small amounts of either acid or base.

• An example of a buffer solution is made up acetic acid (CH3COOH) and acetate

anion (CH3COO-).

• If an acid is added to the system, the acetate ion will serve as a base to neutralize the

added acid:

• If a base is added to the system, the acetic acid will serve as the acid to neutralize

the added acid:

Which of the following are buffer systems? (a) KF/HF; (b) KBr/HBr;

(c) Na2CO3/NaHCO3