1

LECTURE 1—THERMODYNAMICS

Thermodynamic Functions—

• Internal energy (U)—sum of energies for all the individual particles in a sample of matter

• Enthalpy (H)—function related to the heat absorbed OR evolved by a chemical system

o negative enthalpy endothermic o positive enthalpy exothermic

• Entropy (S)—measure of number of ways energy is distributed throughout a chemical system

• Gibbs energy (G)— energy that is available to do work 𝐺 = 𝐻 − 𝑇𝑆

o allows us to predict spontaneity—if in equilibrium can be used to show in which direction the reaction will be spontaneous

o once a spontaneous event begins it continues until it stops of its own accord

Thermodynamic concepts—

• Heat (q) and temperature (T):

o heat is a transfer of energy due to a temperature difference

o thermodynamic temperature measured in Kelvin (K)

o two bodies have same temperature if they are in thermal equilibrium no heat flow between them when they are in DIRECT CONTACT

• A system is a particular part of the universe that we are studying

o everything else is surroundings

▪ open systems gain or lose mass & energy across their boundaries

▪ closed systems absorb or release energy, but not mass, across the boundary

▪ isolated systems cannot exchange matter or energy with their surroundings

• energy of an isolated system is constant (adiabatic processes)

ΔX: the change in X—

• Interested in change in values of U, H, S & G rather than their absolute values

• For any thermodynamic quantity X:

o ∆𝑋 = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑋 − 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑋

• Change in temperature ΔT is defined as:

o ∆𝑇 = 𝑇𝑓𝑖𝑛𝑎𝑙 − 𝑇𝑖𝑛𝑖𝑡𝑖𝑎𝑙

• Both chemical reactions and physical changes occur in one particular direction under particular

conditions SPONTATNEOUS PROCESS

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ΔG AND SPONTANEITY:

• Spontaneity of a process at constant temperature and pressure is given by the sign of ΔG

o ∆𝐺 = ∆𝐻 − 𝑇∆𝑆

▪ ΔG < 0—the process is spontaneous

▪ ΔG > 0—the process is non-spontaneous

▪ ΔG = 0—the system is at equilibrium

1st Law of Thermodynamics—

• Energy cannot be created nor destroyed, only transferred or transformed either through heat or work (conservation energy principle)

o ∆𝑈 = 𝑞 + 𝑤

▪ q = heat

▪ w = work

• U (total internal energy of a system) can be changed by transfer of heat or work with the surroundings

U, q and w—

• Internal energy of a system is the sum of kinetic & potential energies of its components

o 𝑈𝑡𝑜𝑡𝑎𝑙 = 𝑈𝑘𝑖𝑛𝑒𝑡𝑖𝑐 + 𝑈𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙

▪ q is the heat transferred into the system

• +ve for heat transferred into the system

• –ve for heat transferred out of the system

▪ w is the work done ‘on’ the system

• +ve for work done on the system

• –ve for work done by the system on the surroundings

Work (w)—

• In chemical reactions, the generation of gases will lead to volume changes of our system

o work is motion against an opposing force

• 𝑤 = −𝑝∆𝑉 (at constant pressure)

o w is –ve for expansion as system does work on surroundings (lowers internal energy)

o +ve for compression as surroundings does work on system (increases internal energy)

▪ 0 for no volume change

Heat (q)—

• Heat is a transfer of energy due to a temperature difference:

o 𝑞 = 𝐶∆𝑇

▪ q = heat (J)

▪ C = heat capacity (J K–1)

Measurement of heat of reaction—

BOMB CALORIMETER:

• System remains at constant volume work is zero

• ∆𝑈 = 𝑞 + 𝑤

o ∆𝑟𝑈 = 𝑞𝑣 = 𝐶∆𝑇

▪ qv is heat of reaction at constant volume

o 𝑞𝑐𝑎𝑙𝑜𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = −𝑞𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛

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LECTURE 2—ENTHALPY

Enthalpy (H)—

• ΔrH = qp = heat of reaction at constant pressure

o ΔrH > 0 reaction is endothermic (heat absorbed)

o ΔrH < 0 reaction is exothermic (heat liberated)

• ΔH and ΔU (the internal energy change) are related by ∆𝐻 = ∆𝑈 + 𝑝∆𝑉

o difference can be large for reactions involving gases but not for reactions involving only liquids and solids

• Standard enthalpy of reaction (ΔrH˚; kJ or kJ mol-1):

o value of ΔH for a reaction occurring under standard conditions of 105 Pa (1 bar) and

specific temperature (usually 25˚C)

STANDARD ENTHALPY CHANGE FOR CHEMICAL REACTION:

• 𝑁2 (𝑔) + 3𝐻2 (𝑔) → 2𝑁𝐻3 (𝑔) ∆𝑟𝐻° = −92.38 𝑘𝐽 𝑚𝑜𝑙−1

• Always gives physical states of the reactants and products

o value of ΔrH˚ is true when coefficients of reactants and products are numerically equal to

the number of moles of the corresponding substances

▪ enthalpy is a state function—ΔH depends ONLY on final and initial enthalpies not on the pathway to get from initial to final state

▪ this allows ΔH for unknown reactions to be determined from the ΔH data for known reactions (Hess’s law)

Enthalpies of Transition—

• 𝐻2𝑂 (𝑙) → 𝐻2𝑂(𝑔) (vaporisation/boiling)

o ∆𝑣𝑎𝑝𝐻˚(373.15 𝐾) = +40.656 𝑘𝐽 𝑚𝑜𝑙−1 [endothermic process (ΔHθ > 0)]

• 𝐻2𝑂 (𝑠) → 𝐻2𝑂(𝑙) (fusion/melting)

o ∆𝑓𝑢𝑠𝐻˚(273.15 𝐾) = +6.00 𝑘𝐽 𝑚𝑜𝑙−1 [endothermic process (ΔHθ > 0)]

Hess’s law—

• Combining known thermochemical equations to calculate ΔrH˚ for another reaction

• Overall enthalpy change for any chemical reaction is constant

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• A reaction enthalpy is the sum of enthalpies of any sequence of reactions (at the same temperature and pressure) into which the overall reaction may be divided

∆𝐻13 = ∆𝐻12 + ∆𝐻23

CONSIDER oxidation of C to CO2

• 2𝐶 (𝑠) + 2𝑂2 (𝑔) → 2𝐶𝑂2(𝑔)—written as TWO steps:

PARTIAL OXIDATION OF C:

• 2𝐶 (𝑠) + 2𝑂2 (𝑔) → 2𝐶𝑂2(𝑔) + 𝑂2 (𝑔) ∆𝑟𝐻˚ = −221.0 𝑘𝐽 𝑚𝑜𝑙−1

FURTHER OXIDATION:

• 2𝐶𝑂 (𝑔) + 𝑂2 (𝑔) → 2𝐶𝑂2(𝑔) ∆𝑟𝐻˚ = −566.0 𝑘𝐽 𝑚𝑜𝑙−1

OVERALL:

• ∆𝑟𝐻˚ = −221.0 + (−566.0) = −787.0 𝑘𝐽 𝑚𝑜𝑙−1

Rules for manipulating thermochemical equations—

1. When an equation is reversed, the sign of ΔrH˚ must also be reversed

2. Substances can be cancelled from both sides only if the substance is in an IDENTICAL STATE

3. If all coefficients of an equation are multiplied or divided by the same factor, so must the value of ΔrH˚

Standard Enthalpy of Formation (ΔfH˚)—

• ΔfH˚ of a substance is the enthalpy change when 1 mole of the substance is formed at 105 Pa and

specified temperature from its elements in their standard states

o e.g. ΔfH˚ for liquid benzene 𝐶6𝐻6 (𝑙) is +49.0 kJ mol-1

▪ 6𝑆 (𝑠, 𝑔𝑟𝑎𝑝ℎ𝑖𝑡𝑒) + 3𝐻2 (𝑔) → 𝐶6𝐻6 (𝑙)

▪ ΔfH˚ for many substances are tabulated and this allows the calculation of

reaction enthalpies involving these substances

• ΔfH˚ of the elements in their standard states is zero by definition

Determining reaction enthalpies from enthalpies of formation—

• Enthalpy change for any reaction is given by:

o ∆𝑟𝐻˚ = ∑ 𝑛𝑝𝑝𝑟𝑜𝑑 ∆𝑓𝐻˚ − ∑ 𝑛𝑟𝑟𝑒𝑎𝑐 ∆𝑓𝐻˚

o ∆𝑟𝐻˚ = 𝑠𝑢𝑚 ∆𝑓𝐻˚ [𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠] − 𝑠𝑢𝑚 ∆𝑓𝐻˚ [𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠]

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LECTURE 3—ENTROPY

2nd Law of Thermodynamics—

• The entropy of the Universe increases in the course of a spontaneous change

• Consequence is that entropy of the universe NEVER decreases

Entropy & entropy change—

• Entropy (S) describes the number of ways that energy can be distributed in the system

• Entropy is a state function:

o ∆𝑟𝑆∘ = 𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − 𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠

o units of ΔrS are J mol-1 K-1

• Any event that is accompanied by an increase in the entropy of the universe (system + surroundings) will occur spontaneously

ICE MELTING:

• 𝐻2𝑂 (𝑠) → 𝐻2𝑂 (𝑙)

• Water molecules become more disordered

o more ways energy of the system can be distributed higher entropy

o liquid water has higher entropy

• Spontaneous processes tend to disperse energy

Entropy—

• Boltzmann proposed that:

o 𝑆 = 𝑘𝑙𝑛𝑊

▪ k is Boltzmann’s constant (1.381 x 10-23 J K-1)

▪ W is the number of microstates in which energy of a system can be distributed

o microstates correspond to the various ways molecules can occupy the available energy levels

Factors affecting entropy—

VOLUME:

• For gases the entropy increases with increasing volume as gas molecules spontaneously fill up the

space more space available for gases to occupy

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TEMPERATURE:

• Increasing temperature increases the kinetic energy of particles which results in more ways to distribute it

o HIGHER entropy

PHYSICAL STATE:

• Solids generally have small entropies because the molecules are stuck (most ordered)

• Liquids have a slightly higher entropy because it has more movement and flow

• Gases are in larger volumes, free to move, constantly collide, greater disorder contributes to high entropy of gases (least ordered)

NUMBER OF PARTICLES:

• Reactions that increase number of particles in the system have a POSITIVE entropy change

o more molecules produced more ways of distributing the energy among the molecules

Standard entropy of reaction (ΔrS˚)—

• The entropy (S) is zero at T = 0 K (3rd Law of Thermodynamics)

• Provides a reference point to determine the standard entropies (S˚) of substances

• Standard entropy change (ΔrS˚) for a general reaction:

o 𝑎𝐴 + 𝑏𝐵 → 𝑐𝐶 + 𝑑𝐷

o ∆𝑟𝑆∘ = [𝑐𝑆∘(𝐶) + 𝑑𝑆∘(𝐷)] − [𝑎𝑆∘(𝐴) + 𝑏𝑆∘(𝐵)]

o ∆𝑟𝑆∘ = 𝑠𝑢𝑚 (𝑆∘𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠) − 𝑠𝑢𝑚 (𝑆∘ 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠)

2nd Law of Thermodynamics—

• Whenever a spontaneous event takes place, the total entropy of the universe increases

o ΔStotal > 0

• Entropy change of the universe:

o ∆𝑆𝑡𝑜𝑡𝑎𝑙 = ∆𝑆𝑠𝑦𝑠𝑡𝑒𝑚 + ∆𝑆𝑠𝑢𝑟𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑠

• Gibbs energy (G):

o 𝐺 = 𝐻 − 𝑇𝑆

• For constant p & T:

o ∆𝐺 = ∆𝐻 − ∆𝑇𝑆

• A process is spontaneous when ΔG < 0 at constant p and T

3rd Law of Thermodynamics—

• At absolute zero, the entropy of a perfectly ordered pure crystalline substance is zero

o S = 0 at T = 0K

Gibbs energy—

• Standard Gibbs free energy change

o when ΔG is determined at 105 Pa, it is called standard free energy change (ΔG˚)

• There are several ways for determining ΔrG˚ for a reaction:

o ∆𝑟𝐺° = ∆𝑟𝐻° − 𝑇∆𝑟𝑆°

▪ use ΔrH˚ and ΔrS˚

data to determine ΔrG˚

o 𝑎𝐴 + 𝑏𝐵 → 𝑐𝐶 + 𝑑𝐷

▪ ∆𝑟𝐺° = 𝑐∆𝑓𝐺𝐶° + 𝑑∆𝑓𝐺𝐷° − (𝑎∆𝑓𝐺𝐴° + 𝑏∆𝑓𝐺𝐵°)

Gibbs energy & work—

• Maximum conversion of chemical energy to work if a reaction is thermodynamically reversible

o this can be theoretically harnessed as non-pV work (equal to ΔrG)

• This is the energy that need not be lost to the surroundings as heat (i.e. available to do work)

Gibbs energy and equilibrium—

• When a system is in a state of dynamic equilibrium at constant temperature and pressure:

o 𝐺𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 = 𝐺𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 𝑎𝑛𝑑 ∆𝐺 = 0

• For phase changes (e.g. 𝐻2𝑂 (𝑙) ⇌ 𝐻2𝑂 (𝑠)) equilibrium can be established just at ONE particular temperature

o e.g. ice ⇌ water occurs at 0˚C

o ∆𝐺° = 0 = ∆𝐻 − 𝑇∆𝑆 𝑎𝑛𝑑 ∆𝐻 = 𝑇∆𝑆 𝑠𝑜 𝑇 =∆𝐻

∆𝑆

• Equation can also be used to determine at which temperature a non-spontaneous reaction becomes spontaneous

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LECTURE 4—CHEMICAL EQUILIBRIUM

Relationship between Standard Gibbs Energy Change and Chemical Equilibrium—

• 𝑎𝐴 + 𝑏𝐵 ⇌ 𝑐𝐶 + 𝑑𝐷

o 𝐾𝑐 = [𝐶]𝑐[𝐷]𝑑

[𝐴]𝑎[𝐵]𝑏

• Standard Gibbs energy change is given by:

o ∆𝑟𝐺∘ = ∆𝑟𝐻∘ − 𝑇∆𝑟𝑆∘

• Relationship between ΔrG˚ and K

o ∆𝑟𝐺∘ = −𝑅𝑇𝑙𝑛𝐾

Chemical equilibrium—

• 𝑁2𝑂4 (𝑔) ⇌ 2𝑁𝑂2 (𝑔)

• Rates of the forward and reverse reactions are equal

• No net change in overall composition of the reaction mixture

DYNAMIC EQUILIBRIUM:

• Reactants (substances on the left) • Products (substances on the right)

Equilibrium constant—

• 𝑎𝐴 + 𝑏𝐵 ⇌ 𝑐𝐶 + 𝑑𝐷

• The following holds when equilibrium is established:

o 𝐾𝑐 =(

[𝐶]𝑒𝑐∘ )

𝑐

([𝐷]𝑒

𝑐∘ )𝑑

([𝐴]𝑒

𝑐∘ )𝑎

([𝐵]𝑒

𝑐∘ )𝑏

• Equilibrium constant expression

o Kc is the equilibrium constant

o c˚ is the standard concentration of 1 mol L–1

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• Each concentration value [X] in mol L–1 divided by c˚

in mol L–1

o hence all units cancel out and Kc is dimensionless

• The following holds when equilibrium is established:

o 𝐾𝑐 =[𝐶]𝑐[𝐷]𝑑

[𝐴]𝑎[𝐵]𝑏

• Kc dependent on temperature (always specify temperature)

Equilibrium expressions—

• The following reactions have equilibrium expressions;

o 𝑁2 (𝑔) + 𝑂2 (𝑔) ⇌ 2𝑁𝑂 (𝑔)

▪ 𝐾𝑐 =[𝑁𝑂]2

[𝑁2][𝑂2]

o 𝑆𝑂3 (𝑔) + 𝑁𝑂 (𝑔) ⇌ 𝑁𝑂2 (𝑔) + 𝑆𝑂2

▪ 𝐾𝑐 =[𝑁𝑂2 ][𝑆𝑂2]

[𝑆𝑂3][𝑁𝑂]

The equilibrium constant Kc & Kp—

• 𝑁2𝑂4 (𝑔) ⇌ 2𝑁𝑂2 (𝑔)

• 𝐾𝑐 =[𝑁𝑂2]2

[𝑁2𝑂4]= 4.61 × 10−3 at 25.0˚C

• Kc & Kp are related by the following equation: 𝐾𝑝 = 𝐾𝑐(𝑅𝑇)∆𝑛

▪ ∆𝑛𝑔𝑎𝑠 = (𝑚𝑜𝑙 𝑜𝑓 𝑔𝑎𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠) − (𝑚𝑜𝑙 𝑜𝑓 𝑔𝑎𝑠 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠)

The equilibrium constant K, and the reaction quotient Q—

• Define the reaction quotient Qc for systems not necessarily at equilibrium

• Kc can have only one positive value at a specific temperature

• Qc can have any positive value

• 𝑎𝐴 + 𝑏𝐵 ⇌ 𝑐𝐶 + 𝑑𝐷

o 𝑄𝑐 =[𝐶]𝑐[𝐷]𝑑

[𝐴]𝑎[𝐵]𝑏 o 𝐾𝑐 =[𝐶]𝑐[𝐷]𝑑

[𝐴]𝑎[𝐵]𝑏

▪ Qc = Kc at equilibrium

▪ Qc > Kc system uses up products & generates more reactants

▪ Qc < Kc system uses up reactants and generates more products

Manipulating equilibrium constant expressions—

• When the direction is reversed, the new equilibrium constant is the reciprocal of the original

o 𝑃𝐶𝑙3 (𝑔) + 𝐶𝑙2 (𝑔) ⇌ 𝑃𝐶𝑙5 (𝑔) 𝐾𝑐 =[𝑃𝐶𝑙5]

[𝑃𝐶𝑙3][𝐶𝑙2]

o 𝑃𝐶𝑙5 (𝑔) ⇌ 𝑃𝐶𝑙3 (𝑔) + 𝐶𝑙2 (𝑔) 𝐾𝑐′ =

[𝑃𝐶𝑙3][𝐶𝑙2]

[𝑃𝐶𝑙5]

▪ 𝐾𝑐′ =

1

𝐾𝑐

• When multiplying stoichiometric coefficients of a reaction, the equilibrium constant is raised to the power of that factor

o 𝑃𝐶𝑙3 (𝑔) + 𝐶𝑙2 (𝑔) ⇌ 𝑃𝐶𝑙5 (𝑔) 𝐾𝑐 =[𝑃𝐶𝑙5]

[𝑃𝐶𝑙3][𝐶𝑙2]

o 2𝑃𝐶𝑙3 (𝑔) + 2𝐶𝑙2 (𝑔) ⇌ 2𝑃𝐶𝑙5 (𝑔) 𝐾𝑐′′ =[𝑃𝐶𝑙5]2

[𝑃𝐶𝑙3]2[𝐶𝑙2]2

▪ 𝐾𝑐′′ = (𝐾𝑐)2

• When chemical equilibria are added, their equilibrium constants are multiplied

o 2𝑁2 (𝑔) + 𝑂2 (𝑔) ⇌ 2𝑁2𝑂 (𝑔) 𝐾𝑐1 =[𝑁2𝑂]2

[𝑁2]2[𝑂2]

o 2𝑁2𝑂 (𝑔) + 3𝑂2 (𝑔) ⇌ 4𝑁𝑂2 (𝑔) 𝐾𝑐2 =[𝑁𝑂2]4

[𝑁2𝑂]2[𝑂2]4

o 2𝑁2 (𝑔) + 4𝑂2 (𝑔) ⇌ 4𝑁𝑂2 (𝑔) 𝐾𝑐3 =[𝑁𝑂2]4

[𝑁2]2[𝑂2]4

▪ ∴ 𝐾𝑐3 = 𝐾𝑐1 × 𝐾𝑐2

THE MAGNITUDE OF THE EQUILIBRIUM CONSTANT:

• Product concentrations are in the numerator of Kc

o size of Kc indicates how far the reaction proceeds towards completion by equilibrium

Equilibrium expression for heterogeneous systems—

• 𝑎𝐴 + 𝑏𝐵 ⇌ 𝑐𝐶 + 𝑑𝐷

o homogeneous reaction—all reactants and products are in the same phase

o heterogeneous reaction—more than one phase exists in reaction mixture

• 2𝑁𝑎𝐻𝐶𝑂3 (𝑠) ⇌ 𝑁𝑎2𝐶𝑂3 (𝑠) + 𝐻2𝑂 (𝑔) + 𝐶𝑂2 (𝑔)

o 𝐾𝑐 = [𝐻2𝑂 (𝑔)][𝐶𝑂2 (𝑔)]

o don’t include concentrations of pure solids or pure liquid

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Equilibrium expressions—

• 2𝐻𝑔 (𝑙) + 𝐶𝑙2(𝑔) ⇌ 𝐻𝑔2𝐶𝑙2 (𝑠) 𝐾𝑐 =1

[𝐶𝑙2]

• 𝑁𝑎 (𝑠) + 𝐻2𝑂 (𝑙) ⇌ 𝑁𝑎+ (𝑎𝑞) + 𝑂𝐻− (𝑎𝑞) + 𝐻2 (𝑔) 𝐾𝑐 = [𝑁𝑎+ ][𝑂𝐻− ][𝐻2]

Equilibrium and Gibbs Energy (G)—

• 𝐻2𝑂 (𝑙) ⇌ 𝐻2𝑂 (𝑠)

o ΔG > 0 is a non-spontaneous reaction & ΔG < 0 is a spontaneous reaction

Spontaneous and non-spontaneous reactions for ΔS and ΔH—

ΔH > 0 (ENDOTHERMIC) ΔH < 0 (EXOTHERMIC)

ΔS > 0 (INCREASE IN ENTROPY) • ΔG < 0 at high temp. (spont)

• ΔG > 0 at low temp.

• ΔG < 0 at any temp. (spont)

ΔS < 0 (DECREASE IN ENTROPY) • ΔG > 0 at any temp. (non-spont)

• ΔG < 0 at low temp.

• ΔG > 0 at high temp. (spont)