Thermodynamics • Relationships and … - Test II...The Third Law of Thermodynamics The entropy of...

CHEM 2880 - Kinetics

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Thermodynamics

• Relationships and interconversions between variousforms of energy

• Preferred direction by which a system evolves• Understanding of equilibrium

Surroundings, boundaries, system

Types of Systems• Open - both mass and energy may leave and enter • Closed - energy can be exchanged no matter can

enter or leave• Isolated - neither mass nor energy can enter or leave.


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Energy Transfer• heat (q) vs work (w).

Heat• the energy transfer that occurs when two bodies at

different temperatures come in contact with eachother

• depends on the heat capacities involved

Work• an energy transfer between system and surroundings

that is not heat• work of increasing or decreasing volume


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The First Law of Thermodynamics

• Energy can be transferred between the system and surroundings and it can change form, but the totalenergy of the system plus surroundings remainsconstant

Sign Conventionwork done on the system by the surroundings +work done by the system on the surroundings -

heat absorbed by the system from the surroundings +(endothermic)heat absorbed by the surroundings from the system -(exothermic)


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State Variables and Functions

• state variables are independent of path• e.g. P, V, T, n

• q, w, and C (among others) dependent on the pathtaken and are not state variables

• state functions independent of path• e.g. U, H, S, G

• if a system undergoes a long series of steps andreturns to its initial state (a cyclic process), thechange in U or any other state variable is zero

• intensive state properties are independent of the sizeof the system - they do not change when a system isdivided e.g. T, P

• extensive state properties are proportional to the sizeof the system - they do change when a system isdivided e.g. mass, V, n, U

• an extensive property can be converted to anintensive property by describing it per unit ofmaterial (m, n, or V)


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Equations of State• link state variables, most frequently P, V and T

Solids and Liquids• solids and liquids don’t change V much with P or T• first approximation is V�constantGases• first approximation is the ideal gas law PV = nRT• the van der Waals gas equation accounts for

attractive forces between molecules (a) and theintrinsic volume of the molecules (b)

Mixtures• for mixtures, the amount (m or n) of each component

must be specified

Paths• often convenient to pick a path for which the energy

change(s) are easy to calculate - one state variable isheld constant in each step: Isobaric, Isothermal,Isochoric, Adiabatic Cyclic


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Dependence of U and H on P, V and T

Liquids and Solids - volume does not change with PIsobaric

Isochoric

Isothermal

P V P VC .C )U .)U )H = )U


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Gases - significant changes in V and thus w Isobaric

Isochoric

Isothermal


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Relationships between q, )U and )H

For any system undergoing an isochoric process:

Vq = )U

For any system undergoing an isobaric process:

Pq = )H

Phase Changes

Phase Change Name

gas 6 liquid or solid Condensation

solid 6 liquid Fusion, melting

liquid 6 solid Freezing

liquid 6 gas Vaporization

solid 6 gas Sublimation

We are interested in phase changes at constant T and P.

P ex Pw = -P )V q = )H

P P ex)U = q + w = )H - P )VOnly solids and liquids - )V and w are negligible

gasAny gas phase - )V = V .

)H or )U at different T’s:


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Chemical Reactions

A B C Dn A + n B 6 n C + n D

products reagents• exothermic reaction: 3H < 3H , )H<0

products reagents• endothermic reaction: 3H > 3H , )H>0• Hess’ Law

)U Changes at Constant Pressure)U = )H + )(PV)

• only solids and liquids - )V.0 and )U = )H• gases involved, only )V of the gases is important

)(PV) = )nRT)U = )H + )nRT


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Standard Enthalpies of Formation• standard states - most stable state at 1 atm pressure• absolute enthalpy of all elements in their standard

states (H°) is zero

f• standard enthalpy of formation ()H °) of acompound - enthalpy of formation of 1 mole of thecompound at 1 atm pressure from the elements intheir standard states

• for reactions:

f f)H° = 3)H ° (products) - 3)H ° (reagents)

Bond Energies• use a reaction path that involves break and forming

individual bonds• bond dissociation energies are the energies required

to break bonds in the gas phase at 1 atm pressure and25 °C

A-B (g) 6 A (g) + B (g)• for reactions:

)H° = 3BE(reagents) - 3BE(products)


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Entropy• energy considerations alone are not enough to

explain spontaneity of all processes

Statistical View of Entropy• considers the movements of individual molecules and

is concerned with probabilities• example of expansion of a gas from an initial volume

1 2V to a large volume V , probability all molecules

1remaining in V :

• spontaneous processes move from low probabilitysituations, to those with high probability

• entropy is related to probability by the Boltzmann

Bequation: ( k =1.381 x 10 JK ).-23 -1

For an isothermal expansion of a gas:


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Thermodynamic View of Entropy• Entropy is a measure of disorder in the system

rev• q is the maximum q for a given change of state

irrev revq <q

rev irrev irrevbut )S =)S =)S > q /T

The Second Law of Thermodynamics

The sum of the entropy changes in the system andsurroundings is always positive.

system surroundings)S + )S $ 0• entropy is not conserved• disorder occurs spontaneously and thus entropy tends

to increase• the total change in entropy can only approach 0 for

reversible processes - spontaneous processes are notreversible

• for an isolated system where no energy nor materialis exchanged with the surroundings

system)S $ 0


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Factors Affecting Entropy• all entropies increase as T increases• entropy for a gas decreases with increasing pressures

at constant temperature• for monatomic elements, harder solids have lower

entropy than soft• entropy for similar substances increases with

increasing mass• entropy increases with increasing number of atoms • entropy increases with increasing flexibility• solids < liquids < gases

fus revAt constant P: )H = q

fus rev fusand )S = q /T = )H /T• entropy increases when a solid or liquid dissolves in

a solvent• entropy increases when two gaseous species are

mixed together (volume of both parts increase)

• for gas phase reactions • increasing number of molecules - )S +ve• unchanging number of molecules - )S small and

can be +ve or -ve


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• for solution phase reactions the situation is morecomplex as changes in the entropy of both thesolute(s) and solvent must be considered• charge neutralization leads to disorientation of

solvent molecules - )S +ve• charge transfer but no neutralization - small )S• transfer of a non-polar solute from the aqueous

phase to a non-polar solvent leads todisorientation of solvent molecules - )S +ve

The Third Law of Thermodynamics

The entropy of any pure, perfect crystal (A) at 0 K is 0.• as T 60 K, number of states possible for a pure,

perfect crystal 6 1• allows for the calculation of absolute entropies


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Entropy and Chemical Reactions

For a chemical reaction:

A B C Dn A + n B 6 n C + n D

• standard molar entropy (S ) - S at 298 K and 1 atm. 0

• for reactions occurring at other T:


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Gibbs Free Energy

• extensive, thermodynamic, state variable• uses enthalpy and entropy changes to predict if a

reaction is spontaneous• applies to reactions at constant T and P

G / H - TS

A System’s Capacity to do Nonexpansion Work)G =

• , the nonexpansion or useful work, is any work

done on the system that is not expansion (PdV) work• spontaneous process, will be -ve and )G < 0

• non-spontaneous, will be +ve and )G > 0

• at equilibrium, = 0 and )G = 0

Calculation of Gibbs Free Energy• )H and )S for a reaction can be calculated using0 0

tabulated data• at constant T, )G can be calculated at 25°C and 10

atm using:)G = )H - T)S 0 0 0

) completely0f• standard free energy of formation ()G

0fanalogous to )H


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Temperature Dependence of Gibbs Free Energy• if )S is independent of T:

• if )H is independent of T:

• if )H is dependent on T:

Pressure Dependence of Gibbs Free Energy• if all liquids or solids and if )V is independent of P:

• if at least one gas:

Phase Changes• at equilibrium P and T

)G = 0• at other T and P, use equations above,• or if )H and )S are known at the other T and P, use:

)G = )H - T)S


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Helmholtz Free Energy (A)• applies for processes at constant T and V

A / E - TS• )A < 0 (spontaneous process)• )A > 0 (non-spontaneous process)• )A = 0 (at equilibrium)


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Non-covalent Reactions

Ionic• interaction between two fully charged species

Dipole• asymmetric electron distribution in a molecule leads

to partial separation of charge and formation of adipole moment

Induced-dipole• molecule (without a permanent dipole) interacts with

an ion, or permanent dipole, leading to a polarizationand formation of an induced-dipole

London (induced-dipole / induced-dipole)• fluctuations in electron distribution of neutral

molecules lead to an instantaneous dipole whichinturn induces a dipole in a neighbouring molecule,depends on polarizability of the molecule, always anattractive force


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van der Waals• interactions between uncharged molecules, including

permanent dipole - permanent dipole, permanentdipole - induced dipole and steric repulsions

• nonspecific interactions that contribute to energies inall reactions

Hydrogen bond • H attached to O or N can form a weak bond to

another O or NO!HAAAOO!HAAANN!HAAAON!HAAAN

• 15-20 kJ mol ( ~400 kJ mol for a covalent bond)-1 -1

• even weaker in aqueous solution because ofcompetition with the solvent• urea-urea H-bonds in water are only ~5 kJ mol-1

and are considered a model for a peptide bond


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Hydrophobic Interactions• very important in aqueous systems• combination of London, van der Waals and H-

bonding observed in the dissolution of hydrophobicspecies

• water molecules are extensively hydrogen bonded toeach other - moving network of molecules

• hydrophobic molecule does not interact directly withthe water molecules, but disrupts the network

• net result - increase in the order of the system• enthalpy change is small, but entropy change is

significant• the clustering of these groups is favoured

thermodynamically

Amphiphillic species• at surfaces• as micelles• as bilayer vesicles


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Proteins and Nucleic Acids

• proteins - polymers of amino acids• nucleic acids - polymers of nucleotides• primary structure - determined by covalent bonds • secondary structure - determined by the non-covalent

interactions• energy requirements for changes in secondary

structure can provide clues as to the nature of thestructure

Proteins• "-helix - a right-handed helix with a H-bond between

the C=O of one amide and the N!H of another amidefour residue units away on the chain

• a model for the H-bonds in the secondary structuresof proteins is H-bonds between urea molecules inaqueous solution is ~5 kJ mol-1

• consistent with the energy required to denature aportion of a protein largely held together by H-bonds(4.5 kJ mol / amide)-1

• large values of )H for denaturation of proteins0

indicates large numbers of H-bonds being broken


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Nucleic acids• H-bonding between the base pairs on different

strands• London-van der Waals attractions between base pairs

on the same strand and between strands• ionic repulsion between the charged phosphate

groups• these forces as well as interactions with the solvent

and other solutes such as cations determine thesecondary structure

• A-T and A-U base pairs are bound by two H-bonds,while G-C pairs are bound by three so the )H for0

dissociating the G-C pairs is higher• however, the magnitude of the difference depends on

the sequence - the stacking of the base-pairs isstabilized by London and van der Waals forcesbetween neighbouring pairs and between the pairsand the solvent

• binding of small molecules to macromolecules• )H may be positive or negative0

• )S generally large and positive- similar to0

entropy change when two hydrophobic speciesassociate together - the entropy of the solute maydecrease, but the binding releases solventmolecules resulting in a larger increase in thedisorder of the solvent

Thermodynamics • Relationships and … - Test II...The Third Law of Thermodynamics The entropy of...

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