Energy

• Many ways to describe energy changes in thermodynamics

• Originally developed to describe changes in heat and ‘work’ (think a steam engine piston)

• Energy flow also describes chemical reactions in systems – but since there is no energy ‘particle’ we must do all of this in a relative sense i.e. one think has more ‘energy’ than another and wins…

Reference States• We recall that we do not know absolute

energies!!!• We can describe any reaction or description

of reaction relative to another this is all we need to describe equilibrium and predict reaction direction, just need an anchor…

• Reference States:– Standard state: 1 atm pressure, 25°C– Absolute states – where can a value be defined?

entropy at 0 Kelvin

• Aka the Law of conservation of energy, Gibbs in 1873 stated energy cannot be created or destroyed, only transferred by any process

• The net change in energy is equal to the heat that flows across a boundary minus the work done BY the system

• U = q + w– Where q is heat and w is work– Some heat flowing into a system is converted to work and

therefore does not augment the internal energy

1st Law of Thermodynamics

Directionality from the 2nd Law

• For any spontaneous irreversible process, entropy is always increasing

• How can a reaction ever proceed if order increases?? Why are minerals in the earth not falling apart as we speak??

T

dqdS

3rd Law of Thermodynamics

• The heat capacities of pure crystalline substances become zero at absolute zero

• Because dq = CdT and dS = dq / T

• We can therefore determine entropies of formation from the heat capacities (which are measureable) at very low temps

T

configp

abs SdTT

CS

0

T

dTCdS p

Heat Capacity• When heat is added to a phase it’s temperature

increases (No, really…)• Not all materials behave the same though!

• dq=CVdT where CV is a constant (heat capacity for a particular material)

• Or at constant P: dq=CpdT

• Recall that dqp=dH then: dH=CpdT

• Relationship between CV and Cp:

TV

CC Vp 2

Where a and b are coefficients of isobaric thermal expansion and isothermal compression, respectively

Enthalpy at different temps…

• HOWEVER C isn’t really constant….• C also varies with temperature, so to really

describe enthalpy of formation at any temperature, we need to define C as a function of temperature

• Maier-Kelley empirical determination:• Cp=a+(bx10-3)T+(cx10-6)T2

– Where this is a fit to experimental data and a, b, and c are from the fit line (non-linear)

• Heat absorbed by a chemical reaction

• Heat of reaction H0R

• H0R is positive exothermic

• H0R is negative endothermic

• Example: 2A + 3B A2B3

• H0R =H0

f(A2B3)-[2H0f(A) + 3H0

f(B)]

)()( 000 reactantsHnproductsHnHi

fiifii

iR

Heat of Reaction

Entropy of reaction

• A function of energy ‘dispersing’

• Entropy of reaction S0R:

• When S0R is positive entropy increases as a

result of a change in state

• When S0R is negative entropy decreases as

a result of a change in state

)()( 000 reactantsSnproductsSnS ii

iii

iR

Entropy of the Universe

• 2nd law of thermodynamics – entropy always increases.

• Certain amount of heat ‘energy’ in room, an isolated system

• Glass of ice – melts in time energy is dispersing to a point where everything has the same energy

• Gives direction to any process…

Equilibrium Constant

GR – G0R = RT ln K

AT equilibrium, GR=0, therefore:

G0R = -RT ln Keq

where Keq is the equilibrium constant

Equilibrium constants

G0R = -RT ln K

Rearrange:

ln K = -G0R / RT

Find K from thermodynamic data for any reaction

• Q is also found from the activities of the specific minerals, gases, and species involved in a reaction (in turn affected by the solution they are in)RT

GR

eK0

i

ni

nproductsQ

]reactants[

][

J. Willard Gibbs• Gibbs realized that for a reaction, a certain

amount of energy goes to an increase in entropy of a system and a certain amount goes to a heat exchange for a reaction.

• G = H –TS or G0R = H0

R – TS0R

• Gibbs Free Energy (G) is a state variable, measured in KJ/mol

• Tabulated values of G0R are in Appendix

)reactants()( 000i

iii

iiR GnproductsGnG

G is a measure of driving force• GR = HR – TSR

• When GR is negative forward reaction has excess energy and will occur spontaneously

• When GR is positive there is not enough energy in the forward direction, and the BACKWARD reaction will occur

• When GR is ZERO reaction is AT equilibrium

GR – G0R = RT ln K

Free Energy Examples

G0R = H0

R – TS0R

H2O(l)=-63.32 kcal/mol (NIST value: http://webbook.nist.gov/chemistry/)

• Fe2+ + ¼ O2 + H+ Fe3+ + ½ H2O=[-4120+(-63320*0.5)]-[-21870+(3954*0.25)]

=[-67440]-[-19893]=-47547 cal/mol

)reactants()( 000i

iii

iiR GnproductsGnG

Using Keq to define equilibrium concentrations

G0R = -RT ln Keq

GR = G0R + RT ln Q

• Keq sets the amount of ions present relative to one another for any equilibrium condition

i

ni

n

eq reactants

productsQK

][

][

AT Equilibrium

i

ni

n

eq reactants

productsK

][

][

GR = 0