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 1 st Law of Thermodynamics

Directionality from the 2 nd 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??

3 rd 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

Heat Capacity When heat is added to a phase it’s temperature increases (No, really…) Not all materials behave the same though! dq=C V dT  where C V is a constant (heat capacity for a particular material) Or at constant P: dq=C p dT Recall that dq p =dH then: dH=C p dT Relationship between C V and C p : 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: C p =a+(bx10 -3 )T+(cx10 -6 )T 2 –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  H 0 R  H 0 R is positive  exothermic  H 0 R is negative  endothermic Example: 2A + 3B  A 2 B 3  H 0 R =H 0 f (A 2 B 3 )-[2H 0 f (A) + 3H 0 f (B)] Heat of Reaction

Entropy of reaction A function of energy ‘dispersing’ Entropy of reaction S 0 R : When  S 0 R is positive  entropy increases as a result of a change in state When  S 0 R is negative  entropy decreases as a result of a change in state

Entropy of the Universe 2 nd 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  G R –  G 0 R = RT ln K AT equilibrium,  G R =0, therefore:  G 0 R = -RT ln K eq where K eq is the equilibrium constant

Equilibrium constants  G 0 R = -RT ln K Rearrange: ln K = -  G 0 R / 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)

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  G 0 R =  H 0 R – T  S 0 R Gibbs Free Energy (G) is a state variable, measured in KJ/mol Tabulated values of  G 0 R are in Appendix

G is a measure of driving force  G R =  H R – T  S R When  G R is negative  forward reaction has excess energy and will occur spontaneously When  G R is positive  there is not enough energy in the forward direction, and the BACKWARD reaction will occur When  G R is ZERO  reaction is AT equilibrium  G R –  G 0 R = RT ln K

Free Energy Examples  G 0 R =  H 0 R – T  S 0 R H 2 O (l) = kcal/mol (NIST value: Fe 2+ + ¼ O 2 + H +  Fe 3+ + ½ H 2 O =[-4120+(-63320*0.5)]-[ (3954*0.25)] =[-67440]-[-19893]= cal/mol

Using K eq to define equilibrium concentrations  G 0 R = -RT ln K eq  G R =  G 0 R + RT ln Q K eq sets the amount of ions present relative to one another for any equilibrium condition AT Equilibrium  G R = 0