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Energy

Energy. Many ways to describe energy changes in thermodynamics Originally developed to describe changes in heat and ‘work’ (think a steam engine piston)

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Energy

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  1. 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…

  2. 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

  3. 1st Law of Thermodynamics • 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 • DU = 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

  4. 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??

  5. 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

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

  7. 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)

  8. Heat of Reaction • Heat absorbed by a chemical reaction • Heat of reaction DH0R • DH0R is positive  exothermic • DH0R is negative  endothermic • Example: 2A + 3B  A2B3 • DH0R =H0f(A2B3)-[2H0f(A) + 3H0f(B)]

  9. Entropy of reaction • A function of energy ‘dispersing’ • Entropy of reaction S0R: • When DS0R is positive  entropy increases as a result of a change in state • When DS0R is negative  entropy decreases as a result of a change in state

  10. 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…

  11. Equilibrium Constant DGR – DG0R = RT ln K AT equilibrium, DGR=0, therefore: DG0R = -RT ln Keq where Keq is the equilibrium constant

  12. DG0R = -RT ln K Rearrange: ln K = -DG0R / 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) Equilibrium constants

  13. 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 DG0R = DH0R – TDS0R • Gibbs Free Energy (G) is a state variable, measured in KJ/mol • Tabulated values of DG0R are in Appendix

  14. G is a measure of driving force • DGR = DHR – TDSR • When DGR is negative  forward reaction has excess energy and will occur spontaneously • When DGR is positive  there is not enough energy in the forward direction, and the BACKWARD reaction will occur • When DGR is ZERO  reaction is AT equilibrium DGR – DG0R = RT ln K

  15. Free Energy Examples DG0R = DH0R – TDS0R 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

  16. Using Keq to define equilibrium concentrations DG0R = -RT ln Keq DGR = DG0R + RT ln Q • Keq sets the amount of ions present relative to one another for any equilibrium condition AT Equilibrium DGR = 0

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