Transcript Chapter 19
Free Energy and Thermodynamics st 1 Law of Thermodynamics Chapter 6: Energy is conserved. Energy cannot be created or destroyed, rather it is transferred from one place to another. Energy can be transferred in two ways. __________ or __________ Internal energy of a system = KE + PE Enthalpy – the first thermodynamic quantity H = E + PDV Spontaneity The first law does not tell us the extent to which a reaction will happen (or not). Reactions are said to be spontaneous in one direction (and non-spontaneous in the opposite direction). Ex) Releasing a ball – which direction will it go – up or down? Spontaneity Which reaction is spontaneous? H2O(l) H2(g) + ½ O2(g) H2(g) + ½ O2(g) H2O(l) Spontaneity Which reaction is spontaneous? 2Fe(s) + 3/2O2(g) Fe2O3(s) Fe2O3(s) 2Fe(s) + 3/2O2(g) Spontaneity Often, it is dependent on the temperature. H2O(s) H2O(l) Spontaneous above or below 0oC? Spontaneity Scientists first thought that the criteria for spontaneity was based solely on whether a reaction was exothermic or endothermic. However, ice melting at room temperature is endothermic as is the dissolution of some salts like NH4Cl. Clearly, a second criteria is needed to predict spontaneity. Carnot Cycle Sadi Carnot theorized about an ideal steam engine – one that worked at 100% efficiency. No heat energy would be lost – all energy is converted to work. Two Types of Processes Reversible – a system is changed in such a method that BOTH the system and surroundings can be returned to their former states by EXACTLY reversing the change. Irreversible – is one that cannot be reversed without altering the system or surroundings permanently. Reversible Processes Phase changes at their melting or boiling point temperature are always reversible. Equilibrium reactions when they reach a steady state are reversible. Irreversible Processes In (a), we have a gas occupying the right half of the container. In (b), the partition is removed and the gas spontaneously expands to fill the container. In (c), the system is restored by compressing the gas with a piston. But, this requires work done by the surroundings changing it permanently!!! Entropy A second quantity in thermodynamics. A measurement of the randomness of a system. Also a state function just like internal energy (E) and enthalpy (H). Thus, DS = Sfinal – Sinitial For any reversible process, DS = qrev / T Units for DS = J/K mol LEP #1 Entropy When a system undergoes a change, both the system and the surroundings are affected. DSuniverse = DSsystem + DSsurroundings When DSuniverse > 0 J/K, process is spontaneous. When DSuniverse < 0 J/K, process is non-spontaneous. When DSuniverse = 0 J/K, process is reversible. 2nd Law of Thermodynamics = the entropy of the universe always increase for a spontaneous process. LEP #2 Molecular Interpretation Molecules can undergo three basic types of motions. Translational Vibrational Rotational Molecular Interpretation As any gas is heated, its average KE increases – KE is proportional to temperature. This additional KE can be split up among the three types of motion. Ludwig Boltzmann – decided to look at entropy from a statistical viewpoint. S = k ln(W) k = Boltzmann’s constant (1.38 x 10-23 J/K) W = number of possible microstates Molecular Interpretation Number of microstates depends on the relevant numbers of particles and the positions they can occupy. Molecular Interpretation The number of microstates is akin to playing cards. Molecular Interpretation An increase in the entropy means that the randomness (or disorder) of the system has increased. Or – an increase in the number of microstates. More or less microstates if we have four molecules of gas rather than two? More or less microstates if we have two decks of cards rather than one? Entropy and Life Human beings (and all life forms) are highly ordered. Does this violate the 2nd Law of Thermodynamics? Entropy and Life You can’t break even! To recharge a battery with 100 kJ of useful energy will require more than 100 kJ because of the Second Law of Thermo! Every energy transition results in a “loss” of energy Its an “Energy Tax” demanded by nature! Predicting DS Solids are rigid and ordered = low entropy Liquids are confined to a specific volume, but are free to move = more entropy Gases are free to move anywhere = high entropy In general, we can predict an increase in the entropy if: More molecules or particles are produced. More gases are produced. Temperature is increased. Volume is increased. LEP #3 rd 3 Law of Thermodynamics The entropy of a pure crystalline substance at absolute zero is zero. As the substance is warmed, its entropy increases. Large increases are seen for phase changes. Entropy Change Absolute entropies, under standard conditions, can be determined for all substances. Values are found in Appendix C. Sosolid < S0liquid < Sogas So increases with molar mass So increases with more atoms in formula Entropy Change The change in entropy for any reaction can be calculated just like DH was in Chapter 5. DSo = S nSo(products) – S nSo(reactants) n = coefficients in chemical reaction LEP #5 Entropy Change What is DSo for: N2(g) + 3 H2(g) 2 NH3(g) Given So for N2(g)=191.5 J/K mol, H2(g)=130.6 J/k mol, and NH3(g)=192.5 J/K mol? This value is for the system. How does the entropy of the surroundings change? DSsurr. = -DHsys. / T If DHsys. = -92.38 kJ, then what is DSsurr.? What is DS universe? Gibbs Free Energy DSuniv. = DSsys. + DSsurr. We have just seen that DSsurr. = -DHsys. / T. So, DSuniv. = DSsys. + -DHsys. / T. Multiplying both sides by –T yields: -TDSuniv. = -TDSsys. + DHsys. Josiah Gibbs decided to label -TDSuniv. As DG. DG = DH – TDS. Signs for DG and their interpretation. Free Energy and Reactions Why is energy “Free”? The change in free energy (DG) represents the maximum amount of energy available to do work. Consider the reaction: C(s, graphite) + 2 H2(g) → CH4(g) DH°rxn = −74.6 kJ = exothermic DS°rxn = −80.8 J/K = unfavorable DG°rxn = −50.5 kJ = spontaneous DG° is less than DH° because some of the released heat energy is lost to increase the entropy of the surroundings Standard Free Energies Like DHfo, there is also a standard free energy of formation for substances – DGfo. These can then be used to calculate the DGo for any reaction using the values in Appendix C. DGo = S nDGfo(products) – S nDGfo(reactants). LEP #6 Free Energy and Temperature Some reactions are ALWAYS spontaneous whereas some are ALWAYS non-spontaneous. Some reactions are DEPENDENT on the temperature Free Energy and Temperature When a reaction becomes just spontaneous (or non spontaneous), the DG = 0. DG = DH – TDS. 0 = DH – TDS. DH = TDS. T = DH / DS. Warning – DH is in kJ and DS is in J. LEP #7 Applying to a Reaction Once we can predict DS based on looking at the reaction AND knowing our relationship between DH and DS, we can also predict the outcome on DG. Ex) 2 SO2(g) + O2(g) 2 SO3(g) ; DHo = -196.6 kJ What would we predict for DS? What effect does this have on DG? LEP #8 Free Energy and Equilibrium The change in free energy along the reaction path is given by the equation: DG = DGo + RT lnQ. At equilibrium, DG = 0 and Q = K. 0 = DGo + RT lnK DGo = -RT lnK LEP #9, 10, 11 Free Energy and Equilibrium Equilibrium and Temperature From Ch 14, we saw that the equilibrium constant is temperature dependent. We can show why with: • Combining these two equations DG° = DH° − TDS° DG° = −RTln(K) • It can be shown that • This equation is in the form y = mx + b