Brown, LeMay Ch 19 AP Chemistry Monta Vista High School Thermodynamics Brown, LeMay Ch 19 AP Chemistry Monta Vista High School

Review In any process energy is neither created nor destroyed. 1st Law of Thermodynamics In any process energy is neither created nor destroyed. When a system changes from one state to another (DE = q + w), it Gains heat (+ q) or loses heat (- q) and/or Does work (- w) or has work done on it (+ w) T and internal energy, E, are state functions (depend only on initial and final states of system and not path taken between them). q and w are not state functions. But why does a reaction occur in a particular direction?

19.1: Spontaneous Processes Reversible reaction: can proceed forward and backward along same path (equilibrium is possible) Ex: H2O freezing & melting at 0ºC Irreversible reaction: cannot proceed forward and backward along same path Ex: ice melting at room temperature Spontaneous reaction: an irreversible reaction that occurs without outside intervention Ex: Gases expand to fill a container, ice melts at room temperature (even though endothermic), salts dissolve in water

19.2: Molecules & Probability Spontaneity of a reaction is related to the number of possible states a system can have. Ex: 2 gas molecules are placed in a two-chambered container, yielding 4 possible states: There is a ½ probability that one molecule will be in each chamber, and a ¼, or (1/2)2, probability that both will be in the right-side chamber.

With 3 molecules: There is a ¾ probability that one molecule will be in one chamber and two in the other, and only a 1/8, or (1/2)3, probability that all 3 molecules will be in the right-side chamber. Frequency All on left Evenly distributed All on right

As the number of molecules increases to 100, a bell-shaped distribution of probable states, called a Gaussian distribution, is observed. # molecules = 100 Carl Gauss (1777-1855) Frequency All on left Evenly distributed All on right

Expanding this to 1 mole of molecules, there is only a (1/2)10^23 probability that every molecule will be in the right-side chamber. # molecules = 1023 Frequency All on left Evenly distributed All on right The Gaussian distribution is so narrow that we often forget that it is a distribution at all, thinking of the most probable state as a necessity.

This demonstrates that: The most probable arrangements are those in which the molecules are evenly distributed. Processes in which the disorder of the system increases tend to occur spontaneously. spontaneous non-spontaneous We take it for granted that what usually happens, always happens.

high K.E. low K.E. These probability distributions apply to the motion and energy of molecules, and thus can predict the most probable flow of heat. We call a process spontaneous if it produces a more probable outcome, and non- spontaneous if it produces a less likely one. spontaneous non-spontaneous evenly distributed K.E.

S is a state function: DS = Sfinal - Sinitial + DS = more randomness Entropy Entropy (S): a measure of molecular randomness or disorder S is a state function: DS = Sfinal - Sinitial + DS = more randomness - DS = less randomness For a reversible process that occurs at constant T: Units: J/mol.K

2nd Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in a reversible (equilibrium) process. S is not conserved; it is either increasing or constant Reversible reaction: DSUNIVERSE = SSYS + SSURR = 0 or SSYS = - SSURR Irreversible reaction: DSUNIV = SSYS + SSURR > 0 Murphy’s Law, applied to the universe!

Examples of spontaneous reactions: Particles are more evenly distributed Particles are no longer in an ordered crystal lattice Ions are not locked in crystal lattice Gases expand to fill a container: Ice melts at room temperature: Salts dissolve in water:

19.3: 3rd Law of Thermodynamics The entropy of a crystalline solid at 0 K is 0. How to predict DS: Sgas > Sliquid > Ssolid Smore gas molecules > Sfewer gas molecules Shigh T > Slow T Ex: Predict the sign of DS for the following: CaCO3 (s) → CaO (s) + CO2 (g) N2 (g) + 3 H2 (g) → 2 NH3 (g) N2 (g) + O2 (g) → 2 NO (g) +, solid to gas -, fewer moles produced ?

19.4: Standard Molar Entropy, Sº Standard state (º): 298 K and 1 atm Units = J/mol·K DHºf of all elements = 0 J/mol However, S° of all elements ≠ 0 J/mol·K See Appendix C for list of values. Where n and m are coefficients in the balanced chemical equation.

DG = DH - TDS DG° = DH° - TDS° 19.5: Gibbs free energy, G Represents combination of two forces that drive a reaction: DH (enthalpy) and DS (disorder) Units: kJ/mol DG = DH - TDS DG° = DH° - TDS° (absolute T) Josiah Willard Gibbs (1839-1903)

Determining Spontaneity of a Reaction If DG is :ion) Positive Forward reaction is non-spontaneous; the reverse reaction is spontaneous Zero The system is at equilibrium

19.6: Free Energy & Temperature DG depends on enthalpy, entropy, and temperature: DG = DH - TDS DH DS DG and reaction outcome - + Always (- 2 O3 (g) → 3 O2 (g) + - Always +; non-spontaneous at all T 3 O2 (g) → 2 O3 (g) - - Spontaneous at low T; non-spontaneous at high T H2O (l) → H2O (s) + + Spontaneous only at high T ; non-spontaneous at low T H2O (s) → H2O (l)

19.7: Free Energy & Equilibria Nernst Equation The value of DG determines where the system stands with respect to equilibrium. DG = DG° + RT ln Q (Nernst Equation) where R = 8.314 J/K•mol Used for calculating DG under experimental conditions from standard conditions DG°. How do you calculate DG° ? Nernst Equation when the system is at equilibrium: Note that DG becomes zero at equilibrium and not DG°

19.7: Free Energy & Equilibria DG Reaction outcome Negative Spontaneous forward rxn, K > 1 Positive Non-spontaneous forward rxn, K < 1 Zero System is at equilibrium, K = 1