 # Chemical Thermodynamics Unit 14: Chemical Thermodynamics Dr. Jorge L. Alonso Miami-Dade College – Kendall Campus Miami, FL Textbook Reference: Chapter.

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Chemical Thermodynamics Unit 14: Chemical Thermodynamics Dr. Jorge L. Alonso Miami-Dade College – Kendall Campus Miami, FL Textbook Reference: Chapter # 15 (sec.12-17) Module # 3 (sec. VIII-XII) CHM 1046: General Chemistry and Qualitative Analysis

Chemical Thermodynamics First Law of Thermodynamics The law of conservation of energy: energy cannot be created nor destroyed. (James Joule in 1843 )James Joule  E = q + w w = P  V  E = q + P  V  E = q +  RT  E sys +  E surr = 0  E sys = -  E surr Therefore, the total energy of the universe is a constant. Energy can, however, be converted from one form to another or transferred from a system to the surroundings or vice versa.

Chemical Thermodynamics Second Law of Thermodynamics Do all processes that loose energy occur spontaneously (by themselves, without external influence)?????? First Law of Thermodynamics Stone E1E1 E2E2  E = E 2 – E 1 Spontaneity + Work - (work + heat)

Chemical Thermodynamics Spontaneous Processes can proceed without any outside intervention. {Spontaneity} Processes that are spontaneous in one direction are nonspontaneous in the reverse direction.

Chemical Thermodynamics Spontaneous Processes Processes that are spontaneous at one temperature may be nonspontaneous at other temperatures. Above 0  C it is spontaneous for ice to melt. Below 0  C the reverse process is spontaneous. Is the spontaneity of melting ice dependent on anything? Spontaneous @ T > 0ºC Spontaneous @ T < 0ºC

Chemical Thermodynamics Spontaneity Thermodynamics vs. Kinetics C diamond C graphite vs. Speed

Chemical Thermodynamics Stone + Work Irreversible Processes Heat energy is lost to dissipation and that energy will not be recoverable if the process is reversed. Irreversible processes cannot be undone by exactly reversing the change to the system. Spontaneous processes are irreversible. In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process. E1E1 E2E2 - (work + heat) Reversible Processes

Chemical Thermodynamics Entropy (S) Entropy (S) is a term coined by Rudolph Clausius in the 1850’s. Clausius chose "S" in honor of Sadi Carnot (who gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics).Sadi Carnotheat enginesCarnot cycle second law of thermodynamics Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered, qTqT Entropy (S) = Entropy is a measure of the energy that becomes dissipated and unavailable (friction, molecular motion = heat).

Chemical Thermodynamics Entropy (S) Entropy can be thought of as a measure of the randomness (disorder) of a system. It is related to the various modes of motion in molecules. {Entropy.WaterBoiling} Like total energy, E, and enthalpy, H, entropy is a state function. Therefore,  S = S final  S initial Solid Liquid Gas ENTROPYENTROPY

Chemical Thermodynamics Second Law of Thermodynamics the entropy of the universe increases for spontaneous (irreversible) processes. the entropy of the universe does not change for reversible processes.  S univ =  S system +  S surroundings > 0  S univ =  S system +  S surroundings = 0

Chemical Thermodynamics Second Law of Thermodynamics All spontaneous processes cause the entropy of the universe to increase. ENTROPIC DOOM! So what is our fate as a result of the second law operating in our Universe?

Chemical Thermodynamics Entropy on the Molecular Scale Molecules exhibit several types of motion (Kinetic energies):  Translational: Movement of a molecule from one place to another.  Vibrational: Periodic motion of atoms within a molecule.  Rotational: Rotation of the molecule on about an axis or rotation about  bonds. Boltzmann envisioned the motions of a sample of molecules at a particular instant in time.  This would be akin to taking a snapshot of all the molecules.  He referred to this sampling as a microstate (W) of the thermodynamic system Entropy is ……. S = k ln W …..where k is the Boltzmann constant, 1.38  10  23 J/K.

Chemical Thermodynamics Entropy on the Molecular Scale The number of microstates (W) and, therefore, the entropy (S) tends to increase with increases in which variables….  Temperature (T).  Volume (V).  The number of independently moving molecules (  ). S = k ln W …..where k is the Boltzmann constant, 1.38  10  23 J/K.

Chemical Thermodynamics Entropy Changes CaCl 2 (s) Ca 2+ (aq) + 2Cl - (aq) H2OH2O H 2 O (l) H 2 O (g) Heat 2 H 2 O (l) 2 H 2 (g) + O 2(g) Electricity 16 CO 2(g) + 18 H 2 O (g) 2 C 8 H 18 (l) + 25 O 2 (g)  gas= 34-25 = +9  /2 = 4.5  C 8 H 18 In which of the following does Entropy increase & WHY?…….  Gases are formed from liquids and solids.  Liquids or solutions are formed from solids.  The number of gas molecules (or moles) increases. {*EntropySolutions.KMnO 4(aq) } {*Entropy&PhaseOfMatter} Entropy increases with the freedom of motion of molecules. S (g) > S (l) > S (s)

Chemical Thermodynamics Third Law of Thermodynamics The entropy (S) of a pure crystalline substance at absolute zero (-273°C) is 0.

Chemical Thermodynamics Standard Entropies Standard entropies tend to increase with increasing molar mass. Larger and more complex molecules have greater entropies (greater ways to execute molecular motions) {*Entropy&MolecuarSize} {Entropy&Temp}C 7 H 15 @ 500 K S=921J/nK vs, @ 200 K

Chemical Thermodynamics Absolute Entropy (S) @ - 237°C (0 K), S = 0 Standard Entropy (S ˚ ) @ 25°C (298 K), S = ???? Calculate the sum of all the infinitesimally small changes in entropy as T varies from T=0  T= 298, by taking its Integral. Standard Entropies (298 K) from Absolute Entropies (0K) S°S° Temp (K) Solid LiquidGas  H° fus  H° vap q = mc  T 298 S

Chemical Thermodynamics Entropy Changes in the System where n and m are the coefficients in the balanced chemical equation.  S° syst =  S° rxn @ T Entropy changes for a reaction (= system) can be estimated in a manner analogous to that by which  H is estimated:

Chemical Thermodynamics Problem: Calculate the standard entropy changes for the following reaction at 25 o C. N 2 (g) + 3 H 2 (g)  2 NH 3 (g)  S° =  n  S° (prod) -  m  S° (react)  S° = - 198.3 J/  2(192.5) – [(191.5)+3(130.6)] Entropy Changes in the System

Chemical Thermodynamics Thermodynamic Changes in Systems (Chem. Reactions) Appendix 1 (CHM 1046 Module): notice  S° is in J not kJ.  G  rxn =   G  f (products)    G  f (reactants)  H  rxn =   H  f (products) -  H  f (reactants) ☺

Chemical Thermodynamics Entropy Changes in the Surroundings Heat (q) that flows into or out of the system changes the entropy of the surroundings:  S surr ∝ - (q sys ) For an isothermal process:  S surr = (q sys ) T At constant pressure, q sys is simply  H  for the system. System q q q q q q q  S surr =  H sys T Surroundings What in a chemical reaction causes entropy changes in the surroundings?

Chemical Thermodynamics Entropy Change in the Universe Problem: Calculate the  S univ for the synthesis of ammonia @ 25 o C. N 2 (g) + 3 H 2 (g)  2 NH 3 (g)  H° rxn = - 92.6 kJ/mol  S surr = -  H sys T  S surr = 311 J/K·mol  S univ =  S syst or rxn +  S surr  n  S (prod) -  m  S (react)  S° syst = - 199 J/K·mol 2(192.5) – [(191.5)+3(130.6)]  S univ = - 198.3 J/K·mol + 311 J/K·mol  S univ = 113 J/K·mol

Chemical Thermodynamics Entropy Change in the Universe Then:  S univ =  S syst +  H system T  S univ =  S syst or rxn +  S surr  S surr = -  H sys T Since:  T  S univ =  H syst  T  S syst  T  S univ is defined as the Gibbs (free) Energy,  G.  T  S univ =  T  S syst +  H syst J. Willard Gibbs USA, 1839-1903 Multiplying both sides by  T,

Chemical Thermodynamics When  S univ is positive,  G is negative. When  G is negative, the process is spontaneous. Gibbs Free Energy (G) Gibbs Energy (-TΔS) measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Technically, the Gibbs free energy is the maximum amount of non-expansion work which can be extracted from a closed system or this maximum can be attained only in a completely reversible process.isothermalisobaricthermodynamic systemclosed systemreversible process  G univ =  H sys  T  S sys  T  S univ = ☺

Chemical Thermodynamics Free Energy Changes At temperatures other than 25°C,  G° =  H   T  S  How does  G  change with temperature? There are two parts to the free energy equation:   H  — the enthalpy term  T  S  — the entropy term The temperature dependence of free energy, then comes from the entropy term. ☺

Chemical Thermodynamics Spontaneity: Enthalpy & Entropy  G° =  H   T  S  Spontaneous @ all T NonSpontaneous @ all T Spontaneous @ high T Spontaneous @ low T

Chemical Thermodynamics Spontaneity: Enthalpy & Entropy {Entropy Driven Reactions} {Entropy & Enthalpy Driven Reaction} {Enthalpy Driven Reaction} Na 2 CO 3(s) + HCl (aq) NaCl (aq) + CO 2 (g) 2 H 2(g) + O 2 (g) 2 H 2 O (g) NH 4 NO 3(s) NH 4 + (aq) + NO 3 - (aq)  n = 2-3 = -1  S = +  H = +  G =  H  ( T  S  ) {EntropySyst+Surr.FormationOfWater} (-T  S) (+T  S)  H = -  S = -  H = -  S = + Enthalpy Entropy H2OH2O

Chemical Thermodynamics Problems  G° =  H  T(  S  ) (-763) – (-804) +41 (.3549) – (.2219) +.1330  G° =  H   T  S   = (131.3kJ)  T(.133kJ) T = 987 TiCl 4(l)  TiCl 4(g) (-T) Reactant Product

Chemical Thermodynamics Standard Free Energy Changes Analogous to standard enthalpies of formation are standard free energies of formation,  G . f  G  =  n  G  (products)   m  G  f (reactants) f where n and m are the stoichiometric coefficients.

Chemical Thermodynamics Standard Free Energy Changes 12 CO 2(g) + 6 H 2 O (g) 2 C 6 H 6 (l) + 15 O 2 (g)  G  rxn =  n  G  (prod)   m  G  (react) f Calculate the standard free energy changes for the above reaction @ 25 °C. f [12(-394) + 6(-229)] – [2(125) + 15 (0)] – [2 C 6 H 6 (l) + 15 O 2(g) ] [12 CO 2(g) + 6 H 2 O (g) ]  G  rxn = - 6352 J/mol · K Standard Molar Gibbs Energy of Formation (  G° f ) CO 2 (g) -394 H 2 O (g) -229 C 6 H 6 (l) 125

Chemical Thermodynamics Fourth Law of Thermodynamics: Emergence Complex emergent systems spontaneously (-  G) arise when energy flows through a collection of many interacting particles, resulting in new patterns of complex behaviors that are much more than the sum of the individual parts (+  S) The formation of these complex patterns in emergent systems is more efficient in the dissipation of energy (-  H), thus speeds up the increase of entropy in the universe.  G =  H -T  S A precise definition of emergence and a useful mathematical formulation of this phenomenon remains elusive. C  f [n, i,  E(t)] Examples: cells forming living organisms; stars forming galaxies; neurons forming conscious brain.

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