Week 12/Tu: Units ‘30 & 31’ Chemical Change

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Unit 29: Solids -- crystal structure Unit 30: Chemical Spontaneity -- entropy, 2nd Law of Thermo -- spontaneous changes --“free” energy Unit 31: Phase Equilibria -- liquid / gas Issues: Exam 3 next Monday !!! Homework Set 9 due on Saturday @ 08:00AM

http://brownsharpie.courtneygibbons.org/?p=1171

Week 12/Tu: Help Preparing for Exam

© DJMorrissey, 2oo9

★ Tuesday, November 13th, 6 - 8:30pm in N100 BCC (LRC Mock Exam, reservation required (lrc.msu.edu) ★ Thursday, November 15th, 6 - 8:30pm in N100 BCC (LRC Q&A Review Session) ★ Sunday, November18th, 4 - 6pm in 138 Chemistry (Dr. Pollock)

★ Monday, November 19th, EXAM day for everyone

★ Tuesday, November 20th, NO LECTURE – Horray!

Week 12/Tu: There’s more than the 1st Law

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Assume that we have an isolated system that has two identical parts with the exception that one side is hotter than the other. We know that heat will ALWAYS flow from the hot side to the other and establish thermal equilibrium. The change in the total energy of the system and the universe is zero, ΔE = 0, but yet the flow of heat is spontaneous and the direction of the flow is always from the hotter to the cooler part. We need another law that is a concise statement of this experimental fact.

q spontaneously

© DJMorrissey, 2o12

The textbook suggests considering the fate of a ice cube on a table at room temperature. If the ice cube is put into a glass and the system of glass & ice is isolated, the change in the total energy of this system is positive since heat will flow into the glass, every time, ΔEsystem = (+)q. If we put a piece of dry ice inside a flask closed with a balloon, then we will have a different system that does work, ΔEsystem = (+)q + (-)w We would like a descriptive term besides the energy that describes the occurrence of some chemical and other natural processes and not others.

Week 12/Tu: There’s more than the 1st Law

Week 12/Tu: A Famous Description

© DJMorrissey, 2o12

It was noticed a long time ago that Nature seems to prefer “disordered” arrangements over “ordered” arrangements of the same components. Richard Feynman (well known scientist) described “order”: Richard Feynman in the section called “Entropy” of his Lectures on Physics (1963) wrote: “So we now have to talk about what we mean by disorder and what we mean by order. ... Suppose we divide space into little volume elements. If we have black and white molecules, how many ways could we distribute them among the volume elements so that white is on one side and black is on the other? On the other hand, how many ways could we distribute them with no restriction on which goes where? Clearly, there are many more ways to arrange them in the latter case. We measure “disorder” by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy. The number of ways in the separated case is less, so the entropy is less, or the "disorder" is less.”

Thus: It is not that nature particularly favors disordered systems per say, but rather, nature prefer states that have more choices if all other things are equal.

Week 12/Tu: The word “Entropy” itself

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Quoting from Rudolf Clausius (1880): “I prefer going to the ancient languages for the names of important scientific quantities, so that they mean the same thing in all living tongues. I propose, accordingly, to call S the entropy of a body, after the Greek word "transformation". I have designedly coined the word entropy to be similar to energy, for these two quantities are so analogous in their physical significance, that an analogy of denominations seems to me helpful.” The above quote can be found in a book by Leon Cooper: An Introduction to the Meaning and Structure of Physics. Cooper then goes on to comment: “By doing this, rather than extracting a name from the body of the current language (say: lost heat), he succeeded in coining a word that meant the same thing to everybody: nothing.”

The second variable is called entropy and given the symbol S.

The modern understanding of entropy is the number of microscopic states of a system with exactly the same energy. Entropy is a true state function in that the number of microscopic states of the system is independent of the history of that system. For example, we could count them up as indicated by the exercise in the textbook.

Week 12/Tu: 2nd Law Contains an Inequality

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One statement of the second law of thermodynamics is that   ΔSuniv = ΔSsystem + ΔSsurr > 0 for a spontaneous process. Entropy is always increasing, except for those reversible processes with an exact balance between the system and surroundings. Reversible changes take place infinitely slowly (so that the system or observer can’t tell if they are going “forward” or “backward”). The minimum change in the entropy of a system is: ΔS = qrev / T for a reversible process. Note the distinction, the first law is an equality for all processes: ΔEuniv = ΔΕsystem + ΔEsurr = 0 So that there is a fundamental, qualitative difference between energy (conserved) and entropy (increasing).

Week 12/Tu: Combination of ΔH & ΔS

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Chemical reactions and other processes carried out in the laboratory generally involve changes in both the energy and entropy of the system. If the process takes place at constant pressure we should use enthalpy.

ΔS+ ΔH –

Spontaneous All Temp.’s

(0,0)

ΔS + ΔH + Entropy Driven Spontaneous At High Temp.’s

ΔS – ΔH + NOT Spontaneous At all Temp.’s

ΔS – ΔH – Enthalpy Driven Spontaneous At Low Temp.’s

ΔS

ΔH

Week 12/Tu: “Free” energy

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Given the importance of the combination/interplay of enthalpy and entropy in determining the spontaneity of a process, a new state function was introduced by J.W. Gibbs called the free energy. ΔSuniverse = ΔSsystem + ΔSsurroundings > 0 and ΔS = qrev/T ΔSsystem + -ΔH /T > 0 at constant pressure q = -ΔH TΔSsystem – ΔH > 0 ΔH – TΔSsystem < 0 ΔG < 0 One function that describes the overall spontaneity of a process.

Gibbs flipped the equation around to make the sign convention for his free energy function, G, the same as that for enthalpy, H.

Week 12/Tu: DEMO ΔH versus ΔS

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Consider the following chemical reaction: [BaOH2�8 H2O] (s) + 2 NH4Cl (s) à [BaCl2 �2 H2O] (aq) +2 NH3 (aq) + 8 H2O (l) Qualitatively: 3 moles of solids à 3 moles solute & 8 moles liquid Substance ∆H˚f (kJ/mol) S˚298(J/mol·K) ∆G˚f (kJ/mol) Ba(OH)2·8H2O(s) -3342 427 -2793 NH4Cl(s) -341 94.6 -203 BaCl2·2H2O(s) -1460.1 203 -1296.5 NH3(g) -80.3 192 - 26.6 H2O (l) -285.83 75.291 -237.2 ∆H˚ = [-1460 + 2*-80.3 + 8*-285.8] – [-3342 + 2*-341] kJ = 63.5 kJ ∆S˚= [203 + 2*111 + 8*75.3] – [427 + 2*94.6] J/K = 368 J/K ∆G˚ = [-1296.5 + 2*-26.6 + 8*-237.2] – [-2793 + 2*-203] kJ = -46.1 kJ

Week 12/Tu: Examples: ΔS, ΔH, ΔG

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ΔH ΔS T ΔG = ΔH - TΔS H2O (s) à H2O (l), T > 0o C = 273K H2O (l) à H2O (s), T < 0o C = 273K CaSO4 �2 H2O (s) à CaSO4 (s)+2 H2O (l)

Liquid Solid Gas

ΔS+ ΔH +

ΔS+ ΔH +

ΔS++ ΔH++

ΔS – ΔH –

Week 12/Tu: Phase Equilibria, L ßà G

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Solid Liquid Gas The motion of particles in the liquid state can be described by a kinetic theory with a similar distribution to that of a gas but much lower velocities but some are fast.

Fact: all liquids have a vapor pressure that increases with temperature.

Week 12/Tu: Vapor Pressure Example – water

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Atmospheric Pressure (today) Lansing, MI 30.15” 765.7 torr 1.020 bar TBP(water) = 100.2oC 257 m / 846 ft Denver, CO 24.64” 625.9 torr 0.8344 bar TBP(water) = 94.7oC 1655.37 m / 5431 ft Los Alamos, NM 2231 m / 7320 ft 0.772 bar 92.6oC Pressurized Jet plane 0.785 bar – 93oC

760 torr Normal Boiling Pt. à

Week 12/Tu: Vapor Pressure Examples

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