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Chapter2 140330083641-phpapp02
- 1. Chapter 2:Chapter 2: Alkanes,Alkanes, Thermodynamics, andThermodynamics, and KineticsKinetics 2,2,4-Trimethylpentane:2,2,4-Trimethylpentane: AnAn octaneoctane
- 2. CombustionCombustion How warm,How warm, how fast?how fast? PetroleumPetroleum !!!!
- 3. All Reactions AreAll Reactions Are EquilibriaEquilibria -23.4 kcal/mol-23.4 kcal/mol ““Barrier” kcal/molBarrier” kcal/mol ExothermicityExothermicity CHCH33Cl + NaCl + Na++ -- OHOH CH3OH + Na+ Na++ ClCl-- CHCH44 + O+ O22 COCO22 + 2H+ 2H22OO What governs these equilibria?What governs these equilibria? ~20~20 highhigh -213 kcal/mol-213 kcal/mol Equilibrium lies very much to the right.Equilibrium lies very much to the right. oror
- 4. 1.1. Chemical Thermodynamics:Chemical Thermodynamics: Energy changes during reaction, extent ofEnergy changes during reaction, extent of “completion of equilibration,” “to the left/right,”“completion of equilibration,” “to the left/right,” “driving force.”“driving force.” 2. Chemical Kinetics2. Chemical Kinetics:: How fast is equilibrium established; rates ofHow fast is equilibrium established; rates of disappearance of starting materials or appearancedisappearance of starting materials or appearance of productsof products Chemical Thermodynamics andChemical Thermodynamics and KineticsKinetics The two principles may or may not go in tandemThe two principles may or may not go in tandem
- 5. [ ][ ] = concentration in mol L= concentration in mol L-1-1 Equilibria: Two typical casesEquilibria: Two typical cases [[AA]] [[reactantsreactants]] [[BB]] [[productsproducts]] KK = equilibrium constant= equilibrium constant AA BB KK == [[CC][][DD]] [[AA][][BB]] IfIf KK large: reaction “complete,” “to the right,” “downhill.”large: reaction “complete,” “to the right,” “downhill.” How do we quantify?How do we quantify? Gibbs free energy, ∆Gibbs free energy, ∆G°G° KK A +BA +B C + DC + D KK ==KK ==1.1. 2.2.
- 6. Gibbs Free Energy, ∆Gibbs Free Energy, ∆ G°G° ∆∆G°G° = -= -RRTT lnlnKK = -2.3= -2.3 RRTT loglogKK TT in kelvins, K (zero kelvin = -273 °C)in kelvins, K (zero kelvin = -273 °C) RR = gas constant ~ 2cal deg= gas constant ~ 2cal deg-1-1 molmol-1-1 LargeLarge KK : Large: Large negativenegative ∆∆G°G° : downhill: downhill
- 7. At 25ºC (298°K):At 25ºC (298°K): ΔΔGºGº = - 1.36 log= - 1.36 logKK Equilibria and FreeEquilibria and Free EnergyEnergy
- 8. ∆∆G°G° == ∆∆H°H° -- TT∆∆S°S° calcal-1-1 degdeg-1-1 molmol-1-1 oror entropy unitsentropy units,, Kcal molKcal mol-1-1 EnthalpyEnthalpy ∆∆H°H° == heatheat of the reaction;of the reaction; for us, mainly due to changes in bondfor us, mainly due to changes in bond strengths:strengths: ∆∆H°H° = (Sum of strength of bonds broken)= (Sum of strength of bonds broken) – (sum of strengths of bonds made)– (sum of strengths of bonds made) EnthalpyEnthalpy ∆∆H°H° and Entropyand Entropy ∆∆S°S° oror e.u.e.u.
- 9. CCHH33CCHH22――HH ClCl――ClCl CCHH33CCHH22――ClCl ++ HH――ClCl 101101 10310384845858 ∆∆H°H° negative: called “negative: called “exothermicexothermic”” if positive: called “if positive: called “endothermicendothermic”” ∆∆S°S° = change in the= change in the “order”“order” of theof the system. Nature strives for disorder.system. Nature strives for disorder. More disorder =More disorder = positivepositive ∆∆SS °° (makes(makes a negative contribution to ∆a negative contribution to ∆G°G° )) ∆∆H°H° = 159 – 187 = -28 kcalmol= 159 – 187 = -28 kcalmol-1-1 ++ Example:Example:
- 10. Boltzmann’s Tombstone (1844-Boltzmann’s Tombstone (1844- 1906)1906) SS == kk x logx logWW ““ChaosChaos”” EntropyEntropy Boltzmann’s constantBoltzmann’s constant Two balls in two tight boxes:Two balls in two tight boxes: A.A. Confined to one box:Confined to one box: 1 Way1 Way B.B. Open access to second box:Open access to second box: 6 Ways: 1-2, 1-3, 1-4, 2-3, 2-4, 3-46 Ways: 1-2, 1-3, 1-4, 2-3, 2-4, 3-4 (Microstates(Microstates or extent ofor extent of freedom)freedom)
- 11. Ice creamIce cream makers:makers: cool withcool with ice/NaClice/NaCl;; Dissolution ofDissolution of salt issalt is endothermicendothermic,, but driven bybut driven by entropyentropy ∆∆H°H° = -15.5 kcal mol= -15.5 kcal mol-1-1 If # of molecules unchanged,If # of molecules unchanged, ∆∆S°S° small,small, ∆∆H°H° controls ( wecontrols ( we can estimate value from bondcan estimate value from bond strength tables)strength tables) ∆∆S°S° = -31.3 e.u.= -31.3 e.u. CCHH22 CCHH22 ++ HHClCl CCHH33CCHH22ClCl 2 molecules2 molecules 1 molecule1 molecule Chemical example:Chemical example:
- 12. RatesRates All processes haveAll processes have “activation barriers”“activation barriers”.. Rate controlled by:Rate controlled by: 1.1. Barrier heightBarrier height (structure of transition(structure of transition state TS)state TS)
- 13. 2.2. ConcentrationConcentration (the number of collisions(the number of collisions increase with concentration)increase with concentration) 3.3. TT (increased T means faster moving(increased T means faster moving molecules; number of collisions increases)molecules; number of collisions increases) 4. “4. “ProbabilityProbability” factor (how likely is a” factor (how likely is a collision to lead to reaction; depends oncollision to lead to reaction; depends on sterics, electronics)sterics, electronics)
- 14. Boltzmann DistributionBoltzmann Distribution TheThe average kinetic energyaverage kinetic energy of molecules at room temperatureof molecules at room temperature isis ~ 0.6 kcal/mol~ 0.6 kcal/mol.. What supplies the energy to get over the barrier?What supplies the energy to get over the barrier?
- 15. Rate measurementsRate measurements : Give: Give Rate LawsRate Laws, tell us, tell us something about TS structure. Most common:something about TS structure. Most common: If rate =If rate = kk [A][A] UnimolecularUnimolecular reaction (TS involves only A)reaction (TS involves only A) AA BB1.1. Reaction RateReaction Rate 1st1st orderorder rate lawrate law
- 16. If rate =If rate = kk [A][B][A][B] 22ndnd orderorder rate lawrate law BimolecularBimolecular reaction (TS involves both A and B).reaction (TS involves both A and B). How do we measure barrier ?How do we measure barrier ? Energy of activationEnergy of activation from Arrhenius equation:from Arrhenius equation: kk == RTRT --EEaa AeAe 2. A + B C2. A + B C at high T, k = A, “maximum rate”
- 17. Potential EnergyPotential Energy DiagramsDiagrams ReactantReactant ProductProduct [A][A] [B][B] ∆∆HH °° (when(when ∆∆SS °° small)small)∆∆GG °° EEaa kkrr kkff Reaction coordinate =Reaction coordinate = progress of reactionprogress of reaction kk forwardforward kk reversereverse KK == [A][A] [B][B] == [TS][TS] EE ‡
- 18. Many reactions have many steps, but there isMany reactions have many steps, but there is always aalways a rate determiningrate determining TSTS (bottleneck).(bottleneck). TSTS Rate Determining TransitionRate Determining Transition StateState
- 19. AA BB CC Which is right: On heating,Which is right: On heating, a.a. Compound A converts to C directly.Compound A converts to C directly. b.b. It goes first to B and then to C.It goes first to B and then to C. c.c. It stays where it is.It stays where it is. Problem:Problem:
- 20. AcidAcid--BaseBase EquilibriaEquilibria AcidAcid Conjugate BaseConjugate Base Brønsted and Lowry:Brønsted and Lowry: Acid = proton donorAcid = proton donor Base = proton acceptorBase = proton acceptor HHA + HA + H22OO HH33O +O + AA++ --
- 21. OO HH HH HH ClCl HH HH OOHH ++ ClCl AcidAcid--BaseBase: Electron: Electron “Pushing” and“Pushing” and ElectrostaticsElectrostatics ++ -- ++ ++ ++ +1+1 -1-1 AA BB Charge moves:Charge moves: e-pushinge-pushing arrowsarrows
- 22. AcidityAcidity constantconstant mol/Lmol/LSolvent 55Solvent 55KK == [H[H33O] [O] [AA]] [[HAHA] [H] [H22O]O] KKaa == KK x 55 =x 55 = [H[H33O][O][AA]] [[HAHA]] ++ ++ -- -- ppKKaa = -log= -log KKaa HHA + HA + H22OO HH33O +O + AA ++ --
- 23. AcidityAcidity AcidityAcidity increases with:increases with: 1. Increasing size of A (H A gets weaker; charge1. Increasing size of A (H A gets weaker; charge is better stabilized in larger orbital; down the PT)is better stabilized in larger orbital; down the PT) 3. Resonance, e.g.,3. Resonance, e.g., 2. Electronegativity (moving to the right in PT)2. Electronegativity (moving to the right in PT) CCHH33OOHH 15.515.5 CCHH33OO -- :::: :: :::: CCHH33CCOOHH OO :::: :::: 4.34.3 CCHH33 OO :::: :::: OOCC ::-- ppKKaa OOHH OO :::: :::: OO SS::-- OO:::: :::: HH22SOSO44 -5.0-5.0
- 24. StrongStrong WeakWeak VeryVery weakweak Relative Acid StrengthsRelative Acid Strengths
- 25. Lewis acids:Lewis acids: e-deficiente-deficient Lewis bases:Lewis bases: BBFF FF FF Lone e-pairsLone e-pairs 6e6e NN RR RR RR e-pushinge-pushing arrowsarrows BB FF FF FF RR RR OO OO RR RR BFBF33 ++ -- R―R―SSR―R―OO―R―R LewisLewis AcidsAcids andand BasesBases --
- 27. HydrocarbonsHydrocarbons withoutwithout Straight chain:Straight chain: CCHH33CCHH22CCHH22CCHH33 AlkanesAlkanes Branched:Branched: CCCCHH33 CCHH33 CCHH33 HH CC44HH1010 2-Methylpropane2-Methylpropane CC44HH1010 ButaneButane CCHH33 CCHH33 functional groupsfunctional groups Line notation:Line notation: 1 Å = 101 Å = 10-8-8 cmcm
- 28. SameSame molecular formulamolecular formula,, differentdifferent connectivityconnectivity Cyclic:Cyclic: Bicyclic:Bicyclic: Polycyclic . . . . . .Polycyclic . . . . . . CyclohexaneCyclohexane CC66HH1212 Bicyclo[2.2.0]octaneBicyclo[2.2.0]octane CC88HH1414 andand areare constitutional isomers.constitutional isomers.
- 29. InsertInsert-CH-CH22-- groups intogroups into CC-- CC bonds.bonds. Straight chainStraight chain CCHH33((CCHH22))xxCCHH33 General molecular formulaGeneral molecular formula for acyclic systems.for acyclic systems. Cyclic alkanes:Cyclic alkanes: CCnnHH22nn HomologousHomologous series:series:
- 30. Barry SharplessBarry Sharpless (Scripps)(Scripps) NP 2001NP 2001 Dat e Mon Sep 12 23:56:24 EDT 2005 Cou nt 26,676,640 organic and inorganic substances 56,744,740 sequences
- 31. Angew. Chem. Int. Ed. 2005, 44, 1504 –1508 (edited) The development of modern medicine largely depends on the continuous discovery of new drug molecules for treating diseases. One striking feature of these drugs is their relatively small molecular weight (MW), which averages only 340. Recently, drug discovery has focused on even smaller building blocks with MW of 160 or less to be used as lead structures that can be optimized for biological activity by adding substituents. At that size it becomes legitimate to ask how many such very small molecules would be possible in total within the boundaries of synthetic organic chemistry? To address this question we have generated a database containing all possible organic structures with up to 11 main atoms under constraints defining chemical stability and synthetic feasibility. The database contains 13.9 million molecules with an average MW of 153, and opens an unprecedented window on the small-molecule chemical universe. Virtual Exploration of the Small-Molecule Chemical Universe below 160 Daltons Tobias Fink, Heinz Bruggesser, and Jean-Louis Reymond*
- 32. The Names of Alkanes are BasedThe Names of Alkanes are Based on theon the IUPAC RulesIUPAC Rules
- 33. Change endingChange ending –ane–ane toto –yl–yl, as in, as in methmethaneane / meth/ methylyl, hex, hexaneane / hex/ hexylyl Short notation: AlkaneShort notation: Alkane R-HR-H / alkyl/ alkyl R-R- ““Lingo”: RCLingo”: RCHH22 ““primaryprimary”” Naming AlkylNaming Alkyl SubstituentsSubstituents CC RR RR RR ““tertiarytertiary””CC HH RR RR ““secondarysecondary””
- 34. IUPAC RulesIUPAC Rules 1.1. Find theFind the longest chainlongest chain and name it (Table 2-5)and name it (Table 2-5) CCHH33CCHHCCHH22CCHH33 CCHH33 A (methyl substituted)A (methyl substituted) butanebutane AnAn octaneoctane (substituted by ethyl,(substituted by ethyl, two methyls)two methyls) When there are twoWhen there are two equal longestequal longest chains,chains, choose the one withchoose the one with more substituentsmore substituents 4 substituents4 substituents 3 substituents3 substituents
- 35. 2. Name substituents (as alkyl or2. Name substituents (as alkyl or halohalo)) a.a. For straight chain R: Methyl, ethyl, propylFor straight chain R: Methyl, ethyl, propyl etc.etc. b.b. For branched chain R:For branched chain R: αα. Find longest chain (starting from point of. Find longest chain (starting from point of attachment)attachment) ββ.. Name substituentsName substituents Example:Example: (Methylpropyl)(Methylpropyl) Halo: Bromo, fluoro, chloro, iodoHalo: Bromo, fluoro, chloro, iodo
- 36. Branched Alkyl GroupsBranched Alkyl Groups
- 37. c.c. Multiple same substituents:Multiple same substituents: ForFor R = straightR = straight, use prefix di-, tri-, tetra-,, use prefix di-, tri-, tetra-, penta-, etc.:penta-, etc.: DimethylDimethylhexanehexane ForFor R = branchedR = branched,, use: bis-, tris-, tetrakis-,use: bis-, tris-, tetrakis-, etc., and alkyl name in parentheses:etc., and alkyl name in parentheses: Bis(methylpropyl)Bis(methylpropyl)
- 38. dd.. Common names: we will use colloquiallyCommon names: we will use colloquially isopropyl,isopropyl, terttert-butyl, neopentyl-butyl, neopentyl
- 39. 33. Number stem, starting from the end. Number stem, starting from the end closest to a substituent:closest to a substituent: Branched substituents: Number from carbonBranched substituents: Number from carbon ofof attachmentattachment (C(C11)) 11 22 33 44 77 66 55 33 22 11 88 9944 11 22 33 Defined as 1Defined as 1 If both ends equidistant to the first substituent, proceedIf both ends equidistant to the first substituent, proceed until the first point of difference:until the first point of difference: 77 66 55 33 22 11 88 9944
- 40. 44.. NameName the alkane inthe alkane in alphabeticalalphabetical (not(not numericalnumerical)) order of substituents,order of substituents, locationlocation given by number prefix.given by number prefix. 66 11 33 44 55 2277 88 5-5-EEthyl-2-thyl-2-mmethyl-ethyl- octaneoctane 2-Methylbutane2-Methylbutane Alphabet:Alphabet: DDi-,i-, ttri-, etc.ri-, etc. not countednot counted for main stem R.for main stem R. ButBut:: CountedCounted when in branched Rwhen in branched R 66 44 11 33 55 2277 88 66 11 33 44 55 2277 88 5-5-EEthyl-2,2-di-thyl-2,2-di- mmethyloctaneethyloctane 5-(1,1-5-(1,1-DDimethylethyl)-imethylethyl)- 3-3-eethyloctanethyloctane NotNot countedcounted {{ CountedCounted
- 45. Physical Properties of Alkanes:Physical Properties of Alkanes: Intermolecular Forces Increase WithIntermolecular Forces Increase With SizeSize
- 46. Coulomb forces in saltsCoulomb forces in salts Dipole-dipole interactionsDipole-dipole interactions in polar moleculesin polar molecules Intermolecular ForcesIntermolecular Forces
- 47. London forces: Electron correlationLondon forces: Electron correlation (Polarizability: Deformability of e-cloud)(Polarizability: Deformability of e-cloud) IdealizedIdealized (pentane)(pentane) ExperimentalExperimental (heptane)(heptane) Intermolecular ForcesIntermolecular Forces
- 48. The Rotamers of EthaneThe Rotamers of Ethane StaggeredStaggered EclipsedEclipsed StaggeredStaggered
- 49. Newman ProjectionsNewman Projections Note: Newman projection occurs along only one bond. Everything else isNote: Newman projection occurs along only one bond. Everything else is a substituent.a substituent.
- 51. Rotation with NewmanRotation with Newman ProjectionsProjections
- 52. Rotation Around Bonds is NotRotation Around Bonds is Not “Free”: Barriers to Rotation“Free”: Barriers to Rotation e-Repulsione-Repulsion OrbitalOrbital stabilizationstabilization Transition stateTransition state isis eclipsedeclipsed MostMost stablestable rotamer isrotamer is staggeredstaggered Ethane has barrier to rotation of ~3 kcal molEthane has barrier to rotation of ~3 kcal mol-1-1 .. Barrier due to steric and electronic effects.Barrier due to steric and electronic effects. antibondingantibonding bondingbonding
- 53. Potential EnergyPotential Energy DiagramsDiagrams (TS = transition state)(TS = transition state) WalbaWalbaDStrDStr
- 54. Propane: Methyl IncreasesPropane: Methyl Increases BarrierBarrier
- 55. Butane: Isomeric StaggeredButane: Isomeric Staggered and Eclipsed Rotamersand Eclipsed Rotamers
- 56. Rotamers and EnergyRotamers and Energy DiagramDiagram WalbaWalbaDylanDylan
Editor's Notes
- Isooctane defined as 100. If you've read How Car Engines Work, you know that almost all cars use four-stroke gasoline engines. One of the strokes is the compression stroke, where the engine compresses a cylinder-full of air and gas into a much smaller volume before igniting it with a spark plug. The amount of compression is called the compression ratio of the engine. A typical engine might have a compression ratio of 8-to-1. (See How Car Engines Work for details.) The octane rating of gasoline tells you how much the fuel can be compressed before it spontaneously ignites. When gas ignites by compression rather than because of the spark from the spark plug, it causes knocking in the engine. Knocking can damage an engine, so it is not something you want to have happening. Lower-octane gas (like "regular" 87-octane gasoline) can handle the least amount of compression before igniting. The compression ratio of your engine determines the octane rating of the gas you must use in the car. One way to increase the horsepower of an engine of a given displacement is to increase its compression ratio. So a "high-performance engine" has a higher compression ratio and requires higher-octane fuel. The advantage of a high compression ratio is that it gives your engine a higher horsepower rating for a given engine weight -- that is what makes the engine "high performance." The disadvantage is that the gasoline for your engine costs more. The name "octane" comes from the following fact: When you take crude oil and "crack" it in a refinery, you end up getting hydrocarbon chains of different lengths. These different chain lengths can then be separated from each other and blended to form different fuels. For example, you may have heard of methane, propane and butane. All three of them are hydrocarbons. Methane has just a single carbon atom. Propane has three carbon atoms chained together. Butane has four carbon atoms chained together. Pentane has five, hexane has six, heptane has seven and octane has eight carbons chained together. It turns out that heptane handles compression very poorly. Compress it just a little and it ignites spontaneously. Octane handles compression very well -- you can compress it a lot and nothing happens. Eighty-seven-octane gasoline is gasoline that contains 87-percent octane and 13-percent heptane (or some other combination of fuels that has the same performance of the 87/13 combination of octane/heptane). It spontaneously ignites at a given compression level, and can only be used in engines that do not exceed that compression ratio. During WWI, it was discovered that you can add a chemical called tetraethyl lead (TEL) to gasoline and significantly improve its octane rating above the octane/heptane combination. Cheaper grades of gasoline could be made usable by adding TEL. This led to the widespread use of "ethyl" or "leaded" gasoline. Unfortunately, the side effects of adding lead to gasoline are: Lead clogs a catalytic converter and renders it inoperable within minutes. The Earth became covered in a thin layer of lead, and lead is toxic to many living things (including humans). When lead was banned, gasoline got more expensive because refineries could not boost the octane ratings of cheaper grades any more. Airplanes are still allowed to use leaded gasoline (known as AvGas), and octane ratings of 100 or more are commonly used in super-high-performance piston airplane engines. In the case of AvGas, 100 is the gasoline's performance rating, not the percentage of actual octane in the gas. The addition of TEL boosts the compression level of the gasoline -- it doesn't add more octane. Currently engineers are trying to develop airplane engines that can use unleaded gasoline. Jet engines burn kerosene, by the way.
- Boltzmann's principle The concept of entropy was first introduced by Clausius based on the study of heat engines. Though important, this definition of entropy is not the easiest to understand. Therefore, we will first present a later definition of entropy due to Boltzmann, postponing Clausius' ideas to a later section. In Boltzmann's definition, entropy is a measure of the number of possible microscopic states (or microstates) of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties (or macrostate). To understand what microstates and macrostates are, consider the example of a gas in a container. At a microscopic level, the gas consists of a vast number of freely moving atoms, which occasionally collide with one another and with the walls of the container. The microstate of the system is a description of the positions and momenta of all the atoms. In principle, all the physical properties of the system are determined by its microstate. However, because the number of atoms is so large, the motion of individual atoms is mostly irrelevant to the behavior of the system as a whole. Provided the system is in thermodynamic equilibrium, the system can be adequately described by a handful of macroscopic quantities, called "thermodynamic variables": the total energy (E), volume (V), pressure (P), temperature (T), and so forth. The macrostate of the system is a description of its thermodynamic variables. There are three important points to note. Firstly, to specify any one microstate, we need to write down an impractically long list of numbers, whereas specifying a macrostate requires only a few numbers (E, V, etc.) Secondly, macrostates are only defined when the system is in equilibrium; non-equilibrium situations can generally not be described by a small number of variables. For example, if a gas is sloshing around in its container, even a macroscopic description would have to include, e.g., the velocity of the fluid at each different point. Thirdly, more than one microstate can correspond to a single macrostate. In fact, for any given macrostate, there will be a huge number of microstates that are consistent with the given values of E, V, etc. We are now ready to provide a definition of entropy. Let Ω be the number of microstates consistent with the given macrostate. The entropy S is defined as The quantity k is a physical constant known as Boltzmann's constant, which, like the entropy, has units of heat capacity (the logarithm on the right hand side is dimensionless). This postulate, which is known as Boltzmann's principle, may be regarded as the foundation of statistical mechanics, which describes thermodynamic systems using the statistical behaviour of its constituents. It turns out that S is itself a thermodynamic property, just like E or V. Therefore, it acts as a link between the microscopic world and the macroscopic. One important property of S follows readily from the definition: since Ω is a natural number (1,2,3,...), S is either zero or positive (this is a property of the logarithm.) [edit] Disorder and the Second Law of Thermodynamics We can view Ω as a measure of the disorder in a system. This is reasonable because what we think of as "ordered" systems tend to have very few configurational possibilities, and "disordered" systems have very many. As an illustration of this idea, consider a set of 100 coins, each of which is either heads up or tails up. The macrostates are specified by the total number of heads and tails, whereas the microstates are specified by the facings of each individual coin. For the macrostates of 100 heads or 100 tails, there is exactly one possible configuration, corresponding to the most "ordered" state in which all the coins are facing the same way. The most "disordered" macrostate consists of 50 heads and 50 tails in any order, for which there are 100891344545564193334812497256 (100 choose 50) possible microstates. Even when a system is entirely isolated from external influences, its microstate is constantly changing. For instance, the particles in a gas are constantly moving, and thus occupy a different position at each moment of time; their momenta are also constantly changing as they collide with each other or with the container walls. Suppose we prepare the system in an artificially highly-ordered equilibrium state. For instance, imagine dividing a container with a partition and placing a gas on one side of the partition, with a vacuum on the other side. If we remove the partition and watch the subsequent behavior of the gas, we will find that its microstate evolves according to some chaotic and unpredictable pattern, and that on average these microstates will correspond to a more disordered macrostate than before. It is possible, but extremely unlikely, for the gas molecules to bounce off one another in such a way that they remain in one half of the container. It is overwhelmingly probable for the gas to spread out to fill the container evenly, which is the new equilibrium macrostate of the system. This is an illustration of a principle that we will prove rigorously in a subsequent section, known as the Second Law of Thermodynamics. This states that The total entropy of an isolated system can never decrease. Since its discovery, the idea that disorder tends to increase has been the focus of a great deal of thought, some of it confused. A chief point of confusion is the fact that the Second Law applies only to isolated systems. For example, the Earth is not an isolated system because it is constantly receiving energy in the form of sunlight. Nevertheless, it has been pointed out that the universe may be considered an isolated system, so that its total disorder should be constantly increasing. We will discuss the implications of this idea in the section on Entropy and cosmology.
- Air: a single molecule undergoes 10 to the 10 collisions/sec. Cf. breathing 60 times/min; in 80 years: 2.5 billion 2.5x10tothe9
- Le Chatelier Summary Increasing the temperature of a system in dynamic equilibrium favours the endothermic reaction. The system counteracts the change you have made by absorbing the extra heat. Decreasing the temperature of a system in dynamic equilibrium favours the exothermic reaction. The system counteracts the change you have made by producing more heat. ImportantAgain, this isn't in any way an explanation of why the position of equilibrium moves in the ways described. It is only a way of helping you to work out what happens.Note: I am not going to attempt an explanation of this anywhere on the site. To do it properly is far too difficult for this level. It is possible to come up with an explanation of sorts by looking at how the rate constants for the forward and back reactions change relative to each other by using the Arrhenius equation, but this isn't a standard way of doing it, and is liable to confuse those of you going on to do a Chemistry degree. If you aren't going to do a Chemistry degree, you won't need to know about this anyway!
- What should I do about a title Are the numbers okay?