11/11/14 9:59 AM

Lecture 111/11/14 9:57 AM

Lecture 211/11/14 9:57 AM

Bonds from interaction with an sp hybrid AO- Hybridization can be rationalized in terms of allowing AOs (especially s orbital) to project further out into space, and thus achieve better overlap and stronger bonds with other atoms. Sp2 Orbitals, Double Bonds and the Structure of Ethylene: sp2 orbitals-Bonds from Overlap of sp2 hybrid orbitals- Two sp2-hybridized orbitals overlap to form a sigma bond- P orbitals overlap side-to-side to form a pi bond- Sp2-sp2 sigma bond and 2p-2p pi bond result in sharing four electrons and formation of C-C double bond1. Electrons in the sigma bond are centered between nuclei2. Electrons in the pi bond occupy regions are on either side of a line between nucleiPi bonds: Comparison of VB View with MO view- The pi bonding MO results from combing p orbital lobes with the same algebraic sign for pi (additive combination)- The pi antibonding MO results from combining lobes with opposite signs for pi (subtractive combination)- Electron pair occupies bonding MO (lower energy)VBT Predicts Experimental Structure of Ethylene- Contains a C-C double bond, involving 1 sp2 orbital plus unhybridized p orbital- H atoms form sigma bonds with four sp2 orbitals - H-C-H and H-C-C bond angles of about 120 degrees- Note: sp2 hybridize atoms are planar- C-C double bond in ethylene shorter and stronger than single bond in ethane- Bond angle is close to 120 degrees to reduce electron-electron repulsionSp Orbitals and the Structure of Acetylene- Carbon 2s orbital hybridizes with a single p orbital giving two sp hybrid orbitals 1. Remaining two p orbitals remain unchanged- Sp orbitals are co-linear, 180 degrees apart on x-axis- Two p orbitals are perpendicular, on the y and the z-axis 1. An sp carbon can engage in 2 sigma bonds (through the sp orbitals) plus 2 pi bonds (by overlap of the two unhybridized p orbitals)Orbitals of Acetylene- Two sp hybrid orbitals, on from each C, overlap to form sigma bonds- Py and pz orbitals from each C overlap to form two perpendicular pi bonds- The two C atoms are bonded together by six shared electrons, to form a C-C triple bondBonding in Acetylene- Sharing of six electrons form carbon-carbon triple bond- Two sp orbitals form sigma bonds with hydrogen- Sp hybridized atoms are linearHybridization of Nitrogen and Oxygen- Many atoms other than C can have hybridized orbitals Ie: orbitals in the valence shell of N (sppp) can hybridize to form sp3, sp2, or sp orbitals- For sp3 on N:One sp3 orbital is occupied by two nonbonding electronsRemaining three sp3 orbitals have one electron each, allowing bonding to three other atomsExample: Methylamine- One sp3 orbital is occupied by two nonbonding electrons; the other three have one electron each and form sigma bonds to H and CH3The geometry around N is pyramidalBecause the groups bonded to the N atoms are dissimilar, the geometry around N is slightly distorted from a regular tetrahedronExample: Methanol- Two sp3 orbitals are occupied by lone pairs; the other two have one electron each, and form sigma bonds to H and CH3Sp2 and sp Hybridization of Nitrogen and Oxygen- To form a double bond, we need sp2 hybridization- To form a triple bond, we need sp hybridization- Amine: sp3- Imine: sp2- Nitrile: sp- Carbonyl: sp2AldehydeKetoneCarboxylic acid- In stable, uncharged molecules, the total number of bonds to N (3 bonds) and O (2 bonds) is always the same- For each hybridization state, the bond angles are as for C (ie: ~109 degrees for sp3, ~120 degrees for sp2, ~180 degrees for sp). It is only a model- The concepts of promotion and hybridization (and indeed of VBT itself) are not real; they are just ways to conceptualize and apply the behaviors that are properly described only by MO TheoryVSEPR Model: valence shell electron repulsion- Idea: maximize separation around central atom

Key Points- Valence Bond Theory I a method for describing the distribution of electrons in molecules of any size and complexity1. Describes each bond as resulting from the combination of singly-occupied AOs on the two atoms involved- To accurately predict bonding and shaped of complex molecules, two embellishments to the theory are needed- Promotion: electrons can be excited into unoccupied AOs to generate additional- Sp3 hybrid orbitals: s orbital and three p orbitals combine to form four equivalent, unsymmetrical, tetrahedral orbitals (sppp= sp3)All bond angles are tetrahedral-Sp2 hybrid orbitals: 2s orbital combines with - Sp hybrid orbitals: 2s orbital hybridized with a single p orbital giving two sp hybrid orbitalsRemaining two p orbitals remain unchangedSp orbitals are co-linearAn SP carbon can engage in 2 sigma bonds (through the sp orbitals) plus 2 pi bonds (by overlap of the two unhybridized p orbitals)- Hybridization is not restricted to carbon. O, N and many other elements can also form hybrid orbitals- With N and O, one or two of the hybridConjugated Carbon-Carbon Double BondExample: 1,3-butadiene- Double bonds alternating with single bonds are called: conjugated- The uninterrupted stretch of C atoms with unhybridized p orbitals allows the pi electrons to delocalizePi System MOs in 1,3-Butadiene

Conjugation important in Benzene Ring

Lecture 311/11/14 9:57 AM

Carbon-Carbon Double BondTwo different forms of acetate

Real Acetate Ion is a linear combination of the two structures shown

Summary of Key Ideas: Resonance- When three or more adjacent atoms contain unhybridized p orbitals in the same plane, the pi electrons delocalize across all of the p orbitals- In such cases, the pi electrons are best considered in terms of MOs that extend over all of the atoms involved Gives a more accurate picture of the distribution of chargers over the atoms, and the chemical reactivity of the systemSometimes a delocalized system cannot easily be represented using a single line-bond structure; instead we draw resonance structures that collectively represent the true structureThe true structure is aid to be the resonance hybridCarbon-Organic Chemistry is the study of compounds that contain carbon-Of the ~30 million known chemical compounds, about 90% of them are compounds of carbon- Organic MoleculesOrganic molecules typically comprise a hydrocarbon framework decorated with functional groups.

Kinetic Gas TheoryGas Laws:Pressure is the force that a gas exerts on the walls of its container, due to collisions of gas moleculesUnits= pascals (Pa); 1Pa=1N/m^2= 1Kg/msAlternative units include atm, bar, torr, mmHgBoyles Law (V inv. prop 1/P)Charless Law (V inv. prop T in kelvins)Ideal Gas Law PV=nRTPartial PressuresManometer readingStoichiometry-Kinetic Model of Gases: How do the gas laws derive from the collective motions of individual gas molecules?-The Maxwell Distribution of Speeds: What is the distribution of speeds in a collection of gas molecules at a given temperature?-What is temperature?-What is R, kB?-Gas Kinetics: Diffusion and EffusionKinetics: study of molecular motions and rates of changeIf two or more gases are introduced into the same volume, the random motions and collision of the molecules are called Diffusion- will lead the gases to mix togetherSpeed at which mixing occurs depends on the speed of molecular motionIf a container of gas containing a small hole is placed in a vacuum, the random motion of the gas molecules will lead them to gradually escape through the hole. This process is called EffusionSpeed at which escape occurs (ie: pressure inside the container drops to zero) depends on speed of molecular motion- Gas Kinetics: Experimental ObservationsRate of effusion is proportional to the average speed of molecules in a gasThe greater the average speed, the more gas molecules encounter the hole in a given timeExperimental observations from measuring rate of gas diffusion and effusion:(At constant T): Rate of effusion is inv. prop to 1/sqrt. (Molar mass)Called Grahams law of EffusionRate of Effusion is inv. prop to sqrt. TemperatureThe average speed of molecules in a gas is directly proportional to the square root of the temperature and inversely proportion to the square root of the mass.- Kinetic Model of Gases: Starting AssumptionsA gas consists of a collection of molecules in continuous, random motionGas molecules are infinitely small pointsThe molecules move in straight lines until they collideThe molecules do not influence each other except during collisionsIe: no attraction between molecules; no attraction between molecules; no long-range repulsion- Kinetic Model of Gases: Relationship of P and V to Molecular VelocityGas molecules exert pressure on the walls of their container by colliding with them and transferring momentum to themCollisions can be considered as elastic (Ie: no change in speed)P can be related to the n, v by considering how many molecules are within a given distance of the walls and so how many collisions will occur per unit timeAnswer depends on average speed of molecules, and their massLeads to the expression:PV=nMv^2rms/3 where M is the molar mass and vrms is the root mean square of the velocity ^1/2By substituting the above equation into the Ideal Gas Law, we can calculate vrms for any temperature:Vrms=(3RT/M)^1/2- TemperatureT=Mv^2rms/3RTemperature is proportional to the mean square speed of the molecules in a gasTemperature is a measure for motionThe temperature corresponding to the complete absence of molecular motion is -273.13 degrees CelsiusCalled absolute zero (0K)- Meaning of Ideal Gas ConstantPV=nRT, so R=PV/nT (Ie: PV per mole per K)For a given number of moles of gas at a given temperature, PV is a constantPV reflects the amount of thermal energy the gas molecules possess at that temperatureR=Joules/K=thermal energy per mole per kelvinR=8.314 J/molKkB= thermal energy per molecule per K kB=1.38E-23 J/KThermal energy at a given temperature = kBT per moleculeR and kB relate to kinetic energy as follows:Most probable KE= kBT per molecule = RT per moleAverage (ie: rms) KE=3kBT/2 per molecule=3RT/2 per moleCorresponds to (kBT) of KE per translational degree of freedom (ie: (kBT) for movement in respect to each axis of 3D spaceNumber corresponds strictly to atoms- What is the Distribution of Molecular Speeds in a Gas?For a population of gas molecules, the number of molecules, delta N, having a speed between v and v+ dv is given by Maxwells Equation

N=Total number of moleculesM=Molar MassR=Gas ConstantT=Temperature in Kelvin

4pi(M/2piRT)^3/2 is a normalization factor to ensure AUC=1Maxwell-Boltzmann Distribution of Molecular SpeedsThe distribution of speeds in a population of gas molecules is given by the Maxwell-Boltzmann EquationMost probable speed is at Vmp (peak of curve) is (2KbT/m)^1/2Average speed is Vrms (slightly right of the peak)= (3KbT/m)^1/2Vrms at 25C in (m/s): 410 Carbon dioxide, 480 Oxygen, 515 Nitrogen, 640 Water, 1930 HydrogenOnly difference is molecular mass

Distribution of Molecular Speeds in a GasMolecular Beam Apparatus change speed by changing rotational speed of deviceHeavy molecules have lower speed and a narrower range of speedsOffset slits in rotating disks allow molecules to pass through only if they have a particular speedIn a system where gas molecules can undergo a chemical reaction with each other, only molecules having a kinetic energy exceeding a certain threshold will collide with sufficient energy to overcome the activation barrier for reaction.

Lecture 411/13/14 9:59 AM

Deviations from IdealityReal molecules display both attractive and repulsive forces

Electrons react with each otherBoth attraction and repulsion are possibleAttraction at a low potential energy and a small separationRepulsion increases at a high potential energyAttractive and repulsive forces between gas molecules cause the volume per mole to deviate from what is expected from the Ideal Gas LawDeviations from ideality can be quantified by taking the ratio of actual versus ideal molar volumes (Vm) called the compression factor ZZ=PV/nRT=Vm(experimental)/Vm(ideal)Compression factor for ideal gas =1Z1 because repulsive forces dominateWhen b is small, Z