L09S08 CHEM1A Spring 2008 - Chem 1A, L9 REVIEW Lecture...

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Unformatted text preview: Chem 1A, L9 REVIEW Lecture Eight Topics Quantum numbers describe the energy, shape, and spatial orientation of electronic orbital in an atom The angular momentum quantum number "L" can also stand for s, p, d, f, etc. orbitals Orbitals can have radial and/or angular nodes, i.e.; spatial locations where the wave function intensity goes to zero. 2008 Nitsche, UCB L9-1 H-Atom, One-Electron Ions Onen=1 l = 0 (s) (s ml = 0 n=2 l = 0 (s) (s ml = 0 Radial Node n=2 ml = -1, +1 l = 1 (p) (p ml = 0 z - 2px Angular Node z 2py + z y x + 2pz z 1s + z 2s + - + y x - y y x y L9-5 x x 2008 Nitsche, UCB n = 3 l = 0, 1, 2 A.Pines,M.Kubinec UCB 3s, 3p, 3d Orbitals L9-2 L9-6 A.Pines,M.Kubinec UCB Quantum Numbers Q.N. n : Principal values orbital property Energy Shape n: 1, 2, 3 . . . Total nodes =n-1 : Angular Momentum : 0 (s), 1 (p), 2 (d), n-1 (s), (p), (d), Angular nodes = m : Magnetic m: -, -(-1),..,0,..,(-1), 1),..,0,..,( 2008 Nitsche, UCB Orientation L9-3 H. Nitsche UCB 1 Chem 1A, L9 REVIEW 2008 Nitsche, UCB L9-4 Three representations of the hydrogen 1s, 2s, and 3s electron 2008 Nitsche, UCB L9-5 ChemQuiz 8.3 Which has the most radial nodes? y x x z y + - - + z A) 4f 2008 Nitsche, UCB B) 3d C) 4s L9-6 H. Nitsche UCB 2 Chem 1A, L9 REVIEW Three representations of the hydrogen 1s, 2s, and 3s electron 2008 Nitsche, UCB L9-8 Representation of the 3d orbitals 2008 Nitsche, UCB L9-9 Representation of the 4f orbitals in terms of their boundary surfaces. 2008 Nitsche, UCB L9-10 H. Nitsche UCB 3 Chem 1A, L9 REVIEW Summary 2H2 Energy Reactants + Chemical Reactions O2 2H2O High Road (barrier) Products Reaction Coordinate 2001 UC Regents L1-4 Relative Atomic and Molecular Mass H 1.01 12C 2H2 + O2 2H2O Al 26.98 P 30.97 Fe 55.85 Pb 207.2 H2 2.02 O2 32.00 H2O 18.02 CO2 44.01 12.00 C 12.01 O 16.00 2 molecules + 1 molecule 2 moles + 1 mole 2 grams + 16 grams 2 molecules 2 moles 18 grams Lecture One Topics Chemical reaction always occur in stoichiometric ratios Converting between numbers of moles and numbers of atoms Atomic masses are weighted averages of the masses of the natural isotopes of an element 2008 Nitsche, UCB L9-12 Chemical Reactions 2H2 Energy Reactants Products Reaction Coordinate 2008 Nitsche, UCB + O2 2H2O Transition State High Road (barrier) (barrier) L9-13 H. Nitsche UCB 4 Chem 1A, L9 REVIEW Stoichiometry Relationships between quantities of matter that participate in chemical reactions. Macroscopic Bulk matter NA Microscopic Atoms, Molecules Avogadro's Number: NA = 6.022 x 1023 Avogadro' NA atoms in 12.00 g 12C= one Mole Molar Mass (g/mol) 2008 Nitsche, UCB L9-14 is assigned exactly 12 atomic mass units (amu or u) Masses of all other atoms are given relative to this standard Atomic masses are averages of isotopic masses Relation between amu and grams (6.022 x 1023 atoms) (12amu/atom) = 12 g 6.022 x 1023 amu = 1 g 1 amu = 1.661 x 10-24 g = 1.661 x 10-27 kg 2008 Nitsche, UCB 12C Atomic Mass and Mass Units L9-15 Lecture Two Topics The structure and size of the nucleus and the atom Obtaining empirical formula from experimental data (mass spectrometry) Calculating a molecular formula from an empirical formula and molar mass 2008 Nitsche, UCB L9-16 H. Nitsche UCB 5 Chem 1A, L9 REVIEW Mass Spectrometer Ionization - N Magnet Mass Spectrum Sample Acceleration S 1 H 2H 2, 1H 12C 16 O 13C 16O 2 1H 16O 18O 2 , 16O18O 12C16O 2 1H2H 3He , 13C16O 2 0 10 20 30 18O 2 40 50 L2-5 2000 A.Pines M.Kubinec UCB Relative Atomic and Molecular Mass H 1.01 12C Empirical and Molecular Formula Methane Ethylene CH 4 CH2 CH4 C2H8 C3H12 CH2 C2H4 C3H6 CH C2H2 C3H3 L9-17 L2-10 Al 26.98 P 30.97 Fe 55.85 Pb 207.2 H2 2.02 O2 32.00 H2O 18.02 CO2 44.01 L2-5 12.00 C 12.01 O 16.00 2000 A.Pines M.Kubinec UCB Acetylene CH 2000 A.Pines M.Kubinec UCB 2008 Nitsche, UCB (Nucleus + Electron Shells) -Z +Z Z electrons Atomic Structure A Z e X A: Atomic Mass Z: Atomic Number Atomic Symbol A = Z (Protons) + N (Neutrons) 2008 Nitsche, UCB L9-18 Mass Spectrometer Ionization - N Magnet Mass Spectrum Sample Acceleration S 1H 2H 2, 1H 12C 16 O 13C 16O 2 1H 16O 18O 2 , 16O18O 12C16O 2 1H2H 3He , 13C16O 2 0 10 2008 Nitsche, UCB 20 30 mass units 18O 2 40 50 L9-19 H. Nitsche UCB 6 Chem 1A, L9 REVIEW ChemQuiz 2.1 An equimolar mixture of oxygen atomic isotopes forms oxygen molecules. Which is molecules. the correct O2 spectrum? O O 16 O 16 O 18 18 O O 18 16 16 O O 18 O O 16 18 1) 32 34 36 2) 32 34 36 3) 32 34 36 2008 Nitsche, UCB L9-20 Empirical and Molecular Formula Methane Ethylene CH4 CH2 CH4 C2H8 C3H12 CH2 C2H4 C3H6 CH C2H2 C3H3 L9-22 Acetylene CH 2008 Nitsche, UCB Lecture Three Topics Combustion of alcohols- balancing chemical equations Definition of proof and % content of solute in solutions (alcohols) Definition of Molarity 2008 Nitsche, UCB L9-23 H. Nitsche UCB 7 Chem 1A, L9 REVIEW Density of Gases CH3CH2CH2OH = molar density (all gases) = mass density (MW are equal) mass density = 0.0027 g/ml 2002 M. Kubinec H O CH3CHCH3 L1-8 Combustion of Alcohols CH3CH2CH2OH + 9/2 O2 3 CO2 + 4 H2O MM Density (g/ml) gas liquid Reactions in Solution Concentration in Molar (M) 1 mole solute 1M = Liter solution What is [propanol] when 60 ml propanol] propanol is mixed with 40 ml H2O? A) > 1 M 2002 M. Kubinec Propanol CH3CH2CH2OH 60 Isopropanol Ethanol 2002 M. Kubinec (g/mol) OH CH3CHCH3 0.003 0.80 0.003 0.78 0.002 0.94 L3-10 60 46 CH3CH2OH Nitsche, UCB B) ~ 1 M C) < 1 M L9-24 L1-15 LD50 ~ 6g/kg 2008 Reactions in Solution Concentration in Molar (M) 1 mole solute 1M = Liter solution What is [propanol]* when 60 ml propanol] propanol is mixed with 40 ml H2O? *[propanol]= concentration of propanol *[propanol]= 2008 Nitsche, UCB L9-25 Reactions in Solution What is [propanol] when 60 ml propanol] propanol is mixed with 40 ml H2O? 60 ml propanol ~ 60 x 0.8 g/ml = 48 g 60 g ~ 1 mole 48 g ~ 0.8 mole ~ 0.8 mole/0.1 L ~ 8 M 2008 Nitsche, UCB L9-26 H. Nitsche UCB 8 Chem 1A, L9 REVIEW Lecture Four Topics Radiation/light can behave as a wave Visible light is only a small part of the spectrum of electromagnetic radiation Monochromatic light waves cause an interference pattern Matter can absorb and emit radiation/light 2008 Nitsche, UCB L9-27 Summary c Light as a Wave Diffraction and Interference Intensity ~ Electromagnetic Radiation :wavelength A A+B B :frequency c :speed = c Probability Distribution = 400 nm = 700 nm A.Pines,M.Kubinec,UCB c= 3.0 x 108 m/s L6-4 A.Pines,M.Kubinec,UCB L6-6 Electromagnetic Spectrum 400 500 Visible -rays x-rays UV IR MW Radio, NMR, MRI Absorption and Continuous Emission 600 700 nm 10-16 10-12 10-8 A.Pines,M.Kubinec,UCB 10-4 100 104 108 m L6-5 Line 2008 Nitsche, UCB A.Pines,M.Kubinec,UCB L9-28 L6-10 Light as a Wave Electromagnetic Radiation c :wavelength :frequency c :speed =c = 400 nm = 700 nm 2008 Nitsche, UCB c = 3.0 x 108 m/s L9-29 H. Nitsche UCB 9 Chem 1A, L9 REVIEW Diffraction and Interference Intensity A + B ~ Probability Distribution 2008 Nitsche, UCB L9-30 Absorption and Continuous Emission Line 2008 Nitsche, UCB L9-31 Lecture Five Topics Light can also behave as a particle The de Broglie relation unifies this dualism between light as a wave and a particle (photon) Light of a specific minimum wavelength can ionize atoms in metals (Photo Effect) 2008 Nitsche, UCB L9-32 H. Nitsche UCB 10 Chem 1A, L9 REVIEW Summary 400 500 Visible -rays x-rays UV IR Electromagnetic Spectrum 600 700 nm The Particle Nature of Light Light Intensity MW Radio, NMR, MRI 10-16 10-12 10-8 A.Pines,M.Kubinec,UCB 10-4 100 104 108 m L7-4 Ephoton = h 2002 A.Pines,M.Kubinec, UC L8-6 Photoelectric Effect The Particle Nature of Light Light-Wave / Particle LightDuality Wave (length) I II e Ekin Particle (Momentum) c Wave h = p Duality p=mc Particle p= h Ephoton = h A.Pines,M.Kubinec,UCB Ekin= h - = h - ho h L7-2 2008 Nitsche, UCB A.Pines,M.Kubinec,UCB L9-33 L7-6 Wave / Particle Duality Wave (length) Particle (Momentum) Light c Wave h = p 2008 Nitsche, UCB p Particle Duality p= h L9-34 Photoelectric Effect The Particle Nature of Light e- Ekin I o II Ephoton = h 2008 Nitsche, UCB Ekin= h - = h - ho L9-35 H. Nitsche UCB 11 Chem 1A, L9 REVIEW Lecture Six Topics Electrons, which we know to be particles, can also behave as waves they too can form an interference pattern The de Broglie relation also unifies the particle and wave character of electrons Electron in atoms behave like standing waves- their energy is quantized The magnitude of the de Broglie wavelength tells us if we are dealing with a quantum particles L9-36 2008 Nitsche, UCB Summary 400 500 Visible -rays x-rays UV IR Electromagnetic Spectrum 600 700 nm The Particle Nature of Light Light Intensity MW Radio, NMR, MRI 10-16 10-12 10-8 A.Pines,M.Kubinec,UCB 10-4 100 104 108 m L7-4 Ephoton = h 2002 A.Pines,M.Kubinec, UC L8-6 Photoelectric Effect The Particle Nature of Light Light-Wave / Particle LightDuality Wave (length) I II e Ekin Particle (Momentum) c Wave h = p Duality p=mc Particle p= h Ephoton = h A.Pines,M.Kubinec,UCB Ekin= h - = h - ho h L7-2 2008 Nitsche, UCB A.Pines,M.Kubinec,UCB L9-37 L7-6 Diffraction and Interference Intensity A+B Probability Distribution ~ ~ L9-38 2008 Nitsche, UCB H. Nitsche UCB 12 Chem 1A, L9 REVIEW Discrete, Quantized States Standing Waves (x) E n 3 2 1 Nodes 2 1 0 L9-39 Excited States + + + - Ground State 2008 Nitsche, UCB + Absorption and Emission Spectra Electronic Transtions v E = h 2008 Nitsche, UCB L9-40 De Broglie Wavelengths Particle Photon (yellow) (yellow) e- (v ~ 105 m sec-1) Na (80K, v~300 m sec-1) Baseball (170g, v~40 m sec-1) 2008 Nitsche, UCB de Broglie (nm) ~ 600 ~6 ~ 0.06 ~ 6x10-26 L9-41 H. Nitsche UCB 13 Chem 1A, L9 REVIEW Lecture Seven Topics The uncertainty the exact position and wavelength of an atomic electron is given by the Heisenberg uncertainty relation Solutions of the Schrdinger equation gives the energies of the quantum states of an electron Electrons in atoms behave like standing waves- their energy is quantized The magnitude of the de Broglie wavelength tells us if we are dealing with a quantum particles L9-42 2008 Nitsche, UCB Spectra Review E=h E=h Absorption and Emission A.Pines,M.Kubinec,UCB L8-7 Wave Functions Energy: - h2 d2 (x) = ET (x) 82m dx2 n h2 n x A sin L 82m L = ET (x) 2 (x) 2(x) En 16 n=4 n=3 9 En = 2008 Nitsche, UCB h2n2 8mL2 n=2 n=1 4 1 L9-43 L19-9 2004 M.Kubinec (x) = A sin 2 x known momentum () ( h de Broglie relation: mv = p = Uncertainty Principle 2(x) = intensity or probability x uncertainty in position (x) = Ai sin 2 x i i uncertainty in momentum 2008 Nitsche, UCB x p h/4 h/4 L9-44 known position x H. Nitsche UCB 14 Chem 1A, L9 REVIEW Quantum Mechanics Schrdinger equation: Schr - h2 d2 (x) + V(x) (x) = ET (x) (x) V(x) 82m dx2 Kinetic Potential Total H (x) = ET (x) 2008 Nitsche, UCB L9-45 Orbital Energies n : Principal Q. N. -Z 2 R En = n2 = 2.18 x 10-18 J = 3.29 x1015 Hz N0R = 1312 kJmol-1 R 2008 Nitsche, UCB n 3 2 n: 1, 2, 3 . . . Ionized E 0 -R -R 4 9 1 Ground -R L9-46 Lecture Complete 2008 Nitsche, UCB L9-47 H. Nitsche UCB 15 ...
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