Lecture 6: Chemistry PDF

Lecture #6, p. 1 Lecture 6: Announcements Today: Brown 6.1 The Wave Nature of Light 6.2 Quantized Energy and Photons 6.3 Line Spectra and the Bohr Model 6.4 The Wave Behavior of Matter...

Lecture #6, p. 1 Lecture 6: Announcements Today: Brown 6.1 The Wave Nature of Light 6.2 Quantized Energy and Photons 6.3 Line Spectra and the Bohr Model 6.4 The Wave Behavior of Matter 6.5 Quantum Mechanics and Atomic Orbitals 6.6 Representation of Orbitals 6.7 Multielectron Atoms 6.8 Electron Configurations 6.9 Electron Configurations and the Periodic Table 7.2 Effective Nuclear Charge 7.3 Sizes of Atoms and Ions 7.4 Ionization Energy 7.5 Electron Affinity Chemistry  Lecture #6, p. 2 Lecture 6: Announcements Problem Set 5: Due before Exercise #6 tomorrow; upload on Moodle link Problem Set 6: Posted on Moodle; due before Exercise #7 next week Study Center: Wednesdays 18:00–20:00 in ETA F 5 Office Hours: Prof. Norris and Brisby, Thursdays 17:00–18:00 in LEE P 210 No office hours this week ! Next Week: Brown Ch. 8 Basic Concepts of Chemical Bonding Ch. 9 Molecular Geometry and Bonding Theories Chemistry  Lecture #6, p. 3 Review In Lecture 5, we introduced 2nd Law of Thermodynamics Spontaneous versus nonspontaneous processes Reversible, irreversible processes Isothermal processes Entropy, 2nd Law of Thermodynamics Boltzmann’s equation, microstates 3rd Law of Thermodynamics Gibbs free energy, ! ≡ # − %& ∆! = ∆# − %∆& (at constant T) Standard Gibbs free energies Role of Temperature Chemistry  Lecture #6, p. 4 Importance of Temperature ∆" = ∆$ − &∆' Spontaneous for ∆" < 0 ∆! depends on temperature; so how does % affect spontaneity of reaction? 1 2 3 4 Ex 1: 2 O3 (g) 3 O2 (g) Spontaneity favored by both enthalpy and entropy Ex 2: 3 O2 (g) 2 O3 (g) Spontaneity favored by neither enthalpy and entropy Ex 3: H2O (l) H2O (s) Spontaneity favored only by enthalpy Ex 4: H2O (s) H2O (l) Spontaneity favored only by entropy Chemistry EEIIE E i in iii  Lecture #6, p. 5 Today: Electronic Structure Chemistry involves electrons They determine reactivity of atoms They form bonds, leading to molecules (because bonds hold atoms together) Thus, to understand chemistry, we must understand organization of electrons in atoms a Kalin Aka electronic structure Full understanding requires quantum mechanics (4th semester) Today’s goal: sketch basics of electronic structure of atoms Chemistry  Lecture #6, p. 6 Weneedto startwitha description oflight Light Light is an oscillating electromagnetic wave: Important parameters: Wavelength, λ Frequency, " = $/& 2 nu Speed of light in vacuum, $ 2.99810m l 1 landa “Color” of light depends on wavelength λ 430 nm is blue 530 nm is green 630 nm is red But light waves carry energy in discrete amounts: " = ℎ% or " = ℎ&/( Iiiii S These discrete amounts of energy known as photons ℎ ≡ Planck’s constant = 6.626 × 10!"# J / s Chemistry Thefactthatlightbehavesbothlike awaveanda particle isknownasthe waveparticleduality It iscentralideaof quantummechanics Morein 4thsemester  Lecture #6, p. 7 Light Emitted from Hydrogen Atoms Wavelength (nm) Chemistry AtomicspectrumatomiclinesYrigin  Lecture #6, p. 8 Withthisbriefbackgroundonlight wecannow discussearlyexperiments onatoms startingin mid1800sscientists likeSwissschoolteacherandmathematicianJohannBalmer 18251888 studiedlightemitted byhydrogenatoms Mystery of Hydrogen Hot light sources (e.g., sun) emit white light Iiiiii But hydrogen atoms emit photons only at certain energies, ! = ℎ$/& Energy values explained by simple empirical formula: ℎ$ 1 1 !$ ≡ Rydberg constant = 1.097×10' m!% !! = = ℎ$ (! # − # &! *" *# #% , #& ≡ integers ; #& > #% > 0 H Tms Rydberg Equation But why does this equation work?? First explanation given by Niels Bohr... Niels Bohr, 1885–1962 Chemistry (wikipedia.org)  Lecture #6, p. 9 Bohr Model Idea: Atomic-scale solar system Nucleus = “sun” Electron = “orbiting planet” Bohr proposed: electron Electron can occupy only certain orbits Electron has specific “allowed” energies, !! n 1 23 Electron can move between allowed orbits III nucleus n=1 Requires either absorption of photon with !"# = ℎ$ or emission of photon with !"# = ℎ$ n=2 Ex: !$ → !% with !$ > !% ∆!$→% = !% − !$ = −!"# n=3 Bohr proposed these as postulates (though problematic) ⋯ Correct description requires quantum mechanics But appears to be on right track... Chemistry  Lecture #6, p. 10 classicalequations of motionto Offer me gyhisofpfiteuhetctronheincouald.nu I Orbital Energies !! = − ℎ% '* ∆! = !!! − !!" = −ℎ1 2* 1 − 1 (+ 3-+ 3.+ ! Ex: Electron relaxes from n=3 to n=1 0 n=∞ … What is energy of emitted photon? !, n=4 electron !$ n=3 ∆!$→% = !% − !$ = −2.18×10'%( J 1−). % = −1.94×10'%( J !+ n=2 !"# = +1.94×10'%( J /0 Deep 7"# = = 103 nm yyq.io 1#$ !% n=1 Note: Energy levels specified just with “n” Integer Chemistry 10 121nm Extremeultravioletlight IE fiii i i eat It iconography Toolcosts100s ofmillions snaronets 1 13.5nm  Lecture #6, p. 11 it Limitations of Bohr Model iii Cannot explain stable orbits of electron Can only explain hydrogen atom ! Other atoms? Quantum Mechanics Resolves limitations of Bohr model But predicts Uncertainty Principle ∆" 7 ∆$ ≥ ℎ:4* t.EE i i iiiin ⇒ Orbit is ”fuzzy” ∆" The uncertainty in how well iii Must refer to “electron cloud” ∆$ we know position, !, and momentum, ", of electron Chemistry EEnow If electron's positionandmomentum iii iiiiii times.net  Lecture #6, p. 12 Outcomes ofquantum mechanics Quantum Mechanics Says... Function that gives “map” of where electron Electron motion described by its wavefunction is, given constraints of Uncertainty Principle For example, the probability that Due to Uncertainty Principle, we only know probabilities the electron is in a certain region Bohr orbits become atomic orbitals Orbitals described by four numbers: !, ℓ, $ℓ, $3 Principal quantum number, ! ⇒ 1, 2, 3, … Same ! as in the Bohr model ! called “shell” ⇒ size of orbital Chemistry  Lecture #6, p. 13 Quantum Mechanics Says... Orbitals described by four numbers: !, ℓ, $ℓ, $" Angular quantum number, ℓ ⇒ integers between 0 and ! − 1 Note: range of ℓ depends on ! (shell) ℓ 0 1 2 3 ℓ called “subshell” ⇒ shape of orbital s p d f Magnetic quantum number, #ℓ ⇒ −ℓ, ℓ + 1, ⋯ 0, ⋯ ℓ − 1, ℓ Iiii Note: range of $ℓ depends on ℓ (subshell) $ℓ relates to orientation of orbital in space Chemistry  Lecture #6, p. 14 Summarizing Labels for Atomic Orbitals Chemistry  Lecture #6, p. 15 Visualizing Atomic Orbitals n =1 n =2 n =3 orbital size increasing with n ℓ=0 ℓ=0 ℓ=0 Electron Cloud iiiiiiiiiii Proability of where electron is located mℓ = 0 for all s orbitals Makes sense! Sphere only has one possible s orbitals (ℓ=0) have spherical shapes orientation Chemistry  Lecture #6, p. 16 Visualizing Atomic Orbitals: ℓ=1 p orbital mℓ = −1, 0, +1 p orbitals (ℓ=1) have “dumbbell” shapes with two lobes mℓ has three values representing 3 different orientations Chemistry  Lecture #6, p. 17 Visualizing Atomic Orbitals ℓ=2 d orbital mℓ = −2, −1, 0, +1, +2 d orbitals (ℓ=2) have “four-leaf clover” shapes with four lobes mℓ has 5 values representing 5 different orientations Chemistry  Lecture #6, p. 18 Energy of Atomic Orbitals in Hydrogen Hydrogen has one electron If e− in lowest 1s level ⟶ ground state If in higher level ⟶ excited state Energy only depends on n 2s, 2p have same energy 3s, 3p, 3d have same energy Each box in diagram is specific n, ℓ, mℓ What about multielectron atoms? Chemistry  Lecture #6, p. 19 electronatoms letsfinishourquantumnumbers Beforewediscussmulti n e meand Last Quantum Number? !, ℓ, $ℓ, $! Spin magnetic quantum number, "! Has one of two values: +1/2 or -1/2 Spin “up” or spin “down” Rotating electrical current creates magnet Electrons behave as if they were spinning Can measure magnetic field of electron But not really spinning! Chemistry  Lecture #6, p. 20 Last Quantum Number? !, ℓ, $ℓ, $! Spin magnetic quantum number, "! Has one of two values: +1/2 or -1/2 Spin “up” or spin “down” Rotating electrical current creates magnet Electrons behave as if they were spinning Can measure magnetic field of electron But not really spinning! And only two possible spin orientations Outcome of quantum mechanics Chemistry  Lecture #6, p. 21 Energy of Atomic Orbitals in Multielectron Atoms? Beyond hydrogen? Atom has given number of e−’s Fill from bottom up Two e−’s in each box (due to spin) Spin up and spin down in each box Or one e− for each specific n, ℓ, mℓ, ms No two e−’s can have same set of n, ℓ, mℓ, ms Pauli Exclusion Principle For given n, s