CHEM 3 Course web page http://web.chemistry.gatech.edu/~barefield/3/chem3a.html Outline for first exam period Atomic structure and periodic properties Structures and bonding models for covalent compounds of p-block elements Lewis Structures, Valence Shell Electron Repulsion (VSEPR) concepts and oxidation state Hybridization Composition and bond energies in binary p-block compounds Molecular orbitals in homonuclear diatomics First Exam Friday, September 5
Atomic structure and periodic properties Early experiments concerning atomic structure and properties of electromagnetic radiation Bohr model of the hydrogen atom Demise of Bohr model Wave equation and wave model for atom Wave functions and properties Orbital representations Multielectron atoms Periodic properties and their origin Properties of Atoms Consist of small positively charged nucleus surrounded by negatively charged electrons, some at large distances from the nucleus Nucleus consists of positively charged protons and neutral neutrons Charges of proton and electron are equal The atomic number (and nuclear charge) of an atom is equal to the number of protons in its nucleus. The mass number of an atom is equal to the number of protons plus the number of neutrons Isotopes are atoms with the same atomic number but different mass numbers, i.e., H, 2 H, 3 H or 2 C, 3 C, 4 C
Atomic Spectra Irradiation from electronically excited atoms is not continuous Visible region line spectra could be fitted to simple (empirical) formula /λ =.97 x 7 m - (/2 2 -/n 2 ) E = hc/λ = 2.78 x -8 J (/2 2 -/n 2 ) Later work showed several series of lines E = 2.78 x -8 J (/n 22 -/n 2 ) (n 2 <n ) Region Radio Microwave Infrared Visible Ultraviolet X-Rays Gamma Rays Spectrum of Electromagnetic Radiation Wavelength (Angstroms) > 9 9-6 6-7 7-4 4 - -. <. Wavelength (centimeters) > -.. - 7 x -5 7 x -5-4 x -5 4 x -5 - -7-7 - -9 < -9 Frequency (Hz) < 3 x 9 3 x 9-3 x 2 3 x 2-4.3 x 4 4.3 x 4-7.5 x 4 7.5 x 4-3 x 7 3 x 7-3 x 9 > 3 x 9 Energy (ev) < -5-5 -.. - 2 2-3 3-3 3-5 > 5
Visible region of electromagnetic spectrum 7 nm 7 Å 7x -5 cm 4 nm 4 Å 4x -5 cm Color of transmitted light Complementary color Violet Yellow green Indigo Yellow Orange Blue Blue green Red Purple Green Violet Yellow green Indigo Yellow Blue Orange Red Blue green 4 5 6 7 8 Wavelength, nm Properties of Electromagnetic Radiation c = λν c = 2.998 x 8 m s - (vacuum); λ in meters; ν in cycles per sec or s -I cycle per sec is Hz (Hertz) E = hν = hc/λ With Einstein's relationship E = mc 2 hc/λ = mc 2 λ= h/mc
Bohr Model Rule. Electron can exist in stationary states; requires fixed energy. Rule 2. Possible stationary states determined by quantization of angular momentum (mvr) in units of h/2π (mvr = nh/2π) Rule 3. Transitions between stationary states occur with emission or absorption of a quantum of energy, E = hν For a stationary state to occur for the electron moving in a planetary orbital about the nucleus, the centripetal force must equal the electrostatic attraction of the electron by the nucleus mv 2 /r = (Ze)e/4πε o r 2 or mv 2 = (Ze)e/4πε o r Employing the expression for angular momentum from Rule 2: r = n 2 h 2 ε o /πmze 2 v = Ze 2 /2nhε o Note that radius of orbits increase with n 2 and decrease with Z Total Energy for atom (E) = K.E. + P.E. = ½mv 2 + (-Ze 2 /4πε o r) from the previous slide mv 2 = Ze 2 /2πε o r so that E = ½(Ze 2 /4πε o r) - (Ze 2 /4πε o r) = -½(Ze 2 /4πε o r) = -Ze 2 /8πε o r from the previous slide r = n 2 h 2 ε o /πmze 2 E = -me 4 Z 2 /8ε o2 n 2 h 2 E = -(2.8 x -8 J) Z 2 /n 2 E = -(3.6 ev) Z 2 /n 2 Constants m = 9.939 x - kg e =.628 x -9 C c = 8.8538 x -2 C 2 m - J - h = 6.6268 x -34 J s ev =.622 x -9 J E = final energy initial energy E = -3.6 Z 2 ev (/n f2 -/n i2 )
Further evidence for unique properties of light Photoelectric Effect K.E.(ejected electrons) = hν(impinging light) - w(work function) Compton Effect Momentum and energy conserved in collisions of light (photons) with electrons Demise of Bohr Model - Introduction of Wave Model Heisenberg Indeterminacy (Uncertainty) Principle x (mv) h/2π Exact position and exact momentum cannot both be known simultaneously De Broglie's Hypothesis λ = h/mv Particles have wave lengths; proof came from diffraction of electron beam Schroedinger's Wave Equation 2 Ψ/ x 2 + 2 Ψ/ y 2 + 2 Ψ/ z 2 + 8π 2 m/h 2 (E-V)Ψ = (HΨ=EΨ) Solution of this equation requires conversion to spherical polar coordinates and the introduction of three constants, which are what we know as quantum numbers, n, l, m l
Each combination of n, l, and m l, value corresponds to an orbital n values relate to the energy and size of the orbitals. n =, 2, 3 l values specify the total angular momentum of the electron and determines the angular shape of the orbital. l s have letter equivalents: l = (s), (p), 2 (d), 3 (f), 4 (g), etc. l = n- m R, specifies the orientation of the orbitals in space and the angular momentum with respect to direction. m l = -l +l With introduction of the fourth quantum number, m s = +/2, -/2 and the Pauli principle, which states that no two eiectrons in a given atom can have the same four quantum numbers, the development of electron configurations for multielectron atoms is straight-forward. E = -me 4 Z 2 /8ε o2 n 2 h 2 = -3.6 ev Z 2 /n 2 Same as for Bohr model!!!! Wave Functions Ψ n,l,ml (r,θ,φ) = R n,l (r) Θ l,ml Φ ml R n, l 4Z ( r ) = n 3 4 3 ao ( n l )! 3 [( n + l)! ] / 2 2Zr e nao Zr / nao L 2l+ n+ l R, (r) = 2Z 3/2 a o -3/2 e -Zr/a o R 2, (r)= (/2 2)Z 3/2 a o -3/2 (2-Zr/a o )e -Zr/2a o R 2, (r) = (/2 6)Z 3/2 a o -3/2 (Zr/a o )e -Zr/2a o R 3, (r) = (/4 3)Z 3/2 a o -3/2 (27-8Zr/a o +2Z 2 r 2 /9a o2 )e -Zr/3a o l m l Θ φ Θ l,ml (θ) = sin m l2 P l (cos θ) / 2 / 2π Φ ml (φ) = (/ 2π)e ±im l φ ± ( 3/2)cos θ ( 3/2)sin θ / 2π / 2πe ±iφ 2 ( 5/8)(3cos 2 θ-) / 2π
Representations of orbitals s Radial functions 3 25 2 5 5 R, (r) = 2a -3/2 o e -r/a o R,2 (r) = 4a -3 o e -2r/a o r 2 R,2 (r) = 4a -3 o r 2 e -2r/a o 2 3 4 5 r, a o 6 5 4 3 2
2s Radial functions 3.5 3 2.5 2.5.5 -.5 R 2, (r)= (/2 2)a o -3/2 (2-r/a o )e -r/2a o R 2,2 (r)= (/8)a o -3 (4-2r/a o +r 2 /a o2 )e -r/a o r 2 R 2,2 (r)= (/8)a o -3 (4-2r/a o +r 2 /a o2 )r 2 e -r/a o 5 5 r, a o.7.6.5.4.3.2. -. Comparison of ns radial distribution functions.2.8.6.4.2 s 2s 3s 2 4 6 8 2 4 6 8 r, a o
Comparison of s, 2s and 2p radial distribution functions.2.8.6.4.2 s 2p 2s 2 4 6 8 2 r, a o Angular functions as contour maps Angular nodes Radial nodes Relative size
Contour plots of H 2p and C 2p 3 2 Contour lines are set at.36 of maximum values of Ψ 2 (r,θ,φ) -.5 - -.5.5.5 - -2-3 H He Li Be B C N O F Ne Multi-electron atoms; Aufbau Principle n= n=2 s s p.2.8.6.4.2 2 4 6 8 2 r, a o
More on multi-electron atoms Electron configurations in the third period (n=3) mirror those for the second period In the fourth period (n=4) the 3d orbital energies are lower than the 4p so that these orbitals fill before the 4p. The elements with d electrons are referred to as transition elements. Electron configurations of the first transition element series are 4s 2 3d n except for Cr and Cu, which are 4s 3d 5 and 4s 3d, respectively. These irregularities are a result of lower electronelectron repulsion energies. Transition metal cations have d n electron configurations. Periodic properties Ionization energy Atomic and ionic radii Electron Affinity Electronegativity
25 Ionization energy Ionization energy is the minimum energy required to remove an electron from a gaseous atom (or other species). E = E + + e - 2 IE/kJ mol - 5 5 2 4 6 8 Z IE/eV 25 2 5 5 4 8 2 6 Z Effective nuclear charge - -2 s & p orbital energies vs Z s p E/eV -3-4 -5-6 Z eff = Z shielding constant Li Be B C N O F Effective nuclear charges s H. He.69 2s 2p Li.28 Be.9 B 2.58 2.42 C 3.22 3.4 N 3.85 3.83 O 4.49 4.45 F 5.3 5. Ne 5.76 5.76
Atomic radii as function of Z Atomic and ionic radii Radii of some common ions, Å Li +.59 Be 2+.27 N 3-.7 O 2-.4 F-.33 Na +.2 Mg 2+.72 Al 3+.53 P 3-2.2 S 2-.84 Cl -.8 K +.38 Ca 2+. Ga 3+.62 As 3-2.22 Se 2-.98 Br -.96 Rb +.49 Sr 2+.6 In 3+.79 I - 2.2 Cs +.7 Ba 2+.36 Tl 3+.88 Fe 2+.75, Fe 3+.69 Radial distribution functions for alkali metal ions
Electron affinity Electron affinity is the energy change associated with addition of an electron to a atom or ion. E + e - = E - 4 3 EA/kJ mol - 2 - -2 H Li Be B C N O F Na Mg Al Si P S Cl K Ca Note that EA s have been historically recorded as the negative of the energy associated with the electron attachment reaction. Electronegativity Electronegativity is the attraction of an atom for electron density in a chemical bond Pauling electronegativities H 2.2 Li.98 Be.57 B 2.4 C 2.55 N 3.4 O 3.44 F 3.98 Na.93 Mg.3 Al.6 Si.9 P 2.9 S 2.58 Cl 3.6 K.82 Ca. Ga.8 Ge 2. As 2.8 Se 2.55 Br 2.96 Rb.82 Sr.95 In.78 Sn.96 Sb 2.5 Te 2. I 2.66 Cs.79 Ba.89