Chemistry 327 EXAM 3 Name_--L...L!oo""'--.L. _ FaIl, 2009 Dr. Watson Conversion factors and constants: _h_ = 2.79928xl0 -39 g-cm 8n2c hc = 12398 eV-A = 1.985xl0-2s J-m h = 6.626xl0-34 J-s = 4.135xlO-JS eV-s c = 2.9979x108 m/s k = 1.380xlO-23 J/K = 8.617xlO-s eV/K 1 A= lxlO-'O m 1 J = 6.242x 1018 eV electron rest mass = 9.1095xl0-31 kg electron rest mass energy (moc2) = 511xl03 eV proton rest mass = 1.673xlO-27 kg proton rest mass energy = 936xl06 eV C3v E 2C3 3crv h=6 A1 1 1 1 Z Z2, x2+ y2 A2 1 1 -1 E 2 - 1 0 x, y, (xy, x2. y2) (xz, yz)-----1-1. a). Write all the possible the term symbol(s) for each ofthe electron configurations ofthe F2 molecule given below. ,2sc> 22sc> 22pc> 22pn 42pn 32pc> I V\ =\ • g u g u g u t,\,s=)&+k=-11J.a.-.Yz =0 $:1 -~-Y1=--1 -~+y~ =0 $.:0 b). Sketch the geometry of the XeF4 molecule and specify the type of hybridization that is most appropriate for its valence-bond description. Xe-~ B Ve.?--~f'~ ........ 4 bp-+ 2.4> :r '.f~ 1I~4d~3 ·WJAl F-~ ·i .,••••.;. c). Indicate the type of hybridization that is appropriate for each carbon atom in the molecule v• 2. a). The formation of a C>g molecular orbital for H2 may be shown schematically as follows: • 15 15 Draw a similar diagram for each of the following:----2-• a a bonding molecular orbital for CO2using carbon and oxygen 2pz atomic /... orbitals () Co. 0 G)G) -ae+c±:e j). • an antibonding molecular orbital for CO2 c C ...... ):; 1T • a n bonding molecular orbital for l,3-butadiene Co C-c...& ~+ ~+3+li b). The bonding in the ally radical (CH2=CH-CH2 0) may be described in terms of a a-bond framework, formed from Sp2 hybridized orbitals, connecting each of the carbon atoms, and a delocalized n-bond involving the remaining 2pz-electron on each carbon. Set up the secular determinant for the n-orbitals using the Huckel approximation and solve for the energies in terms of a and ~ integrals. S £ E ~-e: ~ 0 o 0 0 ~ o<'-E ~ ==0 o ~ D<-E ~1v~ ~JdX:~ ~ (3 x/7; 1-I ~ ~I =0[r ~ : I=D 4 x (x2 -1)->( = 0 X 3_ 2>< = X. (K~Z) -= 0 X = 0) +-~ -~~ ~= C>(+'f2:~ E"2.. = 0<. Eel = t><.. -'JZ (!J-3-3. a). Draw arrows in the figure below showing each of the following transitions. Be sure to label each arrow with its corresponding number. Internuclear separation R 1. The most probable transition from the ground electronic state to an excited electronic /0state. -(1.@) 2. The most probable fluorescence transition. 3. An intersystem crossing transition. 4. The most probable vibrational transition. 5. The most probable phosphorescence transition. v,J b). In the diagram to the right, draw numbered arrows 2,3;0 to show the following transitions: 2,2 -(2~) 2,1 1. A P-branch transition. 2,0 2. An R-branch transition. 1,3 1,23. A pure vibrational transition 1,1 1,04. A pure rotational transition.. 5. An S-branch Stokes transition. 0,3 0,2 0,1 0,0 , j~ <J) ~ ~ .,.-4-4. Wavenumbers for two P-branch transitions from initial levels J in the fundamental IR spectrum of 12C160 are given below. J Y(cm'l) 1 2139.43 2 2135.55 In addition, the equilibrium vibrational wavenumber for this molecule is Ye = 2169.81 cm'l and the anharmonicity constant is Xe = 6.124xl0-3 . a). Calculate the wavenumber of the pure vibrational transition from initial state v = O. 3 - q -v-I - -~,. = ;Z ~~ --4 k~ -/2, ~e -t-'4 Xe.:z:,e. = ~e.-(I -2~) -"z.£,~ -= 2/~'J.8/ (1-2((../7.4X/"-'!J)J = 2./1-3. 24 c.-m. c<:..f>.. b). Calculate the value of the rotational constant ® for the upper vibrational state. (Hint: write the equation for the P-branch transition from J = 1). "Z1~<:> -= .z7~/O + .:1F(I-?~) == £;" +13,(o)-Bo (IX'Z)= 2/'",,-250 5 - --"B = -z/v'd-~-O _ :Z14-3.24-2./31.~3 -=-;,91LAn.-1 o 2.. 2-8, c). Calculate the rotational constant Bo for the lower vibrational state. ~..., -~IS + ~F:"(2"'1) = ~~ + 28, -~8. "B, _ P":.l-, -Z/1I18 -t-' 8e:> _ 213S";SS'-Zl~3,'Uf+-(P(;.c/t) '2.. Z 13\ == ;,89 .b1t-1 d). Calculate the wavenumber of the pure rotational Raman Stokes transition from initial state J = 0 that would be observed using a laser with a wavelength of2.00x 10-4 m. --i/~~ =-6.~xi()'m)( /~~) - t {/,9/) =r .0-I/' sz. 2/o-?~ = 38. 4& L41t-1-5-5. a). Ethene, C2H4 is a planar molecule. List all of the symmetry operations for ethene. c,.. H, /1-1 ~2. / .... t-\ f-I c)... b). The molecule allene, pictured here, has an Sn symmetry element. Determine the value of n. c). Determine the synunetry designation (AI' A2, or E) of a rotation about the z axis (~, -shown below) for the C3v molecule NH3. (Note: the character table for C3v is given on the front page). ~=-\ }('3-::: 1 Az. Cf'" ==-1 d). Determine which atomic orbitals of nitrogen (2s, 2px' 2py, 2pJ could be used to construct molecular orbitals for NH3 by overlapping with the hydrogen orbital -combination HlsA+ HIss + HIs<:. Explain your answer. 1-l14A + J./ 1.Ii B -+ ~ I.e t!.. ;J!tJ!o ~k~~ {+~~~I-J 2~ N IA. t!VN/ 2p~ LehtJUl c2N Zpx ~~:t:A.a~N 2.fy