Exam I Fall 2008

Exam I Fall 2008 - (10 pts) 1. Write the ground state...

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Unformatted text preview: (10 pts) 1. Write the ground state electron configuration for each of the following species. Use the noble gas core symbol to abbreviate the inner core of electrons and give the electron configuration beyond the noble gas core. Assume the normal filling rules are obeyed. Electron Configuration number of unpaired electrons (a) In (b) In3+ (c) Gd3+ (d) Ni2+ (e) Re (12 pts) 2. (a) Fill in the blanks in the table below. Mark the angular nodes (if any) on your angular wavefunction and the radial nodes on your radial wavefunction. Explain how you arrived at your orbital choice. Overall wavefunction Radial wavefunetion Angular radial density distribution (R(r)n, 1), mark radial wavefunetion (Y1, In); function (R(r)2r2) nos with an x sho ular node (b) How many radial nodes does the plot of the overall wavefunction show? (c) How many angular nodes does the plot of the overall wavefunction show? (d) Which orbital does the above overall wavefunction correspond to? Give the n and 1 values and the letter designation for the orbital. (2 pts) 3. The lowest n value for an h orbital (s, p, d, f, g, h) is ? There are h orbitals. (4 pts) 4. Given the common names for the following groups: Group 1 Group 2 Group 16 The 5f series of elements (36 pts) 5. For each of the following series, write the best choice and explain your selection briefly. (a) the largest size: (i) Li“ B F) explain: (ii) Cl Mg Si explain: (iii) Be Mg Ca explain: (b) the most positive ionization energy: (i) Al Na Mg __ explain: (ii) 0 N C __ explain: (iii) Na+1 Mg+1 Al+1 _ explain: (iv) Na2+ Al2+ Mg2+ __ explain: (c) the most _ngggt_iv_e electron affinity (i) C N B __ explain: (ii) F Cl Br _ explain: (iii) F Ne O __ explain: (d) the most electronegative element (i) Sr Mg Ca _ explain: (ii) P Al Si explain: 4 (10 pts) 6. The valence electron configuration for niobium is 5s1 4d4 instead of 5s2 4d3 as the normal filling rules would predict. (a) Draw an energy level diagram showing the orbitals and their occupancy for the two electron configurations. 5s2 4d}: 5s1 4d“: (b) Indicate whether the following factors are positive (unfavorable), negative (favorable), or zero contributions favoring the 5s1 4d4 electron configuration over the 5s2 4d3 electron configuration. — 5s1 4d“ over 53 4d3 W W —— ene‘gy‘“°) _— (c) Based on your analysis above, suggest a plausible explanation for why the normal filling rules are not followed in this case. (9 pts) 7. Use the molecular orbital diagram provided for a second row homonuclear diatomic to answer the following questions. Give the electron configuration and bond order for each species in your explanation. [eg., for Liz, the electron configuration would be C(25)2 and the bond order would be 1.] 0*(2p) (a) Would you expect C2 or C22‘ to have a longer C-C bond length? Map) Explam. —— "(2m cTap) 0*(25) (b) Would you expect 02 or 022‘ to have a longer O—O bond length? “(25) Explain. (c) Would you expect 02 or 02+ to have a longer O-O bond length? Explain. 8. (12 pts) (3) Briefly describe what effective nuclear charge, 2*, means. Give an equation relating Z* to o. (b) Use Slater’s rules (on the attached information sheet) to calculate the effective nuclear charge felt by the s valence electrons in Sr, Ba, Zr, and Hf. Zeff Sr Zcfi‘ Ba Zcfi‘ Zl‘ Zcfl‘ Hf (c) Barium is larger than strontium but the size of zirconium and halfnitun are about the same. Use your results above to suggest an explanation. 9. (7 pts) (a) The second ionization of C (Cr —> C2+ + e') and the first ionization energy of B (B —) B+ + e') are 24.383 eV and 8.298 eV, respectively. Use Slater’s rules to calculate the effective nuclear charge for a valence electron in each of the ionized species. Show your work. zeff C+ zm B (b) What other factor than effective nuclear charge must be accounted for to explain the large difference in the two ionization energies? 10. (8 pts) (a) The second ionization energy of He is almost exactly four times the ionization energy of H, and the third ionization energy of Li is almost exactly nine times the ionization energy of hydrogen. Explain this trend using the Born equation. (b) Why is the Born equation applicable to this problem? Information Sheet: Slater’s Rules 1. The electronic structure of the atom is written in groupings as follows: (18), (28, 2P), (38, 313), (3d), (48, 413), (4d), (40, (55, 513), (5d), (50 2. Electrons in higher groups than the electron you are considering (to the right on the above list) do not shield those in lower groups. 3. For ns or np valence electrons: a. Electrons in the same ns, np group contribute 0.35, except the Is, where 0.30 works better. b. Electrons in the n-1 group(s) (n is the principal quantum number) contribute 0.85. c. Electrons in the n-2 or lower groups contribute 1.00. 4. For nd and nf valence electrons: a. Electrons in the same nd or nf group contribute 0.35. b. Electrons in groups to the left contribute 1.00. Equations and Constants E=—RH(Zz/n2); RH = 2.1787 X 10‘l8 J Periodic table of the elements 13 14 15 16 I? 1113 “’3 Va VIa VIIa 4 5 6 7 8 9 IO M IVb Vb Ib LIbe b * Numbering system adopted by the International Union of Pure and Applied Chemistry (IUPAC). ** Numbering system widely used, especially in the U.S., from the mid-20th century. *** Discoveries of elements 1 12—1 16 are claimed but not confirmed. Element names and symbols in parentheses are temporarily assigned by MP AC. © 2006 Encyclopaedia Britannica, Inc. (10 pts) 1. Write the ground state electron configuration for each of the following species. Use the noble gas core symbol to abbreviate the inner core of electrons and give the electron configuration beyond the noble gas core. Assume the normal filling rules are obeyed. Electron Configuration number of unpaired electrons (a) In l 55" LB” 5'3! l (b) In“ C Kr] “MN 0 (c) Gd“ [Xe 1 EH; 2 (d) Ni“ W '2- (e) Re [Xe—.1 C51 Lil-HS}; 5 l ecu-k (12 pts) 2. (a) Fill in the blanks in the table below. Mark the angular nodes (ifany) on your angular wavefunction and the radial nodes on your radial wavefunction. Explain how you arrived at your orbital choice. Overall wavefunction Radial wavefunction Angular radial density distribution (R(r),.. ,), mark radial wavefunction (Y L m); function (Rh-)2?) W show anular node 3 (b) How many radial nodes does the plot of the overall wavefunction show? l I (c) How many angular nodes does the plot of the overall wavefunction show? 3 2’43 (d) Which orbital does the above overall wavefunction correspond to? Give the n and 1 values and the letter designation for the orbital. “7"; X“ .3 ‘5' 4? 3ft? (2 pts) 3. The lowest n value for an h orbital (s, p, d, f, ) is 6 ? There are l l h orbitals. 0,11 0.1335 (4 pts) 4. Given the common names for the following groups: Groupl Alhl: Groupz Alkali”; flaw Group 16 Also 3 cm 5 The 5f series of elements AC'l't'noi is (36 pts) 5. For each of the following series, write the best choice and explain your selection briefly. (a) (b) (c) (d) 1—2 malt +1 “91%; the larg est size: (i) Li” B @ (ii) Cl Si (iii) Be Mg Ca explain: [Mia-9' A explain: aw‘on. K M; explain: low-I. ZLFF Mfirlflbb the most positive ionizationenergy: - ma; 219$? Mk Lad” fir 3:15';‘ 3‘- dee m ‘2 , 0) A1 r N: @ fl} explain: AL “Ea-"fl; 4-:- P oan'hl 297194 2:71? ZJ‘Zr“ 216(- O>M>CJ In: liar: a) ran-12- (ii) 0 @ C N explain: “chm PM‘QJ cpl-Hui ‘Qr Hi... 4H4- ‘mn. (iii) Mg+l Al+l fig: explain: Imzaa‘? £0" 2: 4'7- _ ‘3 (iv) Na“ Al2+ @ explain: [1.x 9...; 2.5 o“ “I” LEA EFF Ma. Ion NJ, I “a ] «Qua-data the most neoative electron affinity ‘fl'Jr 0“ “all” T l 1971” 3‘22 25‘? C v (i) © N B i explain: {ELLFII flu? tka'r‘H-i for ‘HV. (ii) F @ Br Fg__ explain: CE. m Cunard-Ia. Hm“ C “(an a I" ling.“ F explain: (iii) CF) Ne O the most electronegative element (i) Sr a (ii) 6 Al Si Ne. "' Culling: e; 1‘5 and: n SMHMJT n ma__ explain: P explain: W‘zlaui' 2&5? 4 (10 pts) 6. The valence electron configuration for niobium is 551 4d4 instead of 55; 4d3 as the normal filling rules would predict. i (a) Draw an energy level diagram showing, the orbitals and their occupancy for the two electron cenfigurations. H 55'4d“: a +__ 4.: 4—4-4“ q t t {sci-L- 53+ 552 4d’: (b) Indicate whether the following factors are positive (unfavorable), negative (favorable), or zero contributions favoring the 5s1 4d‘ electron configuration over the 552 4d' electron configuration. (c) Based on your analysis above, suggest a plausible explanation for why the normal filling rules are not followed in this case. ’l'lu m'e‘Hc raahua‘: luv: CDBJOHI-ub and “than? 60.44"? W? Meal “1 (M3? PGIIA’Jy k ,9th {:5 dun-Jr.“ +5 1L..ch Mini. (9 pts) 7. Use the molecular orbital diagram provided For a second row homonuclear diatomic to answer the following questions. Give the electron confi uration and bond order for each s ecies in our ex lanation. [eg., for U1, the electron configuration would be 0(25)2 and the bond order would be l.] +2. ‘3’ ID 6*(2p) (a) Would you expect C3 or C22" to have a lenger C-C bond length? C2 '1' i Explain: __ wrap) 1 *1- '7.. a '- —- a. .. i mm CL 01, a}, 6;? 11;, 3,0. 3 l 2. H O'(2p) C -'._ a u H 1'" 9' ... BID 2 4., z Lf - 6*(25) II N- 2_ (b) Would you expect 03 or 032' to have a longer O-O bond length? g 2: “(25) Explain. 1_ 'L 1.. 0,;- 5‘: of, 6;? 1r: rrjrr — B.o.= ma 2 o“ " H " 1' 1T‘*2.f'*-B.o.='-l—3=—l 2. (c) Would you expect 0; or 0; to have a longer O-O bond length? 0.3 Explain. O," W “L. VC O} 71"" 5.0.: L+-1.s’= 25 8. (12 pts) (a) Briefly describe what effective nuclear charge, 2*, means. Give an equation relating Z* to o. - 2*: 2.4" 2* .‘5 fig nuclear (Shara-'- f'cH‘ a S¢+ a; gbcz‘wm; v4 an u‘f'om or fan affot accom‘f'u‘na 5r fiddle}? of 1%,. hub..- cLar? La i'nmr Chm (b) Use Slater’s rules (on the attached information sheet) to calculate the effective nuclear charge felt by the 5 +2 valence electrons in Sr, Ba, Zr, and Hf. i " (lsl ‘ (z:,zr)’(;:, SE) 9 (34),”(9s, 9p)” 5: Z W Sr 25.; + 2_ (+1 Sr= 3? -.ss—- 9mg) - zs’ 323g *— rams if: Sam Long} as aJ-we. 'l‘ (9.1); ao- 0.3r—to(.35‘)- If - 3.IS' 8“ A (*5, I (4J)m(5'll ZcfiZr—iL—t—Z. 56-352 2L3?) ~It—2? = 2.35— 9 HQ: sum-as above + New [51)" 42*(1-35' HOLE?) -‘32.-‘ ZcfiI-If 3J5 e2. " 23": 3 LS" I c Barium is lar er than strontium but the size of zirconium and halfnium are about the same. Use your results g abovetosuggestan—oaplamt-ion. a: moa.{€(s+u.n of Sid-“I, "I" _Hm+ MIJH- war-k ‘ F zefiBa 1-5"? "L “ 6“ If Er dual and «19 fine 5am til-c sinu. clec‘l’rmsa qr: cnf’cf‘t‘n a (47¢.- +2 J . _ . . ll IIJ sa‘l" ? N 4‘50 Hf Sana. "Ha "F orbu-f'nlf are fulfil-Ida» twill, TA cmelee. Hm Slw‘clclfng confed- (J 4;, 4i“ (n.4,) 51%“ of: 9. (7 ptS) (a) The second ionization ofC (C+ —> C2+ + e') and the first ionization energy ofB (B -—> B‘ + e‘) are 1‘: Wm 24.383 eV and 8.298 eV, respectively. Use Slater’s rules to calculate the effective nuclear charge for a valence ' electron in each of the ionized species. Show your work. awash-(282?? $41.35) —2.(,g;-) Zcflc u +2 § :3 " 5"— z(.sr)— 2:35”) (b) What other factor than effective nuclear charge must be accounted for to explain the large difference in the I twoionizationenergies? Cf’? shin“. 71M“ Be: 56 flu ekrhnns Lat-H Lg atom?!“ +3 nu- HMOICM, “bk—L will 3W?- 4 Layla“ Lt'mlma cur-57 lO. (8 pts) (a) The second ionization energy ofHe is almost exactly four times the ionization energy of H, and the third ionization energy of Li is almost exactly nine times the ionization energy of hydrogen. Explain this trend using the Born equation. EanE—i “with lirHW-Jz ’ @938 1'6 Ell-L'KH EH += “Lift; EL.'"= ~9£H (b) Why is the Born equation applicable to this problem? 72 71““ are 4“ am. “6156th Sasha‘s ...
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Exam I Fall 2008 - (10 pts) 1. Write the ground state...

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