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Unformatted text preview: a _ ‘ My Problem #1 (worth 20 % of the grade on this exam) (a) Write the Lindemann mechanism for the "unimolecular" decomposition of A into products, P, i.e., the overall reaction is
A  —> P . Both reactants and products are gases. I
a ' I (b) Use the steady state approximation to obtain the differential rate law for this reaction.
/Z* ‘ ,Lt AN law/(WM
we a]: 5mm” Of ,4*= [WE of ﬂeﬂweﬁw tf/v’”
a, mz = 2., 5mm + gar/73:7 4454.77" 2
we; W5]: Mi M];
M 2 {2 + 19.0%] (c) Show that at high pressure, the reaction appears to be ﬁrst order and that at low pressure, it
appears to be second order. @ my fkmﬁ) 44,01] >> A: ’r' 0W : ’ﬂl/Z @ Low f/CfWﬁ) # >> 2 ._ 356%. Lot?” . ' Problem #2 (worth 20 % of the grade on this exam) (a) What are the half cell reactions for the electrolysis of water? State which reaction occurs
at the anode and which occurs at the cathode. ) 214304“ $7533! (/1266) ¢2ﬂzo(r/ (“ﬂ/mu
KP/ZO «:9 ficé<3l+2ﬂjo+ .423,“ (an/o4») (b) Write a balanced equation for the overall cell reaction. aw» H43) r 7202(3) (c) The standard reduction potential E0 for the following reaction is 1.229 V.
1/21;%(g) + 2H30+(aq) + 26’ ———> 3H20(1) Assuming that all gases produged by the reactions are produced at atmospheric pressure,
calculate E for both half cell reactions in the cell. (hint: treat 0.0592 as 0.06 I 0, (A .7 EO— I
gcaﬂt’ ' '5 /67 Q ‘5 ( [Ir/03177 .=69'.2£§‘ :.  r~0.0€ .1. :
gmsc ? /r7<4' / 22/ Z #7 ﬁ ill/0’77
ﬂ 2 3w g5, ‘fz ((1) Suppose that we have a 0.01 M solution of NaI. What reaction will occur at the
anode and what reaction will occur at the cathode. Explain. E0(Na+lNa) = —2.71V EO(I§II) = 0.535 V. Mame. am MW 4”“ 2/73an is» #2 @)rZ/120{,U
ﬂew/5‘ 0671' camya Problem #3 (worth 20 %) (a) Complete and balance the following equations for nuclear reactions: (i) 98cﬂ49 + ? —>103Lr257 +2 (3n
2,3ng + “5’8 + fggLr + 2 an.
(ii) 92U238 + 6C12 —> 93C1244 + ? 2331] + 1:0 —+ 2330f + 6 (1," (b) What is the thermodynamic criterion for why some nuclei are radioactive, i.e., decay
spontaneously? Express this in terms of both AG and AE. A6—<0 _, AE<0 (c) What is the Einstein massenergy relationship?
.'.1 2.
ELsmcz .__—+> A5 = G Am
(d) Together, parts (b) and (c) above lead to what additional criterion for radioactive decay? AM<0 (e) When two nuclei have the same number of protons but different numbers of neutrons, they are
called 1290 O t: .9 , l
(f) During radioactive decay, the kinetics of this process are [cl/(‘97. order. (g) Below, draw the curve showing the variation of the binding energy per nucleon, Eb/A, with
mass number, A. . Problem #4 (worth 20 %) (a) For the photoelectric effect, what is the relationship between the maximum kinetic energy of
the electrons, KEe, the photon energy, hv, and the work function , (l)? fur:K/é+7b (b) Below, plot the intensity of electron emission, 16, vs. photon frequency, v. Acceff e/‘Wv’eﬁ 25 :u'» (c) Below, plot the maximum kinetic energy of the ejected electrons, KEe, vs. the frequency of the
light, v. Indicate the signiﬁcance of the slope, the meaning and location of the intercept, and the K53 :.h2fy—'¢ frequency, v0, at which KEe = 0_ nauch 5'95 (d) Discrete packets of light arepalled 075/” . The photoelectric effect illustrated the fact
that waves cangact like 201,23 . (e) In considering blackbody radaition, classical theory found that the intensity of electromagnetic radiati n increas d continuously ith decreasing wavelength. This became known as the
" uﬁ ‘01.: 0 " _ Problem #5 (worth 20 %) (a) Derive the energy expression for the Bohr model of the atom. To get full credit, you must
deﬁne your symbols and show every step of your derivation. _ 22:" 2,001/
V 5779,)? Z 3 K 9
E: [/ZMCVF” fiEax 2 .2.
F: Mam = MCI—K}! r—g‘a—fz 0) Imam Mum/re of f, =t>LemeVK= 2177“ J page”,
TyeNJ y . n7? .9ali77‘7’a7‘mﬂ 77m» [#70 Em 0) ti) re! m ' 2
2 1 it Jaw/7727M! Emmw fa:
: €07) [7' V : ._‘_____......——
K “We”; ’W 260ml. ’ K M? y W EM, (2.))
\ 4 _ — 6 Me n u  " ' P
Eh 56322252 Nil; ° ﬂ"°2"3’ (b) ‘ As the quantum number, n, goes to infinity, the radius of the electron's orbit goes to (c) As 11 goes to inﬁnity, the energy goes to 2w . (d) For n22, the radius of the electron's orbit is 6" times greater than for n=1. End of exam m Problem #1 (worth 20% of the grade on this exam) @ W @ @ Which of the following combinations of quantum numbers
are allowed for an electron in a oneelectron atom and which arenot? (a)n=3, (=2; m=1, ms=0
(b)n=2, (i=0, m= , ms=%
'(c)n=7,.€= , m=—2, ms=%
(d)'n=3, €=3, m=2, ms=—§ £(a) This combination is not allowed because m. is never equal to zero. If ms
were changed to :l:1/2, this combination would be allowed. (b) This combination is allowed. It speciﬁes a 2selectron.
(c) This combination is allowed. It speciﬁes a 7d—electron. I
(d) This combination is not allowed. The quantum number I is never negative. Label the orbitals described by each of the following sets of
quantum numbers. (a)n=3, €=2
(b)n=7, (=4
(c)n=5, €=1 (a) 34 (b) 79 (c) 5p . Give the groundstate electron conﬁgurations of the follow— ing elements.
(a) P
03) TC
(c) Ho ‘
(a) P: [Nei3523p3 (b) Tcé [Kr14al55s2 (c) Ho: [Xe]4f11652 if} Write groundstate electron conﬁgurations for the ions Li", '
B+, F“, A1“, S”, Ar+, Br+, and Te". Which do you expect to be paramagnetic due to the presence of unpaired electrons? Li" (152252) is diamagnetic; 3* (152252) is diamagnetic;
F‘ (1322522126) is diamagnetic; Al3+ (1322522126) is diamagnetic.
All of the preceding have an even number of electrons and all electrons paired.
S' (1522822p63523p5) is paramagnetic. ‘
Ar+ has the same groundstate conﬁguration as S" and is therefore also para
magnetic. ’
Br+ ([Arl3dm4sz4p“) is paramagnetic; Te‘ ([Kr]4d‘°5525p5) is paramagnetic.
A species with an odd number of electrons must be paramagnetic; species with
an even number of electrons may be diamagnetic or paramagnetic. Problem #2 (worth 30 %) KE/ (a) (Read this entire problem before beginning to do it.) Sketch a one dimensional, particle—ina—
box potential well with inﬁnitely high walls and width, L. Write the expression for the energy of
the levels in this well and draw the first three of them, to scale, in the well. Label these by their
quantum numbers, n. To the right of this drawing, sketch the wavefunctions for each of the above
three energy levels. To the right of the second drawing, sketch the corresponding probabilities (for
finding the particle at a given location) for each of the three energy levels. If you were to shorten
the width of the box to L/2, i.e., if you were to squeeze its width from L to L/2, what would
happen to the ﬁrst (lowest) energy level? Show the resultant energy of that level with a line to the left of your first drawing.
L A 2..
E ‘ M” I
’ — . 2
' 2 t
7" 3M 1. [a 0
WI
 \ / . $2 0
LE M197}? * 1:2
ll’I 0
(a) Energy levels (b) Wave functions
(b) A particle of mass m is placed in a threedimensional rectan gular box with edge lengths 2L, L, and L. Inside the box the
potential energy is zero and outside it is inﬁnite, and so the
wave function goes smoothly to zero at the sides of the box.
Calculate the energies, and give the quantum numbers of the
ground state and the ﬁrst ﬁve excited states (or sets of states of equal energy) for the particle in the box. Ground state: Excited states: FIN 2
$3 0 L
[1% 0 L
2
4,! 0 x L
(c) Probabilities h2 112 "2 n:
En,n,n.= [ ‘ +"+fz‘ 8?; (2L)2 L2
h2 9 h2
E111 = 8 1 + = 
ha 3 h2
E211 8 mL2(4/4+ 1 + 1) — 8mL2
h? 17 h2
E311 — mL2(9/4 +1+ 1) — 32mL2
h: 21 2
E112 = E121 — = Problem #3 (worth 20 %) K 15/ (a) In VSEPR theory, what molecular geometries are expected if the steric number, SN, of the
central atom is 2, 3, 4, 5, and 6? Here, assume that all bonds are equivalent and that lone pairs play no role. I \L" C t o
______+..
. . (b) I 80° I 2: Linear 6: Octahedral 4: Tetrahedral _ Predict the geometry of the following molecules and ions: (a) "C105" , (Ii) , (c) SiH4, (d) IFS. Figure 149
The structure of IFS. Note the distor
tions of F—I—F bond angles from 90° because of the lone pair at the
bottom (not shown). (a) The central Cl atom has all of it’skvalence electrOns (six, because the ion has a
net positive charge) involved in bonds to the surrounding three oxygen atoms and
has no lone pairs. Its steric number is 3. In the molecular ion the central C1 should
be surrounded by the three 0 atoms in a trigonal planar structure. (b) The central Cl atom in this ion also has a steric number of 3, composed of two bonded atoms and a single lone pair. The predicted molecular geometry is a belie
molecule with an angle somewhat less than 120°. (c) The central Si has a steric number of 4 and no lone pairs. The molecu
geometry should consist of the Si atom surrounded by a regular tetrahedron 0' (d) Iodine has seven valence electrons of which ﬁve are shared in bonding pa
with F atoms. This leaves two electrons to form a lone pair, and so the '
number is 5 (bonded atoms) + l (lone pair) = 6. The structure will be based
the octahedron of electron pairs from Figure 146, with ﬁve F atoms and one
pair. The/lone pair can be placed on any one of the six equivalent sites and?
cause the four F atoms to bend away from it toward the ﬁfth F atom, giving
distorted structure shown in Figure 14w9. KE/ Problem #4 (worth 30 % b
(a) What is the equation which defines the de Broglie wavelength? A z 7 (b) Write the equation for the Heisenberg Uncertainty Principle in terms of position and linear momentum. AX A/ z %_r (c) Write the Schrodinger equation (in either of the two forms that we discussed); 2. 2—
HW’EW 0‘ "£37" + Vow/00 =E%v)J (W WM ((1) What is a Hamiltonian? It is the sum of what two things? ENEFK)! 0/4073ﬁ J’aw of If, +V 0/9 :17: 002 7'— 1/00 in If)”.
’ 577% ' SEX? ’ (e) How did Born interpret the probability of finding a particle in terms of its wavefunction, ‘P?
«v y) 2
(f) In the hydrogen atom, there are how many orbitals for each principal quantum number, n? 712 00 (h) The probability density of ﬁnding an electron at the nucleus is nonzero for what kind of orbital?  ,4 3 (,e :0) 01232724
(i) State the Pauli Exclusion Principle. No Two eLecZKdM 1:4! AM Ayn/4 W More We ~(ta/are J’s? 4/: Fuck awn/m NHMk/J’ .0; 1.646% 0mm an.» AIM 47‘
0) State Hund's rules. My)" Two eAecrza/IJ’J owe Lama .Q/V/v 4%, ONE w/‘TA‘
7 , 9/0)»! ﬂow”: (g) Draw the shape of an}: 1 orbital. P “electrons are orbitals infrequ‘alzenergy; ta .‘
smegma orbital before a *’seeondIone enters any orbitals. Insaddmon;
ithe :parallelifrpossible; ' ‘ ' ' ' (k) What is Pauling's electronegativity difference, A, definition? I want two equations here.
A sag”,  VAgAAEB,’ 7g, — 7!, 5 0/02 4‘
(1) What is Mulliken's eleCtronegatiVity deﬁnition? 15 =17 eteezt N ’/2.‘([/77L5/¢), (m) How much energy (in terms. of IP‘s and EA's) does it cost to convert the distantly separated
atoms, Na and I into the distantly separated ions, Na+ and I“? 6057' = +IFM~ EA’I (n) What is the deﬁnition of a dipole moment, [1, and what is the usual unit of ti? end ofexam M 3 We 22 ...
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 Fall '03
 K.H.Brown
 Chemistry

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