Download BCIT Fall 2012 Chem 3615 Exam #2

BCIT Fall 2012 Chem 3615 Exam #2 Name: ___________________ Attempt all questions in this exam. Read each question carefully and give a complete answer in the space provided. Part marks given for wrong answers with partially correct reasoning/calculations. A Periodic Table, Table of Electronegativity and formula sheet are attached at the back. Total points = 50 Good Luck. 1 of 11
Section I: (20 points total, 1 point each) Choose the BEST answer to the following questions. 1. The wave model of the electron of the hydrogen atom produces which of the following results? a) b) c) d) e) 2. Which of the following is not a property of an acceptable wavefunction, ? a) b) c) d) e) 3. An exact tracking of the movement of the electron Quantization of the angular momentum and energy of the electron The exact speed of the electron The exact charge on an electron A new value for Planck’s constant  must singled valued  must be continuous The first derivative of must be continuous The function ||² must have a finite non‐zero integral over all space All the above are properties If a1 and a2 are constants, x) and 2(x) are functions, and  is a Hermitian operator that satisfy the equation, Âx) = a1(x) and Â2(x) = a22(x) where a1 a2. Which of the following statements is false? (x) is an eigenfunction of  . If (x) = (x) + (x) then (x) is an eigenfunction of  a1 is a real number. 1(x) and 2(x) are orthogonal. a) b) c) d) e) Âc1(x) = cÂ1(x) where c is a constant. 4. Which statement is false about the tunneling of a particle through into a fixed height barrier where potential energy on each side of the barrier is the same? a) b) c) d) e) 5. Tunneling is a quantum mechanical phenomenon i.e. it is not predicted by classical mechanics The greater the width of the barrier, the lower the probability the particle will tunnel through the barrier. For constant particle energy, the greater the mass of the particle, the further into the barrier the particle will tunnel. The energy of the particle after it has emerged from the other side of the barrier is less than the energy the particle had before it hit the barrier. More than one of the above is false. Which of the following is an incorrect designation for an atomic orbital? a) b) c) d) e) 1s 7d 3f 2p 6s 2 of 11
6. Which of the following statements about quantum theory is incorrect? a) The energy and position of an electron cannot be determined simultaneously. b) Lower energy orbitals are filled with electrons before higher energy orbitals. c) When filling orbitals of equal energy, two electrons will occupy the same orbital before filling a new orbital. d) No two electrons can have the same four quantum numbers. e) All of these are correct. An atomic orbital with a  value of 2 corresponds to a letter designation of: 7. a) b) c) d) e) 8. d f g p s For a fixed value of n, the number of orbitals having a given value of  is equal to a) b) c) d) e) 9. 2 + 1 2n + 2 n² m 2n +1 Which of the following is not determined by the principal quantum number, n, of the electron in a hydrogen atom? a) b) c) d) e) 10. the energy of the electron the minimum wavelength of the light needed to remove the electron from the atom. the size of the corresponding atomic orbital(s) the shape of the corresponding atomic orbital(s) All of the above are determined by n. The small, but important, energy differences between 3s, 3p and 3d orbitals in multi‐electron atoms are due mainly to a) b) c) d) e) the number of electrons they can hold their principal quantum number the Heisenberg uncertainty principle the penetration effect Hund’s rule 11. Which of the following has the smallest radius? a) b) c) d) e) K+ Cl‐ Rb+ K Ar 3 of 11
12. Which of the following electron configurations belongs to an atom that is most likely to be involved in an ionic bond? a)
b)
c)
d)
e)
1s22s22p6 1s22s22p63s2 1s22s22p63s23p1 1s22s22p63s23p3 1s22s22p63s23p6 13. Which of the following bonds is most polar? a) b) c) d) e) C—O H—C S—Cl Br—Br They are all nonpolar. 14. Consider the following Lewis structure H
H
O
H
H
C
C
C
C
3
2
1
H
H
Which statement about the molecule is false? a) b) c) d) e) There are 10 sigma and 2 pi bonds. C–2 is sp2 hybridized with bond angles of 120. Oxygen is sp3 hybridized. This molecule contains 28 valence electrons. There are some H–C–H bond angles of about 109 in the molecule. 15. If four orbitals on one atom overlap four orbitals on a second atom, how many molecular orbitals will form? a) b) c) d) e) 1 4 8 16 none of these 16. Which of the following molecules has a bond order of 1.5? a) O2+ b) N2 c) O2– d) C2 e) none of these 4 of 11
17. Which of the following electron distributions among the molecular orbitals best describes the ground state of the NO molecule? a) b) c) d) e) 2s 2s* 2py=2px 2pz 2py*=2px* 2pz* 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 2 2 1 2 2 4 4 3 2 1 2 1 0 0 0 18. Which of the following types of molecules has a dipole moment (when polar bonds are present)? a) b) c) d) e) linear molecules with two identical bonds. tetrahedral molecules with four identical bonds. trigonal pyramid molecules with three identical bonds. trigonal planar molecules with three identical bonds. None has a dipole moment. 19. When electrons in a molecule are not found between a pair of atoms but move throughout the molecule, this is called a) b) c) d) e) ionic bonding. covalent bonding. polar covalent bonding. delocalization of the electrons. a dipole moment. 20. Which of the following ionic compounds has the largest lattice energy (the lattice energy most favorable to a stable lattice)? a) BaO b) BeO c) CsI d) NaBr e) BaS Section II: Short answer calculations do not need to be shown (16 points total). 21. Consider an electron moving in a one‐dimensional box where there is a proton at x= 0. The electrostatic potential energy is given by | |
What is the Hamiltonian operator for this system? (1 point) 2
∂
∂x
4
| |
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22. The n=5 set of p orbitals consists of ___3__ orbitals. Each 5p orbital has __1______ angular nodes and ___3_____ radial nodes. (3 points) 23. How many electrons can be contained in all of the orbitals with n = 4? (1 point) __32_____ 24. Write the electron configuration for the following and circle if they are diamagnetic or paramagnetic: (4 points) a) a gallium atom (Ga) 2
2 6
2
6
2
10
Diamagnetic 1
2
10
Paramagnetic Paramagnetic 1
1s 2s 2p 3s 3p 4s 3d 4p or [Ar] 4s 3d 4p b) a NF molecule Diamagnetic 1s2 1s2 2s2 2s2 2p2 2p4 2p2 25. For each of the following molecules and ions draw the best Lewis structure, Name the ideal geometry (from the VSEPR model), give the ideal bond angles, hybridization of underlined atom and indicate if the molecule is polar or nonpolar. The central atom is underlined. (7 points) Best Lewis Structure Molecule or Ion (show all the electrons and resonance structures)


CO32‐ Molecular Geometry Ideal Bond Hybridization Angle(s) of underlined atom Polar or Nonpolar :O :
│ 
O ═ C ─ O:


Trigonal planar 

:O :
:O:
│║
:O ─C ═↔:O ─C ─:
120° sp² nonpolar 120°, 90° sp³d polar 


Seesaw SCl4 or Irregular tetrahedron 6 of 11
Section III: Calculations and reasoning must be shown (14 points total) 26. For which of the following functions is an eigenfunction of the operator . If it is an eigenfunction give its eigenvalue. (3 points) a) 3
3
Therefore, e3x is an eigenfunction with an eigenvalue of 3 b) 3
5
Therefore, e3x + e5x is not an eigenfunction 27. The electronic spectrum of butadiene, CH2=CH‐CH=CH2, can be approximated as one‐dimensional particle in the box. Assume that the box length spans the entire four carbon chain. If when an electron in the n=2 state absorbs a 217 nm photon the electron is excited into the n=3 state. What is the approximate length of the butadiene molecule? (3 points) Δ
²
5
8
5
8
5
8
3
8
2
8
5
8
5 6.63 10 217 10 3.00 10 8 9.11 10 7 of 11
5.74 10
574
28. A particle is describe by the wavefunction  = ei5x. What is the particles momentum in the x direction? (2 points) Ψ
5
5
5 Ψ Therefore the momentum will be 5 = 5.30x10‐34 J s m‐1 = 5.30x10‐34 kg m s‐1 29. Suppose that the wavefunction for a one dimensional system is Ψ
√
Φ
Φ
and that 1(x) and 2(x) are normalized eigenfunctions of the Hamiltonian operator with eigenvalues of E1 and 5E1.respectively. Note that (x) is normalized. (3 points) a) To show that (x) is normalized, what is equation must satisfied (no calculation is needed)? (1 point) Ψ∗
Ψ
1 b) What are the possible values that would be obtained in measuring the energy on identical systems? (1 point) E1 and E2 c) What is the probability of measuring each of these values? (2 points) ProbabilityofmeasuringE
√3
2
ProbabilityofmeasuringE
1
2
3
4
1
4
75% 25% d) What is the average energy associated with this state. (2 points) 〈 〉 0.75
2 0.25
0.75
0.25 5
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Equations and Formulas R = 0.0820575 L atm mol‐1 K‐1 = 8.314 J mol‐1 K‐1 k = 1.38x10‐23 J/K c = 3.00x108 m/s me = 9.11x10‐31 kg h = 6.63x10‐34 J s  = 1.06x10‐34 J s NA = 6.02x1023 
h
mv
̂
∗
,〈 〉
,
E = hf c = f ,
∗

whichin1dimensionis
2
2
∂

∂x

For a particle in a one dimensional box of length L, the normalized eigenfunctions and eigenvalues of the Hamiltonian operator

Ψ
1, 2, 3, ⋯ ² ²
²
1
2

k ²  ²  sinh 2 ( a )
1
4k ²  ²
Decay of a particle’s wavefunction into a barrier of height Vo is given by Ψ
√2
,
2
,
sinh
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2
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Electronegativity Values 11