5.111 Extra Problems - Exam II - Fall, 2005
Here are some extra problems that you can work as preparation for Wednesday’s exam.
Study the material before you attempt these problems. Approach each problem as an exam problem. Many of these problems are former exam problems. If you usually panic when you first read an exam problem, then panic when you first read these problems and then practice how to calm yourself down. Rephrasing the problem in your own words or drawing a sketch of the problem often helps crystallize the physical concept behind the problem. Once you understand the physical principle behind the problem, the equations necessary to work the problem will come to you easily. Remember, there are a limited number of physical principles being tested here. Don’t rely on a fixed, memorized procedure or memorized equation to solve a problem.
You can’t always make a problem fit into the procedure or equation that you have memorized.
You have to modify the procedure or the equation to fit the problem. Don’t modify the problem to fit the equations.
Also, don’t deny yourself the opportunity to intellectually engage and mentally wrestle with these problems by looking at the solutions first. You won’t have this opportunity on the exam. Remember, looking at a map before you start driving is a very different experience than actually driving the roads!
Periodic Trends
1. Write the initial and final electron configurations for the process corresponding to IE
4
(the fourth ionization energy) of Be.
2. The five successive ionization energies of B (i.e IE
1 through IE
5
) are 800, 2420, 3660,
25020 and 32820 kJ/mole. a) Write equations for these ionization processes giving the electron configuration before and after ionization. b) Write equations for these ionization processes seen in the photoelectron spectrum of B, giving the electronic configuration before and after ionization.
3.
Consider the following atoms and ions: Cl-, Ar, K+ a) Which has the smallest radius? b) Which has the lowest ionization energy?
4. Consider the systems Li, Be and Li
+
. a) Give the order of size for these three. Explain.
5. b) Which has the highest IE
1
? Explain. c) Which has the largest EA? Explain.
Arrange in order of size from the smallest to the largest: I , Br , Cl , Cl, Mg 2+ , Ne.
6. Consider the following ions: He
+
, Li
2+
, F
8+
. a) Which has the smallest radius? Explain. b) Which has the highest IE
1
? Explain. c) Which has the largest EA? Explain.
7. Arrange the following seven atoms or ions in order of size: K, F
+
, Rb, Co
25+
8 . Predict the larger ion in each of the following pairs. Give reasons for your answers. a) O – , S 2– b) Mn 2+ , Mn 4+ c) CO 2+ , Ti 2+ d) Ca 2+ , Sr 2+
9.
Consider the atoms As, Cl, K and S. a) Which atom has the greatest electron affinity? b) Which atom has the lowest electron affinity?

10 . The first ionization energy of helium is 2370 kJ mol –1 , the highest for any element. a) Define ionization energy and discuss why that for He should be so high. b) Which element would you expect to have the highest second ionization energy? Why? c) Suppose that you wished to ionize some helium by shining electromagnetic radiation on it. What is the maximum wavelength you could use?
11 . Without consulting any tables, arrange the following substances in order and explain: a) Mg 2+ , Ar, Br – , Ca 2+ in order of increasing radius. b) Na, Na + , O, Ne in order of increasing ionization energy. c) H, F, Al, O in order of increasing electronegativity.
Ionic Bonds
1. For the ionic molecule LiF, calculate the value of r at which the harpoon mechanism becomes energetically allowed. The IE of Li is 519 kJ/mol and the EA of F is 328 kJ/mol.
Thermodynamics
1.
Given the following data at 298.15 K, compute Δ Ho for (a) and (b):
OH(g) = 1/2 H
2
(g) + 1/2 O
2
(g)
H
2
O(g) = H
2
(g) + 1/2 O
2
(g)
Δ
Δ
Ho = -42.26 kJ
Ho = 241.8 kJ
H
2
(g) = 2H(g)
O
2
(g) = 2O(g)
Δ
Δ
Ho = 436.0 kJ
Ho = 494.5 kJ a) The bond energy of O-H, i.e. OH(g) = H(g) + O(g) b) The sum of the two O-H bond energies in water, i.e. H
2
O(g) = 2H(g) + O(g)
2.
Consider the following molecules, all with empirical formula C
4
H
6
:
[1] H
3
C-C ≡ C-CH
3
[2] H
2
C=HC-HC=CH
2
[3] H-C=C-H
| |
H
2
C-CH
2
Bond
C—H
C—C
C = C
O=O
Bond Enthalpy [kJ/mol]
414
347
615
495
Bond
C = O
O - H
C
C
Bond Enthalpy [kJ/mol]
730
464
811 a) Using the bond enthalpy table above, compute the enthalpy change for the isomerization of molecule [3] to molecule [2]. b) Using the bond enthalpy table above, compute the enthalpy change in the following reaction: [2] + (11/2) O
2
⇒ 4 CO
2
+ 3 H
2
O

c) If Δ H o for the reaction in (b) is actually -1743.2 kJ mol -1 , calculate !
H f
° compound [2] .
3. Consider the equilibrium gas phase reaction of n-butane to isobutane n-butane isobutane
H3C-CH2-CH2-CH3 ⇔ H-C-(CH3)3
[n-butane] ⇔ [isobutane]
Δ H o f
(298K) S°(298K)
-126.1 kJ/mol 310.0 J/mol K
-134.4 kJ/mol 294.64 J/mol K for a) Compute the Δ Ho and Δ So for the reaction at 298 K.
b) Compute Δ Go for the reaction at 298 K.
c) Calculate the value of the equilibrium constant at 298 K.
d) Suppose the partial pressure of isobutane is 5.00 bar and that of butane is 1.00 bar.
Calculate Δ G at 298 K.
4.
Consider the molecule NF
3
(g) with a Δ G ° f
= -90.6 kJ/mol and Δ H ° f
= -132.1 kJ/mol. a) Calculate Δ G ° and Δ H ° for the following reaction at 298 K.
N
2
(g) + 3F
2
(g) ↔ 2NF
3
(g) b) Calculate the value of the equilibrium constant K at 298K of the above reaction.
5. Naphthalene, C
10
H
8
, is stabilized by resonance.
(a) Use the tables of bond enthalpies and standard molar enthalpies of formation to estimate the value of !
H f
° for the fictitious, non-resonance-stabilized molecule (hydrogens not drawn).
C-H
C-C
C=C
H-H
∆ H°/kJ•mol
414
347
615
435
− 1 !
H f
°
/kJ•mol − 1
H(g) 218.0
C(g) 716.7
H
2
(g) ?
C(graphite) ?
10C (graphite, 298K) + 4H
2
(g, 298K, 1atm) ⇒ C
10
H
8
(g, 298K, 1atm)
(b) The measured value of !
H f
°
(C
10
H
8
, g, 298K, 1atm) = 151.0 kJ/mol. What is the resonance stabilization enthalpy for naphthalene?
6. The enthalpy change of the following reaction at standard conditions and 298.15 K is –114.38 kJ. The free energy change of the following reaction at standard conditions and 298.15 K is –
75.92 kJ.

4HCl(g) + O2(g) ⇔ 2Cl2(g) + 2H2O(g)
Some additional information is given in the following table.
Δ H o f
(298.15K)
H
2
O (l)
H
2
O (g)
-285.83 kJ/mol
-241.82 kJ/mol a) Calculate the enthalpy change if the H2O product were in the liquid phase, H2O(l). b) Suppose the partial pressures (in bar) of the reactants and products of the above reaction are
P
HC l
= 2.00 x 10 -5 l
P
O2
= 4.5 x 10 -1 P
Cl2
= 2.5 x 10 -3 P
H2O
= 4.8 x 10 -1 c) Is the reaction in part (b) at equilibrium at 298.15 K? Show your calculations that support your conclusion. Your calculations must be precise within two significant figures.
Bonding
1. On a single x-y graph, draw the interaction potential, of the kind that we drew for H
2
, for the
NN bond in each of the following molecules: N
2
, N
2
H
4
, and N
3
-1 . Clearly label the quantities that you are plotting on each axis. Label the equilibrium bond distance for each NN bond. Label the quantity equivalent to the bond strength for each NN bond. The relative values of the bond distances and strengths must be correct. Set the separated atom limit at zero energy. (HINT:
Draw the most stable Lewis structure of each molecule before you draw the interaction potentials.)
2. Give the most stable Lewis structure for each of the following molecules. Include the lone pairs, give formal charges for every atom and, if applicable, give all resonance forms:
(a) S
2
O
3
-
(b) NO
2
–
© NH
3
O (d) N
2
O
4
(e)
(i) F
2
O
(m)
H
2
SO
XeOF
(q) SO
4
-2
4
2
(f)
(j)
(n)
®
C
6
PH
H
3
6
NNO
NH
2
-1
(g) HCP
(k) I3
-
(o) SO
3
H
-
(s) CH
3
COO -1
(h) HPC
(l)
(p)
HOBr
H
3
NBF
3
(t) H
2
CSO (The carbon is bonded to the two hydrogens and the sulfur. The sulfur is also bonded to the oxygen.)
3. Give the symmetry of each bond of HCCCHCHCH
3 and give the hybrid or atomic wavefunctions with their principal quantum number that overlap to form each of the bonds.
Where appropriate, use the x, y, or z designations with the wavefunctions. Then, indicate the geometry around each carbon atom.

4 . Acrylic fibers are polymers made from a starting material called acrylonitrile, H
2
C(CH)CN. bond and give the hybrid or atomic wavefunctions with their principal quantum number that overlap to form each of the bonds. Where appropriate, use the x, y, or z designations with the wavefunctions. Then, indicate the geometry around each carbon atom.
5 . Compare the bonding in formic acid (HCOOH) with that in its conjugate base formate ion
(HCOO – ). Each molecule has a central carbon atom bonded to the two oxygen atoms and to a hydrogen atom. Draw Lewis diagrams, determine the hybridization of the central carbon atom, and give the molecular geometries. How do the π orbitals differ in formic acid and the formate molecular ion? The bond lengths of the C—O bonds in HCOOH are 1.23 Å (for the bond to the lone oxygen) and 1.36 Å (for the bond to the oxygen with a hydrogen atom attached). In what range of lengths do you predict the C—O bond length in the formate ion to lie?
6. Give the symmetry of each bond of NH
2
and give the hybrid or atomic wavefunctions with their principal quantum number that overlap to form each of the bonds. Where appropriate, use the x, y, or z designations with the wavefunctions.
7 . Draw a Lewis electron dot diagram for each of the following molecules and ions. Formulate the hybridization for the central atom in each case, and give the molecular geometry. a) CCl
4 b) CH
3
c) CO
2 d) BeH
2 e) OF
2
8. Draw the Lewis structures, give the hybridization of every atom and predict the geometries of a) ONCl b) O
2
NCl c) CHF
3
.
9. Give an example of a molecule or ion having a formula of each of the following types and structures: a) AB c) AB
3
-
2 planar bent b) d)
AB
AB
3
-2
3 pyramidal planar
10. a) Draw an energy correlation diagram for the molecular orbitals of the valence electrons of
H
2
. Label the atomic and molecular orbitals, including the x, y and z designations where appropriate. The relative ordering of the energies of the states must be correct. b) Draw an energy correlation diagram (as we drew in class) for the molecular orbitals of the valence electrons of O
2
. Label the atomic and molecular orbitals, including the x, y and z designations where appropriate. The relative ordering of the energies of the states must be correct. c) Which is greater: the ionization energy of H or the ionization energy of H
2
? Use your diagram in part (a) to explain your answer. d) Which is greater: the ionization energy of O or the ionization energy of O
2
? Use your diagram in part (b) to explain your answer.

e) Which is greater: the electron affinity of O or the electron affinity of O
2
? Use your diagram in part (b) to explain your answer.
Text Problems
1. 1.77 AJ
2. 1.79 AJ
3. 1.85 AJ
4. 2.33 AJ
5. 2.35 AJ
6. 2.39 AJ
7. 2.41 AJ
8. 2.43 AJ
9. 2.45 AJ
10. 2.47 AJ
11. 2.49 AJ
12. 2.53 AJ
13. 2.57 AJ
14. 2.77 AJ
15. 2.79 AJ
16. 2.93 AJ
17. 3.33b, c, d AJ
18. 3.35a, b, d AJ
19. 3.37a, d AJ
20. 3.45 AJ
21. 3.47 AJ
22. 3.49 AJ
23. 3.53 AJ
24. 3.55 AJ
25. 3.75 AJ
26. 3.93 AJ
27. 5.7 AJ
28. 5.9 AJ
29. 6.53 AJ
30. 6.57 AJ
31. 6.59 AJ
32. 6.61 AJ

33. 6.63 AJ
34. 7.47 AJ
35. 7.51 AJ
36. 7.53 AJ
37. 7.57 AJ
38. 7.59 AJ
39. 7.61 AJ
40. 7.71 AJ
41. 9.11 AJ
42. 9.13 AJ
43. 9.15 AJ
44. 9.17 AJ
After you have studied for the exam and worked the problems above, you should be able to work the following 6 problems in 50 minutes.
1. LEWIS STRUCTURES and HYBRIDIZATION a) Draw the most stable Lewis structure for H
2
PCOCl, with knowledge that the Cl and O atoms are bound to the C. Be sure to include the lone pairs and all resonance forms, if applicable.
b) Give the symmetry of each bond in (a) and give the hybrid or atomic orbitals with their principal quantum number that overlap to form each of the bonds. Where appropriate, use the x, y, or z designations with the orbitals.
c) State the geometry around each atom in (b) that is not a terminal atom.
d) Draw the most stable Lewis structure for S
2
O. Be sure to include the lone pairs and all resonance forms, if applicable. No 3d states are involved in the bonding of this molecule.
e) Give the symmetry of each bond in S
2
O and give the hybrid or atomic orbitals with their principal quantum number that overlap to form each of the bonds. Where appropriate, use the x, y, or z designations with the orbitals.
f) Give the geometry of the S
2
O molecule.
2. IONIC BONDING a) The energy from the bottom of the well of the KCl molecule to the separated ion limit, K + and Cl , is 521 kJ/mol. Calculate the equilibrium bond length of KCl.

b) Calculate the energy, in kJ/mol, required to dissociate KCl into K and Cl. The ionization energy of K is 418 kJ/mol and the electron affinity of Cl is 349 kJ/mol. c) Suppose the electron on K were to jump to Cl at a distance of 3.02 x 10 -9 m. Calculate the barrier to that reaction. That is, calculate how much energy, in kJ/mol, would have to be supplied to the system in order for the electron jump to occur at that distance. The ionization energy of K is 418 kJ/mol and the electron affinity of Cl is 349 kJ/mol.
3. LEWIS STRUCTURES
Draw the most stable Lewis structure for each of the following molecules, subject to the information given. Include lone pairs and, if applicable, give all resonance forms.
a) XeO
2
Cl
2
(Xe is the central atom.) b) C
5
H
5
-
(The carbons form a ring.)
4. THERMOCHEMISTRY
Use the following bond enthalpies to calculate Δ H o f
Bond Enthalpy kJ/mol
(298.15 K) for NH
3
.
H-H
H-N
N-N
N=N
N ≡ N
436
389
163
418
946
5. PERIODIC PROPERTIES a) Order the elements S, Cl, Ar, K, Ca, Sc, Ti from lowest to highest ionization energy. b) Order the elements S, Cl, Ar, K, Ca, Sc, Ti from lowest to highest second ionization energy.
6. THERMODYNAMICS
Consider the following reaction.
Cl
2
(g) ⇔ 2Cl(g) a) Is Δ H ° at 298.15 K for this reaction positive, negative or zero? Justify your answer. b) Is Δ S ° at 298.15 K for this reaction positive, negative or zero? Justify your answer. c) Is Δ G ° for this reaction less than zero at all temperatures? Justify your answer.