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Chem 222 Intro to Inorganic Chemistry Summer 2011 Problem Set 3-Answer Key Tuesday, June 21, 2011 1. (box 6.4 H and S) List the coordination number of the cation, the coordination geometry, the expected r+/r- range and the overall stoichiometry for CsCl and CaF 2 Coordination number of cation Coordination geometry Expected r+/r- Stoichiometry cation: anion CsCl 8 cubic > 0.73 1:1 CaF 2 8 (anion 4) cubic >0.73 1:2 2. Calculate the the r+/r- for LiCl, NaBr, Na 2 O, What structure will each of these adopt? Identify the elements on the appropriate lattice structure. Salt Cation (r+) Anion (r-) r+/r- Structure LiCl 76 181 0.420 NaCl NaBr 102 196 0.520 NaCl Na 2 O 102 140 0.728 Antifluorite Fluorite structure (green=anions, red= cations) or antifluorite structure (green= cations, red=anions) Na 2 O green=Na and red=O Zinc Blende (ZnS with Zn and S on alternating sites) aka Diamond (with C at all sites)
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Chem 222 Intro to Inorganic Chemistry Summer 2011

Problem Set 3-Answer Key Tuesday, June 21, 2011 1. (box 6.4 H and S) List the coordination number of the cation, the coordination

geometry, the expected r+/r- range and the overall stoichiometry for CsCl and CaF2

Coordination number of cation

Coordination geometry

Expected r+/r-

Stoichiometry cation: anion

CsCl 8 cubic > 0.73 1:1

CaF2 8 (anion 4) cubic >0.73 1:2

2. Calculate the the r+/r- for LiCl, NaBr, Na2O, What structure will each of these adopt? Identify the elements on the appropriate lattice structure.

Salt Cation (r+) Anion (r-) r+/r- Structure

LiCl 76 181 0.420 NaCl

NaBr 102 196 0.520 NaCl

Na2O 102 140 0.728 Antifluorite

Fluorite structure (green=anions, red= cations) or antifluorite structure (green= cations, red=anions)

Na2O green=Na and red=O

Zinc Blende (ZnS with Zn and S on alternating sites) aka Diamond (with C at all sites)

Chem 222 Intro to Inorganic Chemistry Summer 2011

NaCl structure (anions are green, cations

are blue, note that this just reflects the relative sizes, as the positions work out to the same crystal structure, regardless)

LiCl, Cl=green, Li=blue

NaBr Br=green, Na=blue

CsCl structure

3.

4. (H and S 6.15) Using data from the Appendices (of H and S) and the fact that ΔfH° (298 K) = -859 kJmol-1, calculate a value for the lattice energy of BaCl2. Outline any assumptions that you have made.

Chem 222 Intro to Inorganic Chemistry Summer 2011

-2050 kJ/mol -assume ΔU (0 K) is approximately equal to ΔH(lattice) (298 K)

5. a) Give a balanced reaction for the burning of methanol in air. 2CH3OH + 3O2 2CO2 + 4H2O

b) Give two half reactions and the overall reaction for a direct methanol fuel cell (methanol instead of H2 is used as a fuel and a proton exchange membrane is still present)

anode (oxidation reaction)

4(CH3OH +H2O CO2 + 6H+ + 6e-) cathode (reduction reaction)

6(4H+ + O2 + 4e- 2H2O) overall reaction

4CH3OH +4H2O + 24H+ + 6O2 + 24e- 4CO2 + 24H+ + 24e- + 12H2O cancel the e- and H+ and H2O from both sides to get:

4CH3OH + 6O2 4CO2 + 8H2O which simplifies to:

2CH3OH + 3O2 2CO2 + 4H2O (same as direct combustion)

6. Draw an MO diagram for the oxygen moiety in peroxide. Comment on the magnetism.

Chem 222 Intro to Inorganic Chemistry Summer 2011

The extra two electrons (in red) go into the anti-bonding orbitals, weakening the oxygen-

oxygen bond. This explains the higher reactivity of peroxides. The resulting complex is diamagnetic (very, very weak force) and will therefore be weakly repelled by a magnetic field.

7. Sulphur miners often have lung problems after a few years of working. Write balanced reactions starting from S8 to account for this damage. Suggest a compound that could be put in a respirator to mitigate this reaction.

This is the same chemistry associated with acid rain, so:

S8 + 8O2 8SO2 (in air, aided by elevated temperatures) 2SO2 + O2 2SO3 (in air, aided by elevated temperatures and surfaces)

SO3 + H2O H2SO4 (water in lungs plus SO2 gas) H2SO4 H+ + HSO4

- (dissociation in lung)

Chem 222 Intro to Inorganic Chemistry Summer 2011

(Recall that for industrial synthesis of H2SO4, it is necessary to bubble the SO2 through H2SO4 to avoid formation of a thick mist. However, due to the low concentrations of H2SO4 in the air, this is not required in this case)

Any base in a respirator would work to react with SO2 vapour or droplets of H2SO4,

before they react with the lungs, but a weak base would be best, so that there is less concern with inhaling caustic.

8. (H and S, section 6.11) Sulphur and selenium have very similar redox activities. For the following (unbalanced) sulphur chemistry, give the analogous reactions for selenium and determine the oxidation state of the selenium in each compound.

[SO4]2- H2SO3SH2S [SeO4]2- H2SeO3SeH2Se Assume O is O2- (most common) and H is H+ (as it is reacting with a non metal),

therefore the oxidation states are 6+, 4+, 0 and 2- for both S and Se.

9. Draw the bonding and anti-bonding molecular orbitals arising from py-py interactions and pz-pz interactions.

Note that px-px bonding and antibonding orbitals would be the same shape and perpendicular to the py orbitals.

Chem 222 Intro to Inorganic Chemistry Summer 2011

10. (H&S 2.9) (a) Use MO theory to determine the bond order in each of [He2]+ and

[He2]2+. He has electron configuration 1s2, and has only the 1s orbital in its valence shell. The

MO-diagram needed to examine the bonding in the two cations is:

E n e r g y1s 1s

He Heg (1s)

u* (1s)

The [He2]+ cation has three electrons instead of the four electrons for neutral [He2], and

the [He2]2+ cation has only two electrons. This gives the following MO diagrams:

Chem 222 Intro to Inorganic Chemistry Summer 2011

E n e r g y1s 1s

He Heg (1s)

u* (1s)

[He2]+

E n e r g y1s 1s

He Heg (1s)

u* (1s)

[He2]2+ Based on these diagrams, [He2]+ would have a bond order of (2–1)/2 = 0.5, and [He2]2+

would have a bond order of (2–0)/2 = 1.

(b) Does the MO picture of the bonding in these ions suggest that they are viable species?

Both are “viable” although the monocationic species would have a fairly weak sigma bonding interaction and a longer He-He distance.

(c) Is either of these ions paramagnetic? The monocation [He2]+ has one unpaired electron, so it is paramagnetic.

11. (H&S 2.25c) Account for the observation that, in the salt formed from the reaction of Br2 and SbF5, the Br-Br bond distance in the Br2

+ ion is 215 pm, i.e. shorter than in Br2.

We didn’t talk about MO pictures for n=4 elements, and it’s not really within the scope of this course to generate such a diagram. However, based on the MO pics we’ve looked at for the first row diatomics (n=1,2, F2 in particular, see H&S Fig 2.9, p.39), we can make an educated guess about what is going on here and thereby develop a reasonable approximation. If oxidation of Br2 to [Br2]+ (i.e. removal of one electron from this diatomic molecule) causes the Br-distance to get shorter, that suggests that the bond gets stronger - i.e. the bond order increases on removal of an electron. The HOMO for Br2 must have antibonding character, which is reduced when one electron is removed.

12. (H&S 15.20) Assuming that it has similar molecular orbital energies to those of NO, use an MO approach to show the bonding in CO. The following MO diagram results. The strength of the bonding is the same (filled versus

unfilled) but the correct relative MO ordering will affect its behavior as a ligand. Also note that for exams, you would be given the filling order for any heteroatomic molecular orbitals.

Chem 222 Intro to Inorganic Chemistry Summer 2011

13. (RC&O 15.5) Contrast the behavior of nitrogen and carbon by comparing the

properties of (a) methane and ammonia, and (b) ethene (ethylene) and hydrazine. (a) Methane and ammonia are both colourless gases, in which the central atom is sp3

hybridized. Because nitrogen has one more valence electron than carbon, this gives it one filled sp3 orbital – a stereochemically active lone pair. Thus methane, CH4, is non-polar and insoluble in water, while ammonia, NH3, is polar and dissolves in water to form NH4OH, which then dissociates to give a basic solution. Methane has no odour, while ammonia has a distinctive, pungent odour.

(b) The same stability versus reactivity is seen in ethylene versus hydrazine. Both ethene and hydrazine contain an element-element bond: H2EEH2. However, carbon can readily re-hybridize from sp3 to sp2 in this structure to offset its lower than optimum valency of three. This places the remaining valence electron on each carbon in a p-orbital perpendicular to the C-C bond axis. The side-on, π-overlap of these orbitals gives a π-bond, which results in the double bond character of ethane: it has a shortened

Chem 222 Intro to Inorganic Chemistry Summer 2011

C-C bond distance, a stronger C-C bond, and is non-polar and reasonably inert (unless you ignite it).

H

H

¹ -bond

C CHH H

H

sp2

N NHH

H

Hsp3

H Hview down the N-N bond axis

Because each nitrogen in hydrazine has an extra electron relative to carbon, such re-

hybridization is much more difficult. This would place two electron pairs in adjacent p-orbitals, a high energy structure because of the electron repulsion between these two lone pairs. Even when the nitrogens in hydrazine remain sp3 hybridized, the single bond twists to rotate the lone pairs away from each other. From H&S p.447: Hydrazine is a clear, colourless liquid (mp 275K, bp 386K) that dissolves in water to give weakly basic solutions (the hydrazinium ion, N2H5

+ forms). It is corrosive, and its vapour forms explosive mixtures with air (no spark needed).

14. How are quartz glass and common soda-lime glass different? Both of these materials are silica-based, comprised of the network covalent solid SiO2.

Quartz glass is pure silica that has been heated above its glass transition temperature (Tg) to give a molten liquid, and then cooled to give a random spatial arrangement of SiO4 tetrahedral units. Common soda-lime glass is prepared in the same way except that about 13% of sodium oxide (Na2O) and 11% of calcium oxide (CaO), with traces of K2O and other oxide impurities, are added to the melt before cooling. This changes the physical properties of the resulting glass:

Quartz glass is very strong and has low thermal expansivity, which means it doesn’t expand or contract too much when you heat or cool it. Soda-lime glass is not quite as strong, although it is strong enough to hold carbonated beverages under pressure. It has higher thermal expansivity, which is why you can’t make tea in an empty pop bottle. The main benefit of soda-lime glass, from a manufacturing point of view, is that it has a much lower Tg than does quartz glass (573°C vs 1140°C), so it is easier and cheaper to “melt” for shaping into the required forms.

15. (H and S, 6.6) What do you understand by the band theory of metals?

The band theory of metals allows us to apply quantum mechanics and the concept of the linear combination of atomic orbitals (LCAO) to make molecular orbitals and extend this concept to a much larger number of atoms (as in a moles worth of atoms). The band theory of metals explains their electronic conductivity, as the electrons can very easily be excited into an unfilled orbital (conduction band) and is therefore delocalised. This sea of delocalised electrons also explains why metals are malleable and ductile, as the electrons can immediately adjust to any deformation in the crystal structure. The shininess of metals results from absorbing and re-emitting photons, as the electrons move between the (very accessible) energy levels.

Chem 222 Intro to Inorganic Chemistry Summer 2011

16. Chemical analysis of a germanium crystal reveals indium at a level of 0.0003 atomic percent.

a) Assuming the concentration of thermally excited charge carriers from the Ge matrix is negligible, calculate the density of free charge carriers (carriers/cm3) in this Ge crystal.

b) Draw a schematic energy band diagram for this material and label all critical

features.

17. a) Aluminium Phosphide (AlP) is a semiconductor with a band gap Eg of 3.0 eV.

Sketch the absorption spectrum of this material (absorption vs. wavelength)

Chem 222 Intro to Inorganic Chemistry Summer 2011

b) Aluminium antimonide (AlSb) is also a semiconductor. Do you expect the band

gap of this material to be greater or less than the bangap of AlP? Explain.

18. You wish to make n-type germanium. a) Name a suitable dopant. You will need to dope with an electron (n-type =negative) donor, which means it must be

from group 16, giving us P, As and Sb as reasonable choices.

b) Name the majority charge carrier. The majority charge carrier is the electron.

c) Draw a schematic energy band diagram of the doped material. Label the valence band, conduction band and any energy levels associated with the presence of the dopant.

Chem 222 Intro to Inorganic Chemistry Summer 2011

19. (H&S 14.16a) Comment on the observation that the pyroxenes CaMgSi2O6 and

CaFeSi2O6 are isomorphous. These two silicate minerals have identical empirical formulas, except that the Mg2+ ions

in one are replaced by Fe2+ ions in the other. If they are isomorphous it means they have the same structure: for silicates this means that the arrangement of the SiO4 tetrahedral units is identical (these ones have the chain structure shown for [SiO3]n

2n- ), as is the placement of the metal cations in interstitial holes throughout the array. Presumably the only difference is that the specific holes containing Mg2+ in one mineral contain Fe2+ for the other. This is reasonable, based on the ionic radii reported for Mg2+ (72 pm for CN=6) and Fe2+ (78 pm for high spin and CN=6) (see Appendix 6 in H&S). [Note: “high spin” means that the Fe2+ ion, in an Oh environment for which its nearest neighbours are oxygens, has a relatively low value of oct. This will be discussed when transition metals are considered ]

Definitions/Concepts: glass, silica, silicates, silicone, molecular orbitals, -bond, π-bond, nodal plane, bond order, , pnictogens, chalcogens, catenation,, fuel cell hygroscopic, deliquescent, desiccant, dehydration, dehydrogenation, diamagnetism, paramagnetism, ferromagnetism, allotrope, photosynthesis, amphoteric, basic oxide, acidic oxide, orbital hybridization, n-type semiconductor, p-type semiconductor, compound semiconductor, metal, metalloid, non metal, band theory.


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