Chem 312, Au13
Problem Set 8 Due in class, Friday, November 22
1. Our focus so far in class has been solids held together by ionic or metallic bonding. But many solids are held together by covalent bonding, and then the rules about molecular structures apply, such as the octet rule. For instance, in diamond, each carbon atom makes four bonds, in a tetrahedral array, just as you would expect for an sp3 hybridized carbon atom. (a) Based on the octet rule, how many bonds are made by each atom in the structure of solid: aluminum, silicon, phosphorus, sulfur, and chlorine? (Chlorine is a solid below -101 ˚C.) Based on the octet rule, each silicon atom in solid silicon should make four bonds (c.f., SiH4), each phosphorus atom in solid phosphorus should make three bonds, each sulfur atom in solid sulfur should make two bonds, and each chlorine atom in solid chlorine should make one bond. Using normal two electron-two center bonding, aluminum cannot attain an octet, but should make three bonds. This should tip you off that a simple octet rule picture will not apply to aluminum. Aluminum is, in fact, a metal -- not a covalent solid. Boron, directly above aluminum, is a non-metal but adopts strange structures to get around this non-octet problem (please look in Wulfsberg, p. 188).
(b) Which of those elements is most likely to be molecular in the solid state (composed of molecules)? Which is most likely to have a linear chain structure (-E-E-E-E- etc.)? Which is most likely to be similar to diamond?
Chlorine is molecular, Cl2, since each atom only makes one bond. Sulfur has a chain structure, -S-S-S-. The most stable form consists of eight-membered rings, S8, and is therefore molecular also. But most samples of sulfur also contain rings of other sizes, and sulfur can be polymeric under some conditions as well. The structure of silicon is the same as the structure of diamond, except that the Si-Si bonds are significantly longer than the C-C bonds.
2. Now consider the heat of atomization of solid aluminum, silicon, phosphorus, sulfur and chlorine. As discussed in Wulfsberg chapter 6 (especially sections 6.1, 6.2, and 6.3), the heat of atomization of an element is the enthalpy required to take a mole of an element from its standard state at 25 ˚C (~room temperature) to individual gaseous atoms. For instance, the enthalpy of conversion of diamond to gas phase individual carbon atoms is quite unfavorable: C (diamond) → C (atomic, g) ΔH˚ = +717 kJ mol-1. (a) From the Tables in chapter 6, how does the heat of atomization vary as one traverses the periodic table from Al to Si to P to S to Cl? The heats of atomization, from Table 6.1, are (in kJ/mol): Al: 326; Si: 456; P: 315; S: 279; Cl: 122. This is shown graphically below.
Heat of Atomization 500 Heat of Atomization per "bond" 400
300
kJ/mol 200
100
0 Al Si P S Cl Chem 312, Au13; PS 8, p. 2
(b) Explain why the heat of atomization has this specific trend (use your answer to question 1a). The heat of atomization parallels the number of bonds made by the element, according to the simple rules used in question 8. Thus Al could make three bonds, silicon four, phosphorus three, sulfur two, and chlorine one. The heat of atomization divided by the formal "number of bonds" is pretty constant for these elements, as shown by the solid squares above.
(c) Formulate a general rule for the heat of atomization across a row of the periodic table: The most favorable heat of atomization is found when the number of electrons is in what ratio to the number of valence orbitals? The maximum number of bonds occurs, for these elements, when the atom has four valence electrons. These atoms have four valence orbitals (3s, 3p). The general rule is that maximum bonding (and maximum heat of atomization) occurs when the number of electrons equals the number of orbitals, in other words when the orbitals are half full (since each orbital can hold two electrons).
(d) Why is the heat of atomization of argon zero? The heat of atomization is defined as the heat required to take an element from its standard state at room temperature to gas phase isolated atoms. Argon at room temperature is already isolated (monatomic) gas phase atoms, so the heat of atomization is zero.
(e) In what way is the definition of the heat of atomization of a solid similar to the lattice energy of an ionic solid? In what way is it different? The heat of atomization and the lattice energy are both enthalpies. They both give the heat required to break up a material (usually a solid) into independent (non-interacting) particles in the gas phase. These two quantities are also different. In the heat of atomization, one is forming gas phase atoms, while the lattice energy refers to the formation of gas phase ions. (Also, the lattice energy specifically refers to a solid while the heat of atomization can apply to solid, liquid, or gas-phase materials.)
(f) How is the heat of atomization of a pure element E related to the heat of formation (ΔHf˚) of gas phase atoms of that element? [Don’t overthink this, the answer is very simple.] They are the same.
3. Now consider the series N2, O2, and F2. (a) Draw Lewis dot structures for each and predict which has the strongest bond. How many valence orbitals are present in each case? How many electrons are present in each case? :N≡N: eight valence orbitals, ten valence electrons. :O=O: eight valence orbitals, twelve valence electrons. :F–F: eight valence orbitals, fourteen valence electrons. N2 has the strongest bond, because it is a triple bond.
(b) The bond strength in a molecule X–Y is defined as: ΔH˚ for X–Y (g) → X (g) + Y (g)
Calculate the bond strengths in N2, O2, and F2 from their heats of atomization. The heat of atomization is defined as the enthalpy of taking one mole of an element at its normal state (25 ˚C, 1 atm pressure) and converting it to gas phase atoms. For an element that exists gas phase diatomic element, X2 (g), the heat of atomization is: Chem 312, Au13; PS 8, p. 3
1/2 X2 (g) → X (g) ΔH˚atm(X) The bond strength is defined as the heat required to cleave the bond: X2 (g) → 2 X (g) ΔH˚(Bond Dissociation Energy of X2) So the bond strength is simply double the heat of atomization: N2, 946 kJ/mol; O2, 498 kJ/mol; F2, 158 kJ/mol.
(c) Do your answers fit with the general rule from band filling in metals, relating the best bonding to the number of electrons and the number of orbitals? Yes, the data from the questions above are consistent with the general rule that the best bonding occurs when the number of electrons is equal to the number of orbitals.
[This breaks down if you consider the molecule C2, which is formed in flames but is not a “stable” molecular species. Because of the shapes of the s and p orbitals, C2 can make only a triple bond, so it cannot use two of its valence electrons to form chemical bonds. This is one reason why elemental carbon is not diatomic but rather an extended structure, graphite or diamond.]
4. (a) List in order of decreasing covalent bond strength: I–I, C–C, P–P, Ge–Ge. In order of decreasing covalent bond strength: C–C, P–P, Ge–Ge, I–I. Covalent bonds get weaker as you go down the periodic table in the p block.
(b) List in order of decreasing covalent bond strength: N–O, C–O, C–F, C–N. Explain your answers in terms of the factors that influence covalent bond strengths. In order of decreasing covalent bond strength: C–F, C–O, C–N, N–O. Covalent bonds are stronger when there is a larger difference in electronegativity. Note that the comparison in part (a) is made between bonds of equal polarity (all are non-polar covalent bonds) while the comparison in (b) is between bonds all involving atoms of the second row. Thus the two trends can be seen separately.
5. (a) Draw a thermochemical cycle for the enthalpy of MgCl2 dissolving in water. Clearly label the lattice energy, heat of solution of each ion, and whatever other terms appear in the cycle. Calculate the lattice energy from the equation with the Madelung constant – based on the radius ratio, which
structure does MgCl2 adopt? Use this lattice energy to calculate the ΔH˚ of solution of MgCl2. (b) Draw a similar thermochemical cycle for the enthalpy of reaction of Mg(s) plus Cl2 (g) to make MgCl2 (s). Again, label all the necessary terms. Calculate the ΔH˚ of reaction. (c) Draw a similar thermochemical cycle for the enthalpy of reaction of Mg(s) plus Cl2 (g) to make MgCl2 (aq) -- that is, MgCl2 dissolved in water. Again, label all the necessary terms. Calculate the ΔH˚ of reaction. (d) Two of these values should add to give the third. Which two need to be added? Explain why this is true, using the chemical equations that describe parts (a), (b), and (c). Chem 312, Au13; PS 8, p. 4
Mg 2+ (g) + 2 -Cl (g)
Lattice !H hyd 2x !H hyd Heats of Energy 2+ - hydration (Mg ) (Cl)
2+ - MgCl 2 (s) Mg (aq) + 2 Cl (aq) Heat of Solution
(b) IP(1) + IP(2)
Mg (g) + 2 Cl (g) Mg 2+ (g) + 2 -Cl (g) Electron Affinity
!H atom 2x !H atom (Cl) Lattice (Mg) Energy
Mg (s) + Cl2 (g) MgCl 2 (s) Heat of Reaction (c) IP(1) + IP(2)
Mg (g) + 2 Cl (g) Mg 2+ (g) + 2 -Cl (g) Electron Affinity
- !H hyd 2x !H hyd (Cl ) !H atom 2x !H atom (Cl) 2+ (Mg) (Mg )
2+ - Mg (s) + Cl2 (g) Mg (aq) + 2 Cl (aq) Heat of Reaction Data: ΔHatm (Mg) = 146 kJ/mol; ΔHatm (Cl) = 122 kJ/mol. 2+ - ΔHhyd (Mg ) = -1922 kJ/mol; ΔHhyd (Cl ) = -355 kJ/mol. For Mg: IP(1) = 738 kJ/mol; IP(2) = 1451 kJ/mol. For Cl: EA = 349 kJ/mol. We need to calculate the lattice energy of MgCl2: 2+ - The radius ratio r (Mg )/r (Cl ) = 86/167 = 0.515 implies that MgCl2 adopts the rutile structure. According to the equation for lattice energy, MZ Z 1 2.408 " 2 " #1 1 U = 138,900 + " (1" )= 138,900 (1# ) = -2310 kJ/mol. r+ + r" n 86 +167 8 2+ - a) ΔHsolution = -U (lattice energy) + ΔHhyd (Mg ) + 2 × ΔHhyd (Cl ) = 2310 + -1922 + 2(-355) kJ/mol = -322 kJ/mol b) ΔHreaction! = ΔHatm (Mg) + 2 !× ΔHatm (Cl) + IP(1) + IP(2) - 2 × EA + U = 146 + 2(122) + 738 + 1451 - 2(349) + -2310 = -429 kJ/mol c) ΔHreaction = ΔHatm (Mg) + 2 × ΔHatm (Cl) + IP(1) + IP(2) - 2 × EA + Chem 312, Au13; PS 8, p. 5
2+ - ΔHhyd (Mg ) + 2 × ΔHhyd (Cl ) = 146 + 2(122) + 738 + 1451 - 2(349) + -1922 + 2(-355) = -751 kJ/mol d) The sum of reactions (a) and (b) must be the answer to (c). You can convince yourself of this from the cycles above, or adding the equations as below: (b) Mg (s) + Cl2 (g) → MgCl2 (s) 2+ - (a) MgCl2 (s) → Mg (aq) + 2 Cl (aq) ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ 2+ - (c) Mg (s) + Cl2 (g) → Mg (aq) + 2 Cl (aq)
6. Compare the reaction of Mg with F2, Cl2 and Br2 to make MgX2 (s), using the thermochemical cycle you derived in question 1(b) [X stands for a halogen: F, Cl, or Br]. (a) Which terms are different in the three cases? Using the data in the Tables of chapter 6 and your own knowledge, compare the magnitude of each of these terms for these three halogens. The differences in the heats of reaction for MgX2 are: (i) in the heats of atomization of X2; (ii) in the electron affinities of X: and (iii) in the lattice energies of MgX2.
(i) The heat of atomization of fluorine is unusually low: 79 kJ/mol vs. 122 for Cl and 112 for Br. Normally the trend is for heats of atomization to decrease going down a column.
(ii) The electron affinities are about the same, Cl (349) > F (328) > Br (325).
(iii) The lattice energies vary in the order F > Cl > Br because of the different radii. Including the changes in both ranion and in the parameter n, the formula for lattice energies gives:
2.408 " 2 " #1 1 U(MgF2) = 138,900 (1# )= -2800 kJ/mol. 86 +119 7
2.408 " 2 " #1 1 U(MgCl2) = 138,900 (1# )= -2310 kJ/mol. 86 +167 8 ! 2.408 " 2 "1 1 U(MgBr2) = 138,900 (1# )= -2200 kJ/mol. 86 +182 8.5 ! The largest difference between the halides is in the lattice energy: MgF2 has by far the largest lattice energy because of the small size of F-. ! (b) Which is the most reactive of these halogens? Why? Fluorine is the most reactive of the halogens, because of the high lattice energy of its ionic compounds. The same answer is obtained for reactions that make aqueous solutions (F– has a high heat of hydration because of its small size), and for reactions that make X–F covalent bonds because F makes strong covalent bonds. The fact that its compounds are so stable is compounded by the very low heat of atomization of F. Typically at the top of a column one finds the highest lattice energies and heats of hydration because of the small sizes. But this is often offset by the higher heat of atomization of the element. Not so in the case of fluorine. The trend in electron affinity is hard to interpret.
Chem 312, Au13; PS 8, p. 6
7. According to Table 5.4, the redox potentials for the alkali metals falls in the order Cs ≅ Li < Rb ≅ K < Na (this is the beginning of the activity series, http://en.wikipedia.org/wiki/Reactivity_series). This is an unusual order, not following any of the periodic trends we have discussed. Explain qualitatively why Li and Cs could be the most reactive, using the trends discussed in class. Do you quantitatively find this order, using the data in the Tables in Chapter 6 and the thermochemical cycle in Figure 6.11?, [This question moved to PS 9]
8. There was a bad spill from a freight train in the Ukraine in 2007. I’ve posted some Yahoo news stories and images that I found at that time. [Note that the element is spelled phosphorus, not
“phosphorous” with an “ous.” Phosphorous acid is H3PO3, using the old nomenclature that uses the –ous suffix for ‘the lower of two common oxidation levels’ (and –ic for the higher level).] (a) Based on the discussion of phosphorus allotropes in Wulfsberg (p. 185-187) and from briefly searching the web, what do you think was spilled in the Ukraine? I had not heard of “yellow” phosphorus before these stories appeared. A quick Google search indicated that yellow phosphorus is used as another name for white phosphorus, for instance in: http://www.speclab.com/elements/phosphorus.htm or http://en.wikipedia.org/wiki/Phosphorus. This makes sense because “white” phosphorus is often off-white or yellow in color.
(b) The fires seem from the pictures to be pretty intense. Assuming that the phosphorus burned as completely as it could, to the highest oxidation state phosphorus oxide, what is the phosphorus product formed (in the absence of water)? Write a balanced reaction. Burning phosphorus completely to the highest oxidation state phosphorus oxide would give P2O5 (or better written P4O10): P4 + 5 O2 → P4O10.
(c) When water is added to the phosphorus product you answered in question 7b, what is made? [Hint: You make a acid we’ve discussed in class already.] Write a balanced reaction.
Water plus P4O10 makes phosphoric acid: P4O10 + 6 H2O → 4 H3PO4
(d) What do you think is the hazard level of the acid formed in part (c) -- is it very hazardous or mildly hazardous or …? It is produced commercially – what is its use? (See one of the first sets of Figures I showed in Chem312, way back in January.) Phosphoric acid is a strong acid and therefore is quite hazardous in concentrated form. When diluted with water and neutralized to closer to pH 7, it’s pretty innocuous. Such phosphate buffers are widely used in biochemistry and as fertilizers.
(e) White phosphorus is also being used for military purposes, including by the U.S. military. See the following stories, including the YouTube from the recent video game “Spec Ops.” http://www.guardian.co.uk/Columnists/Column/0,5673,1642831,00.html http://www.guardian.co.uk/international/story/0,,1643679,00.html http://en.wikipedia.org/wiki/White_phosphorus http://topics.nytimes.com/topics/reference/timestopics/subjects/w/white_phosphorus/index.html http://en.wikipedia.org/wiki/Spec_Ops:_The_Line http://www.youtube.com/watch?v=-b7TaLjdXMc (caution: graphic violence) Why do you think white phosphorus is useful to armed forces? White phosphorus is useful to armed forces because it bursts into flame when exposed to the air. So I assume they shoot a sample coated somehow, and then they get a flame when it contacts the target. This provides light and presumably scares the enemy. It may harm an enemy too, but that would be a chemical weapon which I don’t think would be allowed under treaties we (that means all of us U.S. citizens) have signed. Chem 312, Au13; PS 8, p. 7
(f) What is your opinion of all this? Do you think the spill in the Ukraine was a terrible event that will harm lots of people, or nothing more than a bad fire that was over hyped by the news media? Do you think that what our and other armies have done was necessary in a war zone or inappro- priate under chemical weapons treaties? (I don’t want a lengthy exposition here, or a lot of research on chemical weapons, only that you think about it and formulate a reasonable opinion). My initial reaction to the Ukraine story was the press always makes these larger than they really are. But the fire was clearly hazardous, and anyone exposed to concentrated phosphoric acid fumes or solutions would be badly acid-burned. Comparing the long-term consequences to the nuclear Chernobyl accident, however, seems too much. Radioactive nuclides in the environment are hazardous until they decay, which could be decades to thousands of years. Phosphoric acid, however, once neutralized is just phosphate fertilizer.
I’m much more uneasy about the use of white phosphorus as a weapon. Like many chemists, I’m pleased that there is a treaty banning chemical weapons. The fact that white phosphorus is an “incendiary weapon” and not a chemical one seems to me an oversight or a detail, which doesn’t change that it acts in part like a chemical weapon. The chemical acidity of the phosphoric acid is clearly part of the function of the weapon. I should note, however, that many serious chemical weapons are nerve agents, attacking the central nervous system, and thus are much more dangerous in small quantities than phosphoric acid. I know war is nasty and that it has to be prosecuted in some situations. Still, I find myself revolted by the use of white phosphorus, even in the Spec Ops YouTube video.
9. Look at the four files posted about the new Minamata Convention on Mercury. These are articles more about policy than science, and you really only have to skim them. (a) Do you think that this convention, and the U.S. rules that support it, are a good idea, or another example of government overreach that costs us money and curtail our liberties? My opinion is that this is a very good idea, I completely support it. Mercury is a global issue and we have to tackle it globally. I personally feel that much of the resistance to this is from groups that have a commercial interest in not reducing mercury emissions (like the coal industry) or are politically already convinced that there is way too much government (as Stephen Colbert says, in his persona as an ultraconservative, “government is just welfare for people who can't put out their own fires”). Here are some articles about the resistance to the EPA rule: http://www.reuters.com/article/2012/08/06/us-coal-epa-idUSBRE8751F920120806 http://www.foxnews.com/politics/2012/07/20/epa-reviewing-part-controversial-power-plant-rule-after-complaints/
(b) The article “Global Change and Mercury” states that “Currently, human activities result in mercury emissions of ~2000 metric tons per year.” These are called “anthropogenic emissions.”
Does this seem like a lot? What is the scale of anthropogenic emission of CO2? What do you think of the figure in this article describing the whole global cycle for mercury? Would it be interesting to do one of these for every element? I like these global biogeochemical cycles. They are a major focus of research around the world, and I’ll show some in class. 2000 metric tons per year is a very small amount. It is significant only because of the toxicity of mercury at somewhat low levels. This is MUCH less than
emissions of CO2. Global CO2 emissions are roughly 5 metric tons per year per capita – for every man, woman and child on the surface of the earth!
(c) When gold dissolves in mercury it forms an amalgam, the chemical word for a solution in mercury. If you have had cavities in your teeth filled, they more likely than not used a “dental amalgam,” also called a “silver filling.” What, roughly, is the ratio of mercury to silver in these fillings? What do you think patients would say if their dentist offered them “mercury fillings”? Chem 312, Au13; PS 8, p. 8
According to http://en.wikipedia.org/wiki/Amalgam_%28dentistry%29 an amalgam or silver filling “commonly consists of mercury (50%), silver (~22-32% ), tin (~14%), copper (~8%), and other trace metals. Most people don’t know that these fillings contain mercury. My impression is that these fillings are safe (and I have a number of them in my mouth), but I’m not an expert. I took a quick look on the web and found the following article that seemed a little alarmist but pretty balanced. But I can certainly understand the Swede’s worrying about mercury emissions upon from cremation of corpses with amalgam fillings. http://www.doctoroz.com/videos/toxic-teeth-are-our-amalgam-fillings-safe?page=2
(d) How would you in a sentence or two describe the bonding in pure mercury? When gold dissolves in mercury, how different is the bonding in the resulting amalgam? Mercury has weak metallic bonding (cations in a sea of electrons). The bonding is weak because the s and d valence orbitals are all full in metallic mercury (the bonding comes from some mixing in of the valence p orbitals, so the resulting band is not completely full). When gold dissolves, there isn’t much change, as gold has almost all of its valence s and d orbitals fill (11 e– in the six orbitals).
(e) The editorial about mercury states that “the number of coal-fired power plants [is] projected to rise globally” and references a study from the World Resources Institute. Looking at that website, I found that at least one of the references for that study was from 2010. What has happened in the US since 2010 that is changing the amount of electricity generated from coal? (We had a problem set question on this back at the beginning of class.) Fracking is the key change. The price of natural gas is way down because of fracking, so new power plants are being designed to use natural gas rather than coal. And some coal plants are being converted to natural gas. Fracking is just starting elsewhere in the world, and there are (I’m told) geological reasons why it might not be so effective elsewhere, so we’ll have to see what the global effect will be.
Please note that I’m not trying to scare you with these articles. I personally eat lots of fish and have amalgam fillings. When I make decisions about my non-chemical life, I don’t worry about mercury poisoning. The one exception is that I have properly disposed of the mercury thermometers that we used to have around the house. Of course we are very careful in our laboratories in Bagley and CHB whenever he handle elemental mercury or mercury salts, and we dispose of it properly. You should make your own decisions – my goal (in addition to helping you learn some Chemistry) is to help you make informed decisions.