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AP Chemistry

Allotropes

The reading is optional, the questions are not. You don’t have to read the natural history article at the end to answer the questions but it is interesting.

Allotropes are different forms of the same element. We are most familiar with the allotropy of carbon as graphite is cheap and plentiful while diamonds, which in reality are quite common, have the illusion of scarcity and value created by a monopolistic cartel. Other elements also exhibit allotropy and we’ll learn about them below.

Oxygen has two allotropes, dioxygen (O2) and ozone, (O3). Oxygen (O2) is a vital component of our atmosphere necessary for life. Ozone is a highly reactive gas that is produced when energy is added to oxygen. This energy often comes from electricity, lightning in nature or anthropogenic sparks. The “electricity smell” is actually ozone. In the upper atmosphere the energy of the sun’s rays produces ozone. Ozone absorbs UV from the sun and protects all life on earth. Ozone is highly reactive and can react with the same things oxygen reacts with. For example, rubber burns in oxygen in a combustion reaction. At room temperature rubber is resistant to oxygen but slowly degrades in the presence of ozone. Dioxygen’s bonding is interesting because the Lewis dot structure shows a double bond but the molecule is paramagnetic. The seeming paradox is resolved by looking at the MO diagram and seeing 2 unpaired electrons and calculating a bond order of 2. Ozone’s bonding is interesting because ozone exhibits resonance.

Tin also exhibits allotropy. One form of tin is called beta tin or white tin. This form of tin is the familiar, useful from of tine metal we use in our technology. Gray tin or alpha tin is a gray, crumbly, nearly useless material. Unfortunately Our useful white tin turns to useless gray tin at low temperatures. The process is autocatalytic, which means that once a little bit of gray tin forms it catalyzes the formation of more of itself, resulting in the conversion of the entire tin object into gray tin. This is called tin pest and it was observed on tin pipe organs in the middle ages in Europe where it gets cold in the winter. Supposedly, the tin buttons on Napoleon’s soldiers’ uniforms turned from white tin to gray tin during the Russian campaign, contributing to Napoleon’s defeat. However, it is unlikely that the buttons were pure enough such that tin pest would be a problem for one. Two, it wasn’t cold enough in Russia and the campaign didn’t last long enough for tin pest to manifest. Third, the soldiers were probably more concerned with logistics, freezing and the enemy to be affected by tin pest even if it did occur. It has also been stated that tin solder on food and fuel cans of Arctic and Antarctic expeditions degraded and resulted in issues for the explorers. Maybe, maybe not. What we do know is that tin pest is an issue for us in the 21st century due to tin replacing lead in solder for electronics.

If you look closely you may or may not see tin pest on Napoleon’s buttons. This is dependent upon your eyesight, whether the painter painted in the tin pest, and whether there was any tin pest to paint in the first place.

It’s cold, they’re out of food and Russian cavalry may raid them at any time but they also have to worry about tin pest…or not.

I don’t see any tin pest on these Antarctic supplies but it could be there, maybe.

The photo at left is referenced from a paper by Y. Karlya, C. Gagg, and W.J. Plumbridge, “Tin Pest in Lead-Free Solders”, in Soldering and Surface Mount Technology, 13/1 [2000] 39-40.

There is actually tin pest here.

I see tin pest here as well. (It’s on the right.)

Tin pest video: http://www.youtube.com/watch?v=sXB83Heh3_c

Phosphorus has several interesting allotropes. White phosphorus is set as the standard with its heat of formation at 0. This is despite the fact that red phosphorus is more stable. White phosphorus has been used as a weapon of war as it ignites upon contact with air (it must be stored out of contact with air). Red phosphorus is used in matches.

White phosphorus reacting in air. The white smoke is actually tetraphosphorus decaoxide, the product of the reaction between phosphorus and oxygen.

Red phosphorus

“White” phosphorus stored in an ampoule.

The bonding of phosphorus allotropes is interesting. White phosphorus which is also called yellow phosphorus (even though it looks orange in the ampoule pictured above) is also called tetraphosphorus.

Its formula is P4. Red phosphorus (it looks more Fire Brick or Cornell

than red in the picture) has this structure:

Sulfur has many allotropes. Like the allotropes of other elements they vary in bonding and properties but they’re not really of concern to us in technological terms. However, the chemical bonding is of interest. Each sulfur atom makes 2 bonds. The sulfur can exist as a big polymer chain the ends of which are obviously an issue but which we’ll ignore. There’s also forms like S6, S8, and S12 which are pictured below:

Carbon’s allotropes are the most well-known. Graphite is a soft solid consisting of sheets of carbon atoms with sp2 hybridization. Graphite is actually used as a lubricant in systems where liquid lubricants attracting grit would negatively affect the system. An example is locks. Diamond is a crystal made of sp3

carbon atoms. It is hard and an electrical insulator. It is a thermal conductor. It is hard and brittle but, like graphite, it can be used to reduce friction. The frictional coefficient for diamond on diamond is extremely low. Carbon also exists as amorphous carbon. Lonsdaleite is an allotrope of carbon that seems to be formed when graphite is exposed to a rapid increase in temperature and pressure. It has the sp3 hybridization of diamond but the hexagonal crystal lattice of graphite. Samples of lonsdaleite that exist have a Mohs hardness of 7-8 while diamond is 10. A theoretical study found that pure lonsdaleite should be 58% harder than diamond. The difference in hardness between actual Lonsdaleite and theoretical lonsdaleite is attributed to impurities in the real stuff. Lonsdaleite has been found in meteorites and the Tunguska impact site. Amorphous carbon is said to be soot, charcoal and coal. However, these often consist of other forms of carbon such as graphite. We’ll just gloss over it. You can google it if you like. Instead, we’ll focus on fullerenes and graphene. Fullerenes include buckyballs and nanotubes. These allotropes of carbon exist naturally and were actually formed by humans in the process of making Damascus steel. They were not discovered, however, until the 1980’s. There are a variety of fullerenes, three of the most common being C60, C70, and C540. Nanotubes are a more useful fullerene. They are basically tubes of carbon. The possible applications of nanotubes are numerous and beyond the scale of this article. However, we will mention one, which is the space elevator. It takes an enormous amount of energy to lift objects into space with rockets. Much of the energy is to lift the rocket fuel itself. If we add more weight to the payload (the stuff like satellites and astronauts) we have to add more fuel to lift the payload but we also have to add fuel to lift the fuel, then more fuel to lift the fuel that lifts the fuel, the more fuel to lift the fuel that lifted the fuel…A better approach is a space elevator. This is a space station that has a tether connected to the earth. If the tether is strong enough than an elevator could be attached and electrical energy used to raise payloads to space. The tether must be 23,000 miles long as the space station must be in geosynchronous orbit. A 23,000 mile long metal wire could not hold its own weight but nanotubes could. What is keeping us from this greatest possible technological endeavor? Funding. We, as humans decide we would rather have cable TV, trinkets (like that other allotrope of carbon, diamonds), political pork and other things rather than build a space elevator. With money and time there is nothing holding us back from this future Wonder of the

World. One issue to consider with the space elevator is the elevator car itself. A car traveling 1000 miles per hour would take about 23 hours to get to the station. How will the car travel that fast attached to the elevator cable? Probably with magnets (google maglev).

Graphene is a material that has the potential to revolutionize

technology. It is a single sheet of graphite. Graphite itself is a stack of sheets. Graphene sheets are produced by putting a piece of tape on a piece of graphite and peeling it off. Graphene is so tough that a few layers thick could stop a bullet in bulletproof vests. A few sheets of graphene could hold an elephant in the middle of them. Graphene conducts electricity. It has properties that would make a very good material for integrated circuits. Graphene oxide has been found to kill E. coli bacteria.

The bonding in diamond is what we would expect of an sp3 carbon. Four single bonds are made to adjacent carbon atoms. The structure of diamond allows each carbon to be 109.5 degrees in its bond angles which means it is stable. In graphite and the fullerenes each carbon is sp2. So, it seems like they should be less stable than diamond. Diamond has four single bonds while the others have 3 singles and a double. The four singles should have a higher bond energy than three singles and a double. However, graphite and fullerenes have structures that allow electrons to delocalize. Using the particle in a box model we’ll say that this lowers the energy of those electrons a great deal. So, graphite is a little bit more stable than diamond. Just so you know, a diamond is not forever, it will convert to graphite over time. Someone could then write with it, possibly on an AP chem test. Or, we could convert the graphite to graphene or fullerenes and do technology. Or we could dope another intact diamond and make it into a semiconductor. We could use it to transport heat or as a low friction bearing. By the way, anyone interested in math is invited to check out the mathematics of diamond cutting. Recently the brilliant cut was improved upon using mathematics to make the perfect diamond cut.

Here are some videos of diamond reacting. Note that the SDUHSD policy on non-SDUHSD links applies.

Burning diamonds: http://www.youtube.com/watch?v=WWpm6_Y7ASI&feature=related

Diamond to graphite: http://www.youtube.com/watch?v=7L7BV3IBfFA&feature=related

Bonding in diamond:

Graphite:

Lonsdaelite

A hunk of graphite.

Graphite electrodes

C20

C540

Diamond mine.

Take a look at this diamond mine in Canada. The diamonds are at the bottom of a lake. So, they built a coffer around the lake, pumped the water out and started mining. Not the engineering genius used up and the environmental impact to mine something that can be produced in a factory.

Canadian diamond mine in winter.

Another shot of the Canadian diamond mine.

It rained and filled up this diamond mine.

Black and red selenium. They’re both selenium but they look very different.

Various fullerenes

Colors and cuts of diamond.

The small diamonds are relatively pure, the large one has another element as an impurity, causing the blue color.

The Hope diamond.

The Hope diamond phosphorescing.

Diamond cuts.

Round Brilliant Cut

Emerald Cut Baguette Cut Marquise Cut

Oval Cut Flanders Cut Princess Cut Pear Cut

The article below is from:

http://mineralsciences.si.edu/research/gems/hope_diamond/blue_diamond_research.htm

Natural History HighlightUV Rays Shed New Light on the Hope Diamond’s Mysterious Red Glow By Amanda Thornburg

The 45.52 carat Hope Diamond is in a platinum setting surrounded by sixteen white pear-shaped and cushion-cut diamonds designed by Pierre Cartier in about 1910. Photograph by Chip Clark.

Hundreds of rare precious gemstones are on display in the Gems and Minerals Galleries at the Smithsonian’s National Museum of Natural History. According to Dr. Jeff Post, curator of the United States National Gem and Mineral Collection and avid mineralogist, few of those gems garner more attention than the world famous and Smithsonian’s own, Hope Diamond. With its breathtaking beauty and mysterious past, the Hope Diamond intrigues millions of museum visitors each year; but beyond its rumored curse, the world’s largest blue diamond is proving to be a unique scientific specimen.

The 45.52-carat blue diamond puzzles scientists because of the fiery red glow it gives off for several minutes after being exposed to ultra-violet light. Scientists refer to this phenomenon as phosphorescence. “It looks like a glowing orange coal in your barbeque grill,” explains Post. “It has been described as one of the unique properties of this unique diamond, something special to the Hope Diamond.” No comprehensive studies on the nature of the phosphorescence exist, which has made Dr. Jeff Post question the impressive glow for years. “There didn’t seem to be a lot of consistency, or certainly no quantification of the nature of the phosphorescence,” Post says. Thus, he and a team of researchers took on the challenge to dispel the deep dark secrets of the Hope Diamond.

In a curious effort, Post and colleagues from the U.S. Naval Research Laboratory, Ocean Optics Instrument Company, and Penn State University eagerly snagged the Hope Diamond from its glass enclosure, along with the world’s second largest deep-blue diamond, the Blue Heart Diamond, and blue diamonds from the Aurora Butterfly of Peace, a temporary collection of 240 colored gemstones. They hand carried the gems to the Smithsonian’s highly secure blue room vault, where hundreds of the museum’s most expensive and rare gems are located. Using a portable instrument that measures wavelengths of light, known as a spectrometer, the researchers exposed each diamond to ultra-violet light in order to measure the intensity of light given off,

and the rate at which it faded. As reported in the January 2008 issue of the journal Geology, the researchers developed a better understanding of phosphorescence behavior, and to their pleasant surprise, discovered a way to essentially “fingerprint” blue diamonds.

The intense orange phosphorescence of the Hope Diamond is only visible in a dark room after exposure to ultraviolet light. One of the diamonds surrounding the Hope is phosphorescing blue. Photograph by John Nels Hatleberg.

Post and his team of researchers concluded that red phosphorescence is not just specific to the Hope Diamond, but indeed a property of all natural blue diamonds. Trace impurities of the element boron give rise to a diamond’s deep blue color. Presumably, the boron interacts with trace amounts of nitrogen to give each diamond its unique phosphorescence behavior. Hoping to see a trend among the diamonds tested, researchers found just the opposite. “The plot just scattered, indicating that each of these diamonds had its own set of these characteristics,” said Post. “That gave us a way of fingerprinting a particular blue diamond.” In addition, the researchers tested synthetic diamonds doped with boron and natural heat-treated blue diamonds. The artificially treated blue diamonds had a completely different phosphorescence spectrum than the natural blue diamonds, which could be useful to gemologists when identifying the real from the fake.

Dr. Post’s passion and natural affinity for crystals inspires him to probe for new questions regarding the Hope Diamond. “There is always more to learn, and as new ideas, new techniques, new questions come up, we will continue to learn from it,” says Post, “Usually, one study raises as many questions as it answers, and so it always opens up new lines of potential research that will hopefully lead to a more in-depth understanding of the diamond itself.” This study has also been a nice change for Dr. Post who is used to studying materials that most people have never even heard of. “Much of my day to day research is on mud and muck and clays that are critically interesting to our environment, but yet there is no aesthetic pleasure whatsoever,” he says. “Then on the other side of the research coin is working on things like the Hope Diamond, so it’s an interesting stretch, but also a fun balance to have.”

Questions

1. Why does graphite form hexagons rather than some other polygon.2. Why is diamond so hard?3. Why is diamond a good conductor of heat?4. Why is diamond a poor conductor of electricity?5. Why is graphene so strong?6. Looking at the Lewis structures of dioxygen and ozone explain why dioxygen is more

stable.7. Why is white phosphorus less stable than red phosphorus?8. Propose a structure for tetranitrogen N4.9. Propose a structure for octanitrogen N8.10. Octanitrogen is also called octaazacubane. It is predicted to have an energy density

of 22.9MJ/kg. Calculate its heat of formation.11. Calculate how many liters of gas a kilo of octanitrogen would produce if it

decomposed into N2 gas at 1 atm and 298K.12. Calculate the pressure if the gas in 11 were confined to a volume of 1L.13. Propose a structure for the ionic compound N5

+N5-

Answers:

1. Hexagons have 120 degree angles which is the angle for sp2.2. In order for it to deform carbon atoms have to move out of place and disrupt the

strong covalent bonding. It’s more likely that the atoms of whatever is pushing on the diamond will move.

3. The heat is transferred by atomic vibrations. When one atom vibrates it causes the 4 bonded to it to vibrate which each vibrate 4 more until the heat spreads quickly through the diamond.

4. Diamond has no easily delocalizable electrons to move and carry a current.5. To break it, covalent bonds must be broken.6. Dioxygen has a double bond with no formal charges while ozone’s Lewis

structure places an unfavorable positive formal charge on an oxygen atom.7. White phosphorus has the strained pyramidal structure shown above so the bond

angles are far from the ideal which is around 109.5.8. Since N is right above P on the table do the same structure as P4:

9. Whatever you guessed is a fine guess, as long as it follows our rules for Lewis structures and you tried to minimize formal charge and such. Here’s what chemists believe the structure will be when it is finally synthesized:

Note that it is very unstable. It would be the most powerful nonnuclear explosive known if it is made.

10. This another of the dreaded stoichiometry questions. Convert megajoules to kilojoules to get a better idea of the massive energy stored in this molecule. 22,900 KJ per kilogram. Now, divide that number by the number of moles of N8 in a kilogram. 1000grams/112grams per mole = 8.9 moles. 22,900/8.9 = 2573KJ/mol. That is the energy stored. How is the energy released?N8(s) = 4N2(g) Products – reactants but the products have a heat of formation of zero so the heat of formation = 2573KJ/mol. Please do not synthesize this molecule at home or at school!

11. 1000g = 8.9 moles. Multiply by 4 because of the balanced equation in the above problem. 35.6 moles of gas goes into the ideal gas law. I got 870L

12. 870 atm.13. I just did a linear cation and a linear anion. The cation has 24 electrons, the

anion 26. Just put them in some logical arrangement and try to get no N to have more than 8 electrons no matter what and try to avoid any N having 6 electrons if at all possible.