Random Facts about Ludwig B.

Not that Ludwig B. - the other Ludwig B: Ludwig Boltzmann, an Austrian physicist.

Boltzmann's name is familiar to many science students through the eponymous constant: 1.381 x 10^-23 Joules/mole-Kelvin, which appears in many equations. The constant (usually written as k) arises from the proportionality between the absolute entropy of a system (S) and the number of possible arrangements of that system (W). Boltzmann's expression of the entropy, S=k ln W, is inscribed on Boltzmann’s tombstone in Vienna, Austria. Boltzmann did not write it in this form, however, Planck did.

Boltzmann also has two other equations named for him, the first is a diffusion equation used in neutron transport theory and the second describes particles in a gravitational field. In 1904, Boltzmann gave lectures on mathematics at the World’s Fair in St. Louis. He was also a popular lecturer in philosophy at the University of Vienna. Boltzmann is considered the founder of statistical mechanics, and a strong proponent of the “atomistic” view that underscored the importance of understanding the behavior of atoms and molecules in order to understand the bulk.

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Loosely, the entropy is a measure of the "randomness" in a system.

Allotropes and architects: buckminsterfullerene

Responding to an earlier post on inert gases, a commenter wondered if buckminsterfullerene might act as an inhalation anesthetic - given that, like xenon, it's a large, polarizable ball of electron density. It might, if you could get enough to inhale. At room temperature, the vapor pressure is 5 x 10^-6 torr. Very roughly, that's about a billionth of atmospheric pressure. For comparison's sake, the pressure of xenon necessary to induce anesthesia is about 500 torr, or 65% of normal atmospheric pressure. If you want higher pressures, you need higher temperatures: buckminsterfullerene sublimes (goes directly from the solid to the gas phase, like dry ice) just above 1000F. Not great to breathe...

While likely impractical as an anesthetic, buckminsterfullerene has asthetic properties. It's a highly symmetric molecule - having iscosohedral symmetry. Kroto and Smalley discovered the new allotrope of carbon, C₆₀, in vaporized graphite and named it for the architect (Buckminster Fuller) who made famous the geodesic domes it resembled. Two more familiar allotropes of carbon are graphite and diamond.

Allotropes are differing forms of the same element. The roots of the word are Greek - allos for different and tropos for "turn of mind". A different turn of mind? It's what Smalley needed to propose the now iconic structure, over a beer at his kitchen table.

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Another allotrope of carbon is lonsdaleite - named for Kathleen Lonsdale, an Irish crystallographer who determined the structure of benzene and my brother-in-law's godmother.

Inert gases aren't always inert

Earlier this week I posted about the intoxicating effects of nitrogen gas at high pressures, which leads divers to substitute helium for nitrogen. An astute reader wondered in the comments why argon wasn't used, as it is substantially cheaper. It turns out that argon is even more potent intoxicant than nitrogen at high pressures! But aren't argon and helium inert gases?

The elements in the last column in the periodic table comprise what IUPAC (the International Union of Pure and Applied Chemists is to chemists what the IOC is to sports) calls Group 18, but what most of us learned in high school to call the noble or rare, gases. Helium, argon, neon, krypton, xenon and radon are indeed all gases under standard conditions, but the modifier misses the mark by a bit.

Rare? Take a deep breath, you've just inhaled about 100 mg of argon. Almost 1% of the atmosphere is argon; there is almost three times as much argon in the air as there is CO₂. "Noble" generally means "unreactive" to a chemist. The noble metals, such as gold and platinum are resistant to oxidation - they don't rust - unlike the "base" metals such as iron and copper. Much like gold and platinum, under the right conditions these inert gases can be made to react. The first noble gas compound - xenon hexafluoroplatinate - was synthesized in 1962, but there were earlier clues that these gases might not be completely unreactive. The anesthetic effect of xenon had been observed in the 1930s, and reports of its use in clinical settings appeared in the late 1940s.

The mechanism by which nitrogen, argon and xenon behave as anesthetics isn't completely understood. The best theories at the moment suggest that the gases interact with ion channels - but whether they binding chemically or physically is not clear.

Breathing Deeply

The tunnels deep beneath New York that bring crystal clear water from the reservoirs upstate to the city are aging. Divers are busy assessing the infrastructure - and it's literally a high pressure job. In order to avoid time consuming daily decompressions, the divers are living in a high pressure environment for weeks at time, almost 20 times normal atmospheric pressure. As AP reports, the pressures require that the men breathe a helium-oxygen mixture. Unfortunately, the reason given in the article for breathing the squeaky voice inducing mix: "the nitrogen in regular air is too heavy at 600 feet and their lungs could not handle the pressure." is utter nonsense.

Nitrogen does not weigh more under pressure, and the total pressure of the gas in the divers lungs is high, regardless of the identity of the gas (oxygen gas weighs more than nitrogen does, in fact). The real reason has to do with Dalton's law of partial pressures, and the fact that at high pressures, neither oxygen nor nitrogen are benign substances.

Dalton's law says that the pressure of each gas in a mixture is a function of the percentage of that gas and the total pressure of all the gases. For example, at 30,000 ft, where the total pressure is 0.3 atm and the fraction of oxygen in the air is 21%, the partial pressure of oxygen is 0.063 (humans need a partial pressure of about 0.1 atm to oxygenate their blood).

At the depth of the NYC tunnels, the total pressure is just over 18 atm, so the partial pressure of oxygen would be 3.8 atm. Above a partial pressure of roughly 1.5 atm oxygen gas is seriously toxic. The partial pressure of nitrogen 600 feet below the surface is about 14 atm. Nitrogen narcosis, rapture of the deep, sets in at pressures above 4 atm. At these depths, nitrogen is essentially an anesthetic!

Introducing an inert gas into the breathing mix, such as helium, reduces the percentage of oxygen and nitrogen in the air, thus reducing their partial pressure and reducing the danger of oxygen toxicity and nitrogen narcosis. The need for the specialized breathing mix has nothing to do with the heaviness of the nitrogen and everything to do with the toxic effects of these gases at high partial pressures.

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Eliminating nitrogen completely from the mix can also reduce the potential for developing the bends (bubbles of gas that form in the tissues when pressure is reduced) - but that has to do with Henry's Law and ladies corsets, and is another blog post!

Hydrazine: Hype or Hypergol?

Last week the US government announced that it believes it has successfully breached the fuel tank on a dead satellite, effectively destroying the toxic fuel stored on board: 1000 pounds of hydrazine. Hydrazine is a simple nitrogen compound, two NH₂ groups joined by a NN single bond. How does such a simple compound power a rocket?

Hydrazine is a hypergolic propellant - one that ignites as soon as it comes into contact with an oxidant (something that will react with it to effectively strip away some electrons from the reactant and force the molecule to bond differently, the changes in the bonds between atoms are what release the energy). Hypergolic is apparently a term coined by the German rocket program from hyper (very) + ergon (Greek for work) + ol (from oleum, the Latin for oil). Hydrazine is that, a liquid (if not particularly oily one) that can be used to push satellites around in orbit - to do work.

Hydrazine is a solid in the satellite's tanks, and once thawed can be catalytically and rapidly decomposed. Almost any metal will do, though iridium is the usual choice. The reactions produce lots of very hot gases, which you can direct through a thruster:

3 N₂H₄ → 4 NH₃ + N₂
N₂H₄ → N₂ + 2 H₂
NH₃ + N₂H₄ → 3 N₂ + 8 H₂

A little thermochemistry can quickly tell you just how much energy you might produce from 1000 pounds of hydrazine. The overall reaction is:

5 N₂H₄ → 5 N₂ + 10 H₂

which releases 50,000 Joules of energy per mole of hydrazine. A mole of hydrazine weighs about 32 grams, so you get enough energy to make a cold cup of coffee hot from just over an ounce of hydrazine (do NOT try this at home!). If all the hydrazine in that satellite went up at once, it would release about 8 billion Joules (enough to keep the average US citizen in energy for more than a week).

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A photo of a standard satellite thruster.

Melting Points

Pain perdu - a delicious part of my New Orleans heritage and better known in most of the US as french toast - has a long history. The earliest extant recipe is in Latin and dates to the 4th or 5th century! Friday brought a snow day for my kids, and come evening, some experimental time for me in my favorite home lab.

After a day spent teaching and shoveling in the sleet, I made pain perdu aux pommes from Simon Hopkinson's Second Helpings of Roast Chicken. Think french toast, vanilla custard, apples and caramel sauce. The first step in making the caramel sauce is to melt sugar over high heat. As I stirred the dry sugar in my heaviest sauce pot, alert for the first sign of melting, I flashed back to my days in an organic chemistry research lab. Melting points were used both to identify products (though even then, spectroscopic methods such as NMR were the gold standard) and to verify purity. Taking an accurate melting point required patience - and being attentive to the appearance of that first glistening drop of liquid in the fine capillary tube. It looked almost as if the crystals were sweating.

How is the purity of a compound related to its melting point? An impure sample will tend to melt over a few degree range, pure samples will melt at a sharp temperature. Impurities in a solid will also depress its melting point, in the same way that applying salt to ice (another application of chemistry appropriate for a snow day) lowers the freezing point. This phenomena also offers a low tech way to confirm the identity of a compound. Make a mixture of the sample to be identified and a known sample of (presumably) the same stuff. If the melting point is sharp and the same as the pure compound, the unknown is certain to be what you think it is. This will work even if the melting points of the two compounds are fortuitously the same.

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A nice film of a melting in a capillary tube can be found at Wellesley's organic chem lab site.

Repackaging Vitamins: Niacin

Vitamins are small molecules (where small is relative to proteins!) that a living organism cannot synthesize, but are nevertheless required. The word vitamin was coined by a Polish biochemist, Kazimierz Funk by sandwiching together "vital" and "amine". Not all vitamins turned out to be amines (molecules with an NH₂ group in them), however the name stuck.

One such non-amine "vital amine" has the structure shown below. It's a carboxylic acid (the COOH group). Originally designated as vitamin PP, it is now better known as the third of the B vitamin complex or B₃. PP stood for pellagra preventing factor. Pellagra is a nutritional deficiency, once common in Italy, that results in rough skin - pella is Italian for skin.

The original common chemical name for B₃ was nicotinic acid. (The synthetic form can be made by oxidizing nicotine with nitric acid.) In the late 1930s, niacin (NIcotinic ACid vitamIN) was adopted as the preferred name, to avoid confusion with nicotine. (I'm unclear why this was undesirable; smoking was pervasive.)

Repackaging scientific terms to make them less frightening for the general public is not just a historical phenomenon. Much more recently the application of NMR (nuclear magnet resonance) to medical imaging saw its "nuclear" dropped (thus forestalling any potential association with nuclear radiation) to become MRI (magnetic resonance imaging). It should be made clear, that like nicotinic acid, which contains no nicotine, NMR does not require nuclear radiation.

Ant-acids

I'm teaching general chemistry this semester. Acids and bases are currently on our agenda, in particular how to assess the strength of an acid based on its molecular structure. When dissolved in water, strong acids, such as hydrochloric acid (HCl) or sulfuric acid (H₂SO₄) always transfer their protons (H) to water. For example: HCl + H₂O → Cl^– + H₃O⁺. Weak acids result when only some acid molecules transfer their protons to water. Organic acids, containing only carbon, oxygen, hydrogen and nitrogen, are generally weak acids. The archetypical weak organic acid is acetic acid, better known as vinegar: CH₃COOH. It's not the simplest organic acid, that would be formic acid: HCOOH.

Formic acid was first characterized in the late 17th century. Naturalists had observed that the vapors emitted by ant hills were acidic (using the equivalent of litmus paper), and in 1671 John Ray extracted the pure acid by distilling the crushed remains of red ants. Formica is Latin for ant, hence the name translates pretty literally as "ant acid". Formic acid is at least partially responsible for the sting in bee stings, ant bites and stinging nettles.

Even though chemists call formic acid weak, a 0.10 M solution has a pH of 2.4 (for comparison's sake, the same concentration of HCl has a pH of 1.0).

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I remember find ants all over my Formica counter in my post-doc days. Does the ubiquitous counter-top material have any connection to ants? Apparently not. It was originally created as a substitute for mica insulators. For mica....

Weird Words of Science: calcium

The isolation of metallic calcium was reported by Humphrey Davy 200 years ago this year. The name comes from the Latin for lime: calx. Compounds of calcium are like duct tape – they hold lots of stuff together. Calcium carbonate keeps clams covered, calcium oxide (lime) is the mortar that held the Roman Colliseum together, and calcium sulfate (plaster of Paris) has been holding broken bones in place for more than a millennium. Calcium keeps us from being a puddle on the floor as well. More than 90% of the body's calcium stores are in the bones.

Carbon Dioxide Curiousities

• It won't burn.
• No matter how cold you make it, you can't turn it into a liquid at atmospheric pressures.
• It sublimes, going directly from a solid (dry ice) to a gas (one way to make very creepy fog).
• It's heavy. Burning 1 gallon of gasoline (weighing about 8 pounds) produced 25 pounds of CO2.
• You can make a supercritical fluid out of it - a state of matter that is neither solid, liquid, nor gas.
• It's a critical ingredient in chocolate chip cookies - produced in situ by the reaction of sodium bicarbonate and the potassium salt of tartaric acid.