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.