Sunday, 28 October 2012

Bond Chemistry

Today, I watched Skyfall, the new Bond film. It's a fantastic film, with gorgeous actors, actresses, cars and explosions abound. I would do a post critiquing it and examining the themes throughout, but that's not what this blog is for, and it'd just be a drop in the online ocean of fan-made reviews of films they've just seen.

So instead, I thought I'd look into the sciencey medically bit that intrigued me. The main villain is revealed to have bitten a cyanide pill in the past, which failed to kill him; he now has very few teeth and  has to wear a false set. When he takes them off, the muscles in his face seem to sag, and the lower half of his eyeball is revealed, as if someone had pulled down on the skin around his cheek, seemingly because his dentures also include supports for his maxilla or something.

But what I thought I knew about cyanide was that it works by inhibition of one of the enzymes used in respiration. Could it really eat away at the inside of your mouth? The first clue was in the name of the actual chemical inside cyanide pills, hydrogen cyanide. This tells you that it is a compound of the formula HX, where X is some negative ion (here, it is cyanide). These kind of compounds dissociate in solution to form H+ ions and X- ions. They're also known as acids. In this case, the "X" is cyanide, which forms CN- ions; this is what inhibits the respiratory enzyme.

It is conceivable that, because it is an acid, it could erode the teeth and bone away (acid erosion of teeth is permanent, at least). For this to happen, you would need an acid of a very low pH, and in sufficient quantities that it can react with enough teeth.

Now for some wild assumptions and quick calculations:
The fatal dose of cyanide, according to Health Canada, is about 1.52mg/kg bw. So for the sake of argument, we will say that he took as close to the fatal dose as possible without it being fatal. helpfully informs us that Javier Bardem, the actor playing Silva, weighs 84 kg. Therefore in order to be just non-lethal, the pill would have to contain 127.68mg of cyanide ions. The Mr of CN is 26, so the lethal amount of HCN is 0.004910769231 moles.
The pill was stored in his 2nd molar, which we will model as a 9mm*9mm*7mm cuboid (assuming it is on the upper jaw); therefore its volume is 0.000567dm^3. The pill would have had to have taken up much of this space in order to be easily accessible, so we can say that the pill has the same dimensions as the molar. Therefore the concentration of HCN (which used to be known as prussic acid, on an unrelated note), is 8.660968661moldm^-3.
Hydrogen cyanide's pKa is 9.2. Therefore its acid dissociation constant is 10^(-9.2). This is [H+][CN-]/[HCN]. Given that the concentrations of H+ ions and CN- ions are the same (because they dissociate in a 1:1 ratio), and given the concentration of HCN, it is possible to work out the concentration of H+ ions:
[H+][CN-]/[HCN] = 10^(-9.2)
[H+] = [CN-], therefore ([H+]^2)/[HCN] = 10^(-9.2)
[HCN] = 8.660968661, therefore [H+]^2 = 8.660968661*10^(-9.2)
Therefore [H+] = sqrt(8.660968661*10^(-9.2))
[H+] = 7.392362131*10^(-5)

Therefore pH (= -log[H+]) = 4.131216766
= 4.13 to 2 decimal places

Wikipedia says that there is a paper saying that solutions with pH<5.0-5.7 cause dental erosion. Therefore, Silva's pill may well have damaged his teeth. However, it seems unlikely that it could have destroyed so much of his jaw and face: the pH of wine, for instance, is around 3-4. So the acidic effect of the cyanide pill would actually be less than if you just squirted the inside of your mouth with some sauvignon blanc.

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