It’s the bewitching hour and all through the blog not a creature was stirring not even a Pokémon…wait, what? I think a few wires and electrodes have got crossed there. Inspired by another recent Reddit post and wonderful little blog post by Sustainable Nano, where the authors celebrated International Mole Day and Halloween by hypothesising the chemical and physical properties of the classic ghostly Pokémon, Gastly, I thought we could have a go at something similar here. We love Pokémon, science, and tricking people into learning maths, so I thought I’d explore the idea a further, doing a little Pokémon ecology and spiriting you away into the possible coloured compounds and physical qualities of this poison poltergeist.
Our Ghastly Gastly
It’s always been one of our early favourites as we journey out into the world of Pokémon as nerdy teenagers all those years ago – Gastly is a transparent mischievous ghost manifesting as a big ball of toxic gas. It uses its body to envelope its prey to poison and render them unconscious but may also may make use of its dark arsenal of psychic attacks.
Source: Kokodriliscus: Deviant Art
Sustainable Nano decided to base their Gastly on elemental iodine (I2), a toxic dark solid which readily turns directly from solid to gas without having to transition via a liquid state like most compounds (sublimation). It’s a pretty neat effect to watch, especially when you have a solid subliming from the bottom of a container, turning into gas, and forming large iodine crystals on the roof of a container – check out a video of it here. Using the official vital stats of the average Gastly and the molar mass (Mr = 126.9 g mol-1) of iodine that we’ve discussed last time in the Avocado blog post for International Mole Day, the authors worked out the number of moles of gas in their Gastly.
While iodine is quite toxic (so ticks that box for Gastly), one might expect it to deposit itself around the world as solid iodine (I2) resulting in our poor little ghost Pokémon dwindling away over time until it’s a mere shadow of itself. So, for our Gastly we’re on the lookout for a collection of interesting chemical compounds which may better simulate Gastly’s gaseous look and suffocating and toxic abilities.
The authoritative authority on all aspects Pokémon states that Gastly has a height of 1.30 metres, a weight of 90.7 grams, and that its body is made up of 95% gas. We’ll assume the remaining 5% of this mass makes up those sinister white teeth plus whatever colourful compounds that may imbue Gastly with its characteristic purple hue. I’ve opted to use a mixture of two gases to prepare my Gastly with the appropriate combination of transparency, toxicity, and ability to cause sudden fainting in its enemies (Figure 1).
Figure 1: Our chemical composition of Gastly.
The Colour of Magic: Tyrian Purple and a history of purple dyes
The colour purple is actually pretty rare in nature and difficult to produce artificially due to the way specific way molecules would need to interact with visible light. As such, purple dyes were expensive and highly prized in the ancient world, often being associated with royalty (Youtube vid here). Historically, simple inorganic compounds including potassium permanganate (KMnO4) and cobalt phosphate (Co3(PO4)2 have been used as purple pigmentation (Figure 2). The first synthetic purple dye was a barium copper silicate (BaCuSi2O6), called Han purple, synthesised around 1045 BCE in china.
Figure 2: Inorganic purple compounds: a) solution of potassium permanganate (KMnO4), b) cobalt phosphate (Co3(PO4)2), c) Han Purple (BaCuSi2O6).
It wasn’t until 1856 that the first organic synthetic dyes were created in the lab by the combination of aniline, p-toluidine, and o-toluidine in acidic potassium dichromate to give a mixture of related molecules, including mauveine A (Figure 3). Don’t be scaled of the molecular structures; they’re your gateway to the colourful world of synthetic dyes. Pretty ay?!
Figure 3: Reaction of to make mauveine A (left) and a solid mixture of mauveine powder (right)
One such ancient and natural purple pigment that caught my eye is known as Tyrian Purple, the principal component of which is a molecule called 6,6’-dibromoindigo (Figure 4). Isolated from the mucous secretions of a number of different species of seas snails belonging to the muricidae family, it’s a lot of snails that you need to milk…or sometimes squish, to get your purple colouration. Poor snails.
Figure 4: Composite image of 6,6’-dibromoindigo (right), mauveine dyed fabric source from Wikipedia (centre), and a member of the muricidae family of sea snails sourced from Wikipedia (right).
Irrespective of the mass snail squishathon required to get a hold of a significant quantity of the dye, the attractive molecule structure (trust me) and purple hue made Tyrian purple a winner for the choice of our Gastly colouration. 6,6’-Dibromoindigo is a funky moderately-sized molecule with a molar mass (Mr) = 420.06 g mol-1. We’ll say that of the 5% of Gastly’s 90.7 gram mass that is not gas, only 1% of that is needed for the dye – this is completely arbitrary, but gives us 0.86 grams of Tryian Purple to fling at the problem.
For our Gastly, we’re imagining an extremely fine dispersion of this dust in our gas mixture (and hoping it doesn’t settle out of the sky leaving out Gastly naked and transparent). Wishful thinking perhaps, but it won’t be prone to crystalisation like iodine gas would otherwise be.
All the Better to Eat You With: dental details & ionic solids
The main mineral component of human teeth is a hard ionic solid called hydroxylapatite (Ca2(PO4)3OH), a calcium-based white salt with a molar mass of Mr = 502.32 grams per mol. We don’t know if our Gastly comes from human ghosts, but maybe it’s a good place to start. Here we’ll work out the general dimensions of these pearly whites and see what they might be good for.
Gastly’s total mass is 90.72 grams with 5% of its body is not being made up of gas. We’ll make the assumption that 99% of this remaining solid fraction makes up Gastly’s two dagger sharp teeth, with a mass of:
eq. 1 mass(1x tooth) = ½ x mass(Gastly) x 5% x 99% = 2.25 grams
Pure hydroxylapatite, Ca2(PO4)3OH, has a density (d) of 3.14 grams per mL. Using this we can work out the volume each tooth and from this, their general dimensions:
eq. 2 Volume(tooth) = mass(tooth) / density(tooth)
Volume(tooth) = 2.25 grams / 3.14 grams per mL
Volume(tooth) = 0.72 mL = 0.72 cm3
On casual inspection, one given tooth seems to be approximately tenth of Gastly’s overall height (1.30 m) making them 13 cm tall. We’ll make the assumption that the teeth can be approximated by a triangle-based pyramid shape (Figure 5), and thus, the volume is defined by:
eq. 3 Volume(tooth) = 1/3 x base area x height(tooth)
Figure 5:triangle-based pyramid with dimensions shown. Source: LDnifty modification of imagine from Ontrack Media.
Rearranging eq. 3 gives us eq. 4,
eq. 4 base area = 3 x volume(tooth) / height(tooth)
base area = 3 x 0.72 cm3 / 13 cm
base area = 0.17 cm2
The width of the tooth looks to be about 80% of its height, so let’s say it’s about 10.4 cm. From this we can work out the depth of the tooth using the base area:
eq. 5 base area(tooth) = ½ x depth(tooth) x width(tooth)
depth(tooth) = 2 x base area / width(tooth)
depth(tooth) = 2 x 0.17 cm2 / 10.4 cm
depth(tooth) = 0.032 cm = 32 mm
So, these are very, very thin teeth indeed! Probably not so good for biting things but they may have a better chance of not falling out of Gastly’s light gassy head.
Ghostly Wisps: molecular volumes & ideal gas laws
I’ve chosen a mixture of two compounds to make up my Gastly’s body: 95% ethyl methyl ether (CH3CH2OCH3) and 5% chloroform (CHCl3) (Figure 6). Ethyl methyl ether (EtOMe) imparts the transparent toxic nature of this Pokémon’s bulk while also possessing a low enough boiling point (b.p. = 7.4 °C) that it will be gas at room temperature. This will be mixed with the vapour of chloroform (CHCl3), a dense colourless liquid (b.p. = 61.2 °C), known for its fainting properties. The boiling point of a mixture of gases is related to the fraction of each of the different molecules and so I’m hoping with a relatively low concentration of chloroform, we can essentially keep the chloroform mixed in with the ethyl methyl ether to provide a sufficiently noxious gas with the properties we want.
Figure 6: “Ball-and-Stick” (top) and “skeletal” (bottom left) molecular structures, and condensed molecular formulas (bottom right) for chloroform and ethyl methyl ether. Green = chlorine, white = hydrogen, grey = carbon, red = oxygen.
Now, there are two methods we could use to work out the volume that Gastly takes up. The most straight forward is to assume Gastly is a perfect sphere and hence using its radius (half its height) and the following equation, eq. 6:
eq. 6 Volume(sphere) = 4/3 x π x radius3
Volume(sphere) = 4/3 x π x (6.48 cm)3
Volume(sphere) = 1138 L
Alternatively, we could calculate the expected volume if we know how many molecules of gas we are working with. For this we’ve made the assumption that our mixture is going to be a well behaved “Ideal gas” and won’t do anything funky like try to separate out or do anything weird with pressure. In which case, there is a relationship between the pressure (P), volume (V), temperature (T), and number of molecules (n) of a gas (or mixture of gases) called the Ideal Gas Law, eq. 7:
eq. 7 P x V = n x R x T
The average air pressure on a lovely sunny day here is Auckland, NZ is about 1027 hPa or 1.014 atm, the temperature is about 25 °C (which converts to 298.15 K to keep the units consistent for calculation) and that little R in the eq. 7 is the “gas constant” – a number relating the other pieces to each other (R = 8.206 x 10-2 L atm K-1 mol-1).
Now we just need to know the number of molecules literally floating around: something we’ve looked at before in our previous post about Avocadoes. Casting your mind back, we can use the mass (m) of a substance and its molar mass (Mr) to calculate the number of molecule (n) such that:
eq. 8 n = m / Mr
We know that m(ethyl methyl ether) = 95% x 95% x m(Gastly) = 81.9 grams, and that Mr(ethyl methyl ether) = 60.1 g mol-1, and so from eq. 8:
eq. 8a n(ethyl methyl ether) = 81.9 g / 60.1 g mol-1
n(ethyl methyl ether) = 1.36 mol
and, knowing m(chloroform) = 95% x 5% x m(Gastly) = 4.3 grams, and Mr(chloroform) = 119.37 g mol-1 we get:
eq. 8b n(chloroform) = 4.3 g / 119.37 g mol-1
n(ethyl methyl ether) = 0.04 mol
Adding these together (n = eq. 8a + eq. 8b), and we get:
eq. 9 n(gas) = 1.40 mol in total.
Rearranging ideal gas law above (eq. 7) to eq. 7a, we can work out the expected volume this amount of gas should occupy given the temperature and pressure on this ill-chosen sunny day. In hindsight perhaps a cooler night time setting would be more suited for a ghost, but oh well, never mind.
eq. 7a Volume(gas) = n x R x Temperature / Pressure
Volume(gas) = 1.40 mol x (8.206 x 10-2 L atm K-1 mol-1) x 298.15 K / 1.014 atm
Volume(gas) = 33.7 L
Well! That’s a bit different than our initial calculation. It seems that under our normal sunny conditions that that amount of gas would be expected to occupy quite a considerably smaller volume than the Pokémon’s size would imply. This brings us to the conclusion that our Gastly might be confining an extremely low internal pressure if the original volume based on its height (eq. 6) is to be believed. We can rearrange the ideal gas law (eq. 7) again, giving us eq. 7b, and work out the pressure, P (sphere), we’d expect from the volume (sphere) based on Gastly’s height (1.30 m) and the number of molecules present (eq. 8b):
eq. 7b P (sphere) = n x R x Temperature / Volume(sphere)
P (sphere) = 1.40 mol x (8.206 x 10-2 L atm K-1 mol-1) x 298.15 K / 1138 L
P (sphere) = 0.03 atm
So, yeah. If Gastly is as tall as it is stated, then it would have quite the implosive vacuum contained somehow within its boundaries. Makes you wonder what’s keeping those teeth in place and not having them sucked into its head rendering it looking like a octogenarian who’s lost their dentures.
Source: LDnifty modified image from Pintrest.
So, there you have it – another exploration through the absurd. We’ve “learned” that our Gastly must be under quite a considerable amount of negative pressure, threatening to collapse violently in on itself at any moment, haphazardly flinging razor sharp teeth and dispersing a haze of purple powder all over the show – much like one might imagine a poorly constructed indigo hedgehog balloon animal passed to an unexpecting small child holding something pointy … or perhaps like a sample of feather-tickled nitrogen triiodide (this is actually a thing!) … or something.
Hopefully, in addition to some chemical tomfoolery, this was also an amusing illustration of how the practical application of analytical chemistry might be used to delve into the inner makeup of our (or in this case a fantasy) world. I leave you with this wonderful rainbow-toned creation of Gastly and its evolutions as another example of the extremely talented artistic work occupying the internet (Figure 7) and a promise for a somewhat less fantastical topic in the Matter Matters series of blog post.
Figure 7: Left to right: Gastly and its evolutions, Haunter and Gengar. Source: Pintrest.
Notes and Sources