The Avocado Molecule: A celebration of International Mole Day

Introduction

Recently, we chemists threw open the dusty vaults of our minds to remember those old high school formulas and the supposed ease of doing basic arithmetic without a calculator, in celebration of International Mole Day (23rd October). A quirky excuse to mash together some chemistry fundamentals, internet animal memes, and hipster food favourites – pitted against as many avocado puns as I can sink my teeth into. I make no apologies. So, the questions we have here are: what’s a mole and why are we talking about avocados? All shall be revealed.

What is a mole?

Basically, the mole is just a way to relate the number of atoms or molecules in something to each other. If two things have the same number of moles, they have the same number of molecules or atoms. For example, if I have a spoon full of table sugar with 2.3 moles of sucrose molecules it will have the exact same number of molecules as a party balloon containing 2.3 moles of helium atoms. It can also be used to relate the parts of substances, e.g. a salt of magnesium chloride (MgCl2) contains 1 mole of magnesium (Mg2+) ions to every 2.0 moles of chloride (Cl-) ions. The unit of the mole is … “mol” – of the seven universal (SI) units of measurement.

mole of mole

Source: imgur

So, why don’t we just count the number of atoms and compare them directly? In short, because the numbers become very, very, big very, very quickly and it’s useful to be able to compare to some external standard. This is where Avogadro’s number (not avocado!) comes in.

 

Avogadro’s Number

By definition, 1 mole is the number of atoms in 12.0 grams of carbon-12 (12C)[1] and we call this number, Avogadro’s number/constant: 6.02 x 1023.[2] It’s a huge number! A little more than 6 with 23 zeros after it. That’s why we write it in that funny form above, called Scientific Notation or Standard Form – to save space for really massive or really tiny numbers. Alternatively, we’d have to write it down as 602,140,857,000,000,000,000,000.

Fun bonus fact: International Mole Day is celebrated between 6:02 AM and 6:02 PM on October 23rd (or 10/23 using the American date format) to give the key digits of the standard form number.

avo number

Source: biostrata marketing.

 

With two new terms in our chemistry fruit basket, it’s not hard to see how memes of moles and avocados have quickly smashed their way onto the internet – the memoshere doesn’t leave low hanging fruit for too long.

how_many_atoms_in_a_guacamole_avocados_number_t

Source: CafePress

 

Calculating the number of atoms & molecules in stuff

Once we know how many moles of a substance we have we can do all sorts of handy things like work out how heavy a molecule is or how much we might need to make a chemical reactions work properly – can be helpful for baking and food.

The equations below relate (Figure 1):

  • the mass (m) of a substance, measured in grams (g),
  • the number of moles (n), measured in moles (mol),
  • a quantity called the molar mass (Mr) which is a measure of the size of the molecule in question, measured in grams per mol (g mol-1)

mass equation

Figure 1: Different forms/rearrangements of the same three quantities: mass (m), moles (n), and molar mass (Mr).

Don’t be scared…math is your friend,[3] and we’ll use it below to work out the size of our imaginary Avocado molecule 😀

The Avocado Molecule

Hopefully it won’t be too surprising (because you’ve been studiously scrawling through all the other sciencey blog posts) that there’s no such thing as an avocado molecule. Avocados are made up thousands of different types of molecules with tonnes of different sizes. BUT… if we were to imagine one – an imaginary “Super Avocado molecule” – what might that look like? How big would it be and what might it’s molar mass (Mr) be? This is the challenge the internet has given us and we shall indulge this alchemical madness in this Jabberwockey of molecular calculation.

Like good everyday scientists, we start by spreading out our assumptions:

  1. We’ll select the most common variety of avocado: California Hass (Persea Americana) which has an average mass off 170 g.
  2. The average serving size of the flesh component is 68 g, of which 72%w/w is water.
  3. To actually work out the molar mass (Mr) of this imaginary avocado molecule we’d need to know the exact mass (m), check, and the number of moles (n), damn!

To work out the number of moles of each different type of the thousands of molecules in an avocado we’d also need the molar masses (Mr) of each different molecule: each fat, sugar, protein, etc, some of which are often undefined for large random polymers like polyphenols). This is a tonne of data.

Failing this, we could think of that theoretical “super avocado molecule” with an imaginary molar mass, Mr(avocado), which captures the size and its possible chemical formula. Unfortunately, data for this doesn’t exist either. BUT…it does for humans! Kinda.

All life has the same general building blocks, so using humans as a starting point seems like as good a place to start as any. As early as the 18th century, scientists have been trying to work out the ratios of the various different elements (empirical formula) in the human body.[4] If we take one useful example from New Scientist in 2005, reduced it down to the remove most of the inorganic components to give us something that might look like a big organic molecule, we might get C150H1050N21O233Ca4P3SK.[5] This imaginary human molecule would have a molar mass (Mr(human)) = 10,406 g mol-1. Technically, this imaginary “human molecule” would be some sort of organic salt due the inclusion of the potassium ion (K+) – “potassium humanate”, perhaps. Hey, if we’re making this up as we go along, so might as well go full crazy, right?

human molecule

Source: modified image from Wikifoundry.

 

We could stop there, but the chemical makeup of an avocado is a little different than a human – this likely why they’re better on toast and make poor conversation partners. By mass, avocados have 29% more fat, 90% less protein, and nearly 22 times the amount of carbohydrates.[6] All these different types of molecules have different molar masses in general (e.g. proteins are more likely to contain heavy sulfur atoms) and so this will mean Mr(avocado) will be different than Mr(human). But because of the diversity of structures of fats, sugars, proteins, there’s no average/general formula for these categories of molecules to work the difference out – so let’s make some up (warning: now, this is where it’s all going to become large imaginary/gibberish.

Imagined a sub-set of idealised major molecules (Table 1, a) and their theoretical empirical formulas (Table 1, b).[7] For fats, we could use the general hydrocarbon formula of CnH2n+2 as both are primarily composed of just hydrogen and carbon atoms. For carbohydrates, the general formula is usually quoted as C6H12O6, whereas in a recent scientific paper which analysed 10,739 proteins found that most have a similar general molecular formula.[8] The remainder of the chemical components we’ll estimate with the same formula as the general human composition. We then “normalise” or round all these numbers to get an idealised formula (Table 1, c) as if all types of molecule have 100 carbon atoms, so that we can compare the ratios of the molar masses. From these we can work out our imaginary molar masses (Table 1, d).

a: Molecule type

b: Idealised formula c: Normalised formula

d: Imaginary molar mass (Mr)

Fats C10H22 C100H200

1,402 g mol-1

Carbohydrates C6H12O6 C100H200O100

3,002 g mol-1

Proteins C100H158N28O30S C100H158N28O30S

2,264 g mol-1

Other C150H1050N21O233Ca4P3SK C100H700N14O155Ca3P2SK

3,736 g mol-1

Table 1: Imaginary major molecules of our “super avocado” molecule.

We can construct a set of ratios of the above imaginary molecular masses (Table 2, c), in this case based on the molar mass of fats as the lightest class of molecule (Table 2, b). Then, using the known masses (m) of the different molecule types in 68 grams of human (Table 2, d), from the formulas above (Figure 1), we can calculate the ratio of moles of each (Table 2, e).[9]  It should be noted that you’re unlikely to find 68 g of human in your local supermarket, so we’ll just pretend it’s a nice thigh steak.

a: Molecule type

b: Imaginary molar mass (Mr) c: Ratio of molar mass (Mr) for humans d: Masses (m) of molecule types in 68 g of human

e: Ratio of moles (n) for human

Fats

1,402 g mol-1 1.00 8.16 g 8.16

Carbohydrates

3,002 g mol-1

2.14

0.727 g

0.13

Proteins

2,264 g mol-1

1.61 13.6 g

8.42

Other

3,736 g mol-1

2.66 45.97 g

17.26

       

f: 3.397

Table 2: Ratios of molecular categories for different major molecular types in humans.

If we compare the relative amounts of fat, carbohydrate, and protein between avocado and humans, we can get a percentage difference (Figure 3, d) [6],[9]. These numbers aren’t too surprising; avocados are a little more fatty (29%w/w more), they’ve got a much greater proportion of carbohydrates (nearly 22 times by mass), and far less protein (90% less) (Figure 3, e). One must keep in mind these are just average values – how your friendly avocado gorging brunch hipster or millennial would compare in composition, one can only guess – you are what you eat … to a limited degree.

a: Molecule type

b: Masses (m) of molecule types in 68 g of human c: Masses (m) of molecule types in 68 g of avocado d: percentage difference (b/c)

e: Ratio of moles (n) for avocado

Fats

8.16 g

10.5 g

129%

10.5

Carbohydrates

0.727 g

5.9 g

2169%

2.8

Proteins

13.6 g

1.3 g

10%

0.8

Other

45.97 g

50.3 g

109%

18.9

       

f: 3.296

Table 3: Estimated ratios of molecular categories for different major molecular types in avocados.

If we add these mole ratios (Figure 3, f) together and compare them to the summed ratio from humans (Figure 2, f) we see that there are 97% fewer moles in the avocado for a given mass compared to humans. Or, similarly, for the same number of molecules, an imaginary avocado molecule would be lighter than a human molecule – makes sense I guess if it’s more fatty and less proteiny.[10]

So… based on this (largely imaginary analytical chemistry) we can arrive at a theoretical molar mass for our avocado: Mr(avocado) = 10,096 g mol-1.

 

Final Thoughts

So, there it is: real analytic chemistry about imaginary molecules. See, chemists are fun! Also, turns out avocado puns were harder to think of than I would’ve ‘g-hass-ed’ and relating imaginary analytical chemistry to anything meaningful was quite a stretch.[11] But, there we go. We have a theoretical molar mass for an imaginary “super avocado molecule” of simply massive proportions. Well, it’s actually about the size of the average protein, so it’s not actually as unrealistic as I originally thought it might be, however this would all changed if we used a different starting empirical formula for the idealised molecules. Not unlike that spotty brown avocado you’ve got sitting in the fridge since yesterday, some of the calculations might be a little suspect, but hopefully it’ll still serve its purpose and give you the much needed nutrition we crave.

cat

Source: pinimg

Notes and Sources

[1] Carbon-12 (12C) is the isotope of carbon with 6 protons and 6 neutrons in its nucleus. It is a useful standard due to its high natural abundance and non-radioactivity. We need to define the mole based on a single isotope as protons and neutrons have different masses, so a sample of elemental carbon in general won’t have the same number of atoms for a given mass as it as other isotopes of carbon in it (e.g. ~1% 13C)
[2] Avogadro’s number/ constant = 6.022140587 x 1023 mol-1.
[3] The triangle can be useful in working out the relationship between the other quantities – cover over the quantity you’re looking for and the relationship between the remaining to quantities is revealed. If the two remaining are next to each other, multiply them; if one is above the other divide the top by the bottom. This works nicely for all multiplying/dividing relationships with three variables.
[4] Homopedia: encyclopaedia of human thermodynamics. http://www.eoht.info/page/Human+molecular+formula. (accessed October 25th, 2017).
[5] Haworth, J. W. That’s Life. Nature. 2005. https://www.newscientist.com/lastword/mg18825282-300-thats-life/. (accessed October 25th, 2017).
[6] Dreher, M. L; Davenport, A. J. Hass Avocado Composition and Potential Health Effects. Crit Rev Food Sci Nutr. 2013, 53, 738
[7] The atomic coefficients are numerically rounded off for clarify – but they’re pretty much all imaginary in the first place, so it doesn’t really make much of a difference to what we’re trying a achieve.
[8] Torabizadeh, H. All proteins have a basic molecular formula. World Academy of Science, Engineering and Technology. 2011, 54, 961.
[9] Freitas, R. A. Nanomedicine, 1999. Landes Bioscience. Tables 3–1 & 3–2.
[10] Proteins can often contain heavier atoms like sulfur when compared to other organic molecules, so in general might be expected to be heavier.
[11] If there are logical errors in the analytical chemical approach … this may not be entirely surprising for calculating imaginary molecules. But as such, we are scientists and any improvement in our models are always welcome and encouraged. (That is to say, I’m pretty sure this ratio approach is kosher due to the multiplicative relationship of the various quantities). As for the idealised molecular formulas and molar mass of humans – those are largely arbitrary, but we had to start somewhere, right.
Heading image source: Sams Club Resources

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