Weight, weight, do tell me, why are you using a “concentration” that’s oh so confusing?! I’m absolutely fine with absolute concentrations, and true relatives are fine, but start mixing measurements and calling it a percentage and there you cross the line… So today’s a bit of an aha moment and a bit of a rant, because coming to terms with with weight-volume (aka mass-volume) percentage I can’t… I hate this measurement, it seems to seek to make me confused, but here’s why, for biological solutions, you might find it used.

note: originally posted January 2020, updated and added video 10/21/21

As a biochemist, you have to make a lot of solutions in order to find solutions to scientific conundrums! At different times you need different amounts (like sometimes you want to bake 100s of cookies while other times you just need a couple). So instead of recipes, telling you exactly how much of each ingredient tell you to add protocols often give you descriptions of how much of the final product is made up of a certain ingredient (the concentration).

e.g. instead of telling you to add 200 chocolate chips to some amount of cookie dough for enough to make 10 cookies it’ll tell you to make cookies with 20 chocolate chips per cookie. This way you can scale up or down as desired.

Most of the times in the lab when I come across a solution that needs to be made, the concentration of the “final product” is reported in molarity which is a measure of moles per L. A mole is 6.02 x 10^23 of something (anything, but here we’re usually referring to molecules or at least groups of them) and liter (L) is a measure of volume. But sometimes you come across a “final product” described with a percentage. So you might be asked to make the biochemical equivalent of cookies that are 5% chocolate chip. But what does that even mean? When it comes to concentrations, % can refer to % mass/mass, % volume/volume, or % mass/volume. I hate that last one but here’s why it’s sometimes used.

How many chocolate chips there are per cookie can be considered the “concentration” of chocolate chips. The more chocolate chips per cookie, the higher the concentration of chocolate chips – assuming that the size of the cookie stays constant.

This is because concentration doesn’t just tell you about how much of something there is – it tells you about how “stuffed” the overall thing is with it – the more chocolate chips you add, the closer together they’ll have to be (assuming the batter’s been beautifully beaten). And speaking of the batter, for the sake of the analogy, we’ll consider it a pure liquid.

If you have a ton of chocolate chips, they’ll take up a lot of space in the batter and, since they’re denser than the batter, a spoonful of the batter will get significantly heavier.

A note on weight vs. mass —> outside of physics-type stuff, weight & mass are often used interchangeably – they both tell you about how “heavy” something is but weight takes into account the force of gravity so it kinda tells you about how heavy that thing feels. So a handful of chocolate chips will have the same mass anywhere (because mass is a measure of how much “matter” there is) but those same chocolate chips will weigh less on the moon, where gravity’s lower.

The reason things have mass is because they’re made up of atoms, which although tiny, do have mass – and lots of atoms add up. Solids like chocolate chips usually have their atoms squished closer together, so you get more atoms in a smaller volume. How much a certain volume of something (like a tablespoon of batter) weighs is its density: density = mass/volume. So chocolate chips are more dense than the batter.

So, the chocolate chip is denser than the batter -> if you were to take a tablespoon of chocolate chips & compare it to a tablespoon of batter, the chocolate chips would weigh more. And atoms also take up space, so of you mix the 2, some of the chocolate chips will “push apart” some of the batter molecules – the volume will increase so when you take a teaspoon of the mixture you’ll have a little less batter than pure batter, because the chocolate chips have stolen its space.

But if you only add a couple of chocolate chips into a giant batch of batter, that little bit of weight from the chocolate chip hardly seems to matter. It’s just a “drop in the bucket” of batter. This is the principle behind why “percentage” weight-volume (aka mass-volume) is sometimes used as a form of concentration measurement, especially in biology. You might have heard that your body’s mostly water – and this is true. There’s lots going on in there, but most things are happening in an internal “sea.” And the thing you’re most likely to see in this sea is the water.

Water-based solutions are referred to as “aqueous” and since biochemistry is mainly looking at how bodily molecules work, we usually try to study them under bodily conditions – so we are usually dealing with aqueous solutions. And dilute ones – few chocolate chips per cookie so we don’t need to worry too much about the chips changing the density.

So the density of most biological solutions is close to the density of pure water, and the density of pure water is ~1g/mL (if you had 1ml of pure water it’d weigh 1g). So the density of most biological solutions is ~1g/mL.

So if you say that there’s 1g of something else in there, and the solution still had a density of 1g/mL it’d have to mean that the solution was 100% your thing. So 1g/mL is 100% w/v. It’s like if you calculated % w/v for water in water. But start adding in solute and in order to still be ~1g/mL the thing you’re adding has to be similar to the density of water and/or there’s just so little of it compared to water that it doesn’t make too much of a dent. If you add a lot of a more dense something, you end up with solutions that are >100% solute?!

So it only works for dilute aqueous solutions – Outside of these dilute aqueous solution contexts, this concentration style isn’t very helpful. Even for dilute solutions with other solvents, because different solvents have different densities – water just happens to have a really convenient one.

Apart from those limitations, there’s a bigger reason the weight-volume “percentage” gets the side-eye from me. You can’t just go mixing and matching units of measurement and calling it a percent!

It’s not percentages in general that I find problematic. If you’re mixing 2 solids and you want to tell me, of the combined weights, what’s the percentage of the combined weight that comes from one solid that’s cool by me. Add 2g of NaCl (table salt) to 98 g of pepper and you have a mix that’s 100g total (2 + 98 = 100), but only 2g of that weight comes from the salt, so it’s 2/100 = 2% mass/mass (% m/m).

So here you’re taking adding & dividing units of the same thing. And the same units. For something to be a legit percentage, it has to be unitless – you need to have the same units in both the top & the bottom so they cancel out. So you can’t mix 2mg of NaCl and 98g of pepper and tell me it’s 2% NaCl. You either need to first convert 2mg to 0.002g or convert 98g to 98000mg. Either way, the units cancel out and give you ~ 0.000020 x 100%= ~0.0020%

You can also do something similar for liquids. Mix 50mL of ethanol with 50mL of water and you get a solution that’s 50% volume/volume of ethanol. So if your whiskey’s 10% v/v alcohol this is what that means. A common way this is reported is in “proof” which, in the US is twice the % v/v -> So this could be labeled “100-proof”

But units of mass and volume don’t cancel out – which is why density is reported in units of mass over units of volume. So “percent” isn’t really applicable in the case of “percent” mass-volume. But here’s an example, of why it sometimes approximates one.

Biochemists aren’t the only people working with biological solutions – doctors do too. And a common thing they use is “normal saline” which is 0.9% (w/v) NaCl in water. This means that there are 0.9g of NaCl per 100mL of water. Let’s take a look at how else this value could be reported in a way that could get the bumbling biochemist’s stamp of approval.

the “gold standard” – molarity. Molarity is moles per L. So we need to convert 0.9g of NaCl to moles of NaCl and 100mL of water to L of water. And this is a case for dimensional analysis! more on dimensional analysis: http://bit.ly/dimensionalanalysising

we need to look up the formula weight for NaCl. NaCl is an electrolyte, meaning it’ll dissociate in water, splitting into Na⁺ & Cl⁻. If you look at the formula weight on the bottle it tells you their combined weight, which is 58.44 g/mol.

a little dimensional analysis & you see that 0.9g of NaCl is

0.9g NaCl x (1 mol/58.44g) = 0.015 mol NaCl

and there are 1000mL per L, so 100mL of water is

100mL x (1L/1000mL) = 0.1 L

0.015 mol NaCl/ 0.1L water = 0.15 M NaCl (which can also be written as 150mM NaCl)

% weight – this also involves using the weight of the salt, but you also use the weight of the water instead of the water’s volume.

to convert 100mL of water to g of water, we need the water’s density which we’ve seen is 1g/mL

100mL x (1g/mL) = 100g

So the overall combined weight is weight of water (100g) + weight of NaCl (0.9g) = 100.9g
And the % weight of NaCl is 0.9/100.9 = 0.0089 x 100% = 0.89% (see why the % w/w “worked”?)

Since salt’s a solid, the 3rd type of % concentration (% volume) isn’t really relevant to this case, but it is relevant to a different kind of case – a case of liquor!

This isn’t a “real” way to remember it, but I’m all about using whatever tricks help to remember things, and one way I remember the weight/volume thing is by thinking about the time I encounter it most often in the lab – making 10% ammonium persulfate (APS) to polymerize my SDS-PAGE gels when I’m pouring them (get the individual Acrylamide molecules to link together into a PolyAcrylamide mesh Gel I can use Electrophoresis to send unfolded proteins through to separate them by size. more here: https://bit.ly/polyacrylamidepolymerization

I make this 10% w/v APS by dissolving 1g of APS in 10mL of water. And if I can remember this I can figure it out  
more on molarity: https://bit.ly/c1v1vid

more on other concentration forms: http://bit.ly/solutionconcentrations 

more on buffers: http://bit.ly/phbuffers

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉 http://bit.ly/2OllAB0

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