How many invisible friends do I have in here? I don’t have imaginary friends, but I do have invisible ones (at least invisible to the naked eye) – and when I *concentrate* while I going about my work in the lab I visualize the molecules like little friends of mine whose stories I’m trying to tell  I’m always wanting to know how many of these friends I have, but Instead of “follows” and “likes” I’m more worried about things like molarity and molality. Can the bumbling biochemist use candy to bring a mole fraction of clarity to this concentration-reporting hilarity and shed some light on electrolytes?!

A mole (mol) is like the biochemist’s “dozen” – it is just a set number of things – anything – but if you ordered a mole of bagels you’d get 6.02 x 10²³ of them… (that’s 602 and and then 21 0’s…) which, if you were to divide up among the human population would be about 86 trillion bagels per person. Talk about carbo-loading! 

Yet, in this bottle of Tris buffer (pH-stabilizer) there’s a whole mole of Tris molecules (which are obviously way smaller than a bagel). I know there’s this many because “I” looked at the chemical bottle’s equivalent of a nutrition label & used the FORMULA WEIGHT (F.W.) to see that 1 mole of Tris weighs 121.14 grams & I weighed that much out. And then I put that in ~800mL of water, added HCl to get it to the right pH, then topped off the volume to 1L to get a 1M solution (M stands for molar and it means mol/L). 

note: I’ve done that many times before, but one of our awesome lab techs actually made this batch – thanks Seraya! 

I stuck 1 mol of particles (“friends”) in and now there are 1 mol of particles hanging out in the water. I didn’t gain any friends, just moved them & got them to hang out with my water friends. But if I looked at the “nutrition label” for table salt (NaCl), saw it had a F.W. of 58.44 g/mol, measured that much out & stuck it in 1L of water, my “friend count” would double?! This is because NaCl is an electrolyte, so when it dissolves it also *dissociates* so you get more particles than you put in. To explain more, let’s step back a bit so I can assure you this is legit… And bring in that candy I promised you – I mean, it is almost Halloween after all! 

Basically, if we want to know how much of some chemical we have, we usually describe it in terms of how many “formula units” we have. Sounds a bit intimidating, but formula unit is just kinda like “what you buy it as.” Just as you might buy rolls of Rolo’s (those little chocolate-covered caramels) and bars of KitKat’s, we buy “table sugar” as sucrose & “table salt” as sodium chloride (NaCl), and if you look at the “nutrition label” on a chemical bottle, this formula unit (e.g. NaCl or sucrose) is what things like the chemicals’ “molar mass” and “chemical formula” are based on. 

molar mass tells how much 1 mole of the formula unit weighs. Other terms for molar mass include formula weight or molecular weight, so you might see it abbreviated F.W. or M.W. (note: we typically use “mass” and “weight” interchangeably, but weight technically takes into account the force of gravity, but mass doesn’t. you don’t need to worry about that here it was just always something that confused me so wanted to add this little note)

For example, take our table sugar, sucrose. It has a chemical formula of C₁₂H₂₂O₁₁. This tells us that each sucrose contains 12 carbon atoms, 22 hydrogen atoms, & 11 oxygen atoms. If you were to add up the atomic weights of each atom it contains (you can find these on the periodic table of elements) you’d get the weight of 1 single molecule of sucrose. That’d be a really tiny number. BUT if you multiplied that by 6 x 10²³ you’d get the weight of 1 mole of sucrose (an easier-to-work-with number) & we call this the “molar mass”.

The sucrose label tells me the formula unit is sucrose & that 6 x 10²³ sucroses weigh 342.3 grams (g). So, if I want 1 mol of sucrose, I need to weigh out 342.3g 

But what am I going to do with that mole of sucrose? Maybe I want to dissolve it in some water. When you “dissolve” a bunch of somethings in water, what that means is that each “something” is going to replace all its something-something and something-otherthing interactions with something-water interactions. For this to happen, some water-water interactions have to be broken, so in order for something to be soluble in water, it has to offer attractive surfaces to the water (such as charged or partially-charged parts). Similar thinking applies for solvents (dissolvers) but in biochemistry we’re usually dealing with water-based (aka “aqueous”) solutions and, except for cases like membrane protein, “soluble” usually refers to “water-soluble” in the context of biochemistry and biology. 

So, going back to our sucrose, which *is* water-soluble (at least to a certain extent (there’s only so much of anything you can fit into a certain amount of water!))… if I dissolved that 1 mole of sucrose in a glass of water, I’d get a super-sweet solution (but don’t taste anything in the lab!) BUT if I dissolved it in a pool I’d probably not even be able to taste it (don’t drink that either…)

Clearly, when it comes to solutions, just knowing # of mol of solute (the thing we’re dissolving) is NOT sufficient!  Instead, what we really care about is the # of mol of solute *compared* to amount of solvent (the thing it’s dissolved in – often water). We want to know its “molar concentration.” 

There are different ways to report the molar concentration. Some common ones are molarity, molality, mole fraction & partial pressure (this one is used for gases) we’ll get back to these later, but when it comes to particle concentrations, it’s important to know how many particles you’re gonna get (cuz it might be different than what you put in…)

I’ve been talking about particles as “friends” but what really is a particle? A “particle” is basically just a thingamabob that’s held together. It’s another one of those overly-broad terms that scientist use that can be helpful sometimes but confusing other times, and which resists being tied down by a strict definition… 

Can water take apart a particle? It depends on what’s holding it together. Basically, “matter” (physical stuff) is made up of atoms and those atoms are made up of smaller parts (subatomic particles) called protons (which are positively-charged), neutrons (which are neutral), and electrons (which are negatively-charged). The protons and neutrons live together in a dense central nucleus and they’re “heavy” so they contribute to the mass. The electrons whizz around the atomic nucleus in an “electron cloud.” These electrons are super duper duper tiny so they do not contribute significantly to the mass, but they do contribute significantly to the atom’s properties! The electron clouds of different atoms can interact with each other and stick atoms together. 

Atoms link up into *molecules* by merging electron clouds (“sharing pairs of electrons”) in covalent bonds.  But atoms can also be attracted to one another and thus “stick together” without actually merging their electron clouds (no electron sharing). These “non-covalent bonds” include things like hydrogen bonds & ionic bonds and they’re easier to break up, so they’re good for intERmolecular interactions (reversible sticking between different molecules).

So, “molecule” is a term we use for a chemical thing where all the bonds are those strong, covalent bonds. Remember, In this type of bond, neighboring atoms are actually sharing electrons so they “need” each other Covalent bonds *can* be broken, but it’s not easy. To split up a covalent bond you need to go through an energetically costly “divorce process” that often requires helpers like proteases (protein-cutting proteins) or nucleases (DNA or RNA-cutting proteins).

“Dissolving” cannot take apart a molecule into atoms but it *can* take apart a particle into molecules. So, it can take a sugar cube and dissolve it into sugar grains and dissolve those into individual sucrose molecules. BUT it can’t break those sucrose molecules down further. If you look at the chemical structure of sucrose you can tell it has two ring-y things linked together. This is because sucrose is formed by joining 1 molecule of fructose with 1 molecule of glucose through a *covalent* bond. This bond is not broken by dissolving, so the sucrose stays sucrose. 

But not all particles are held together by strong bonds. In our non-covalent “weak” bonds, neighboring atoms don’t “need” each other, they just “want” each other. They’re held together by +/- charge attraction but they’re not “committed.” We often refer to them as “bonds” but it can be more helpful to just think of them as “attractions.” The strength of these attractions depends on whether those charges are partial or full, permanent or temporary. 

On the strong end of these weak “bonds” are ionic bonds, like those holding together the sodium & chloride in our table salt. These are strong *attractions* (because the charges are full not just partial), but they’re still just attractions – they’re still “weak,” non-covalent bonds – they’re happy to leave if they find better partners, like water, so things held together by these bonds *can* come apart when you dissolve them (assuming the water likes them). 

You can visualize this with candy – if your formula units are a Rolo roll & a KitKat bar – if you unwrap them (dissolve) the Rolos will separate (dissociate), but the Kit-Kat pieces will stay stuck together.  You’ll need to put in some real effort to break off the pieces of KitKat bars! Similarly, if you dissolve a NON-ELECTROLYTE (like sucrose), you don’t separate its formula unit, but when you dissolve an ELECTROLYTE (like sodium chloride), you separate its formula unit into IONS (positively charged particles)

That’s cool & all but often what we really want to know how many particles there are in a certain space or compared to a certain amount of total particles. Especially because the # of PARTICLES in a solution affects that solution’s COLLIGATIVE PROPERTIES 

COLLIGATIVE PROPERTIES are properties of a solution that only depend on # of dissolved particles, NOT the identity of those particles – e.g. when you have more particles stuffed in there are fewer water molecules at the surface where they have the best chance of escaping into the air – so you get boiling point elevation – if you want to know more, check out my post on why you should bring salt if you want to cook spaghetti on top of Mt. Everest…)

When it’s outside of water, a grain of sugar could be considered a “particle” – it’s made up of lots of individual sucrose MOLECULES bound to each other. But these bonds are weak, so when you put it in water it starts to dissolve – the sucrose MOLECULES come apart – now each of these is a particle – but the sucrose doesn’t come apart further – we have the same number of particles as we have formula units, so any calculations we did stand

Now consider a grain of salt – it too is made up of smaller parts that come apart when we put it in water (dissolve it) – but these parts are smaller than the formula unit we calculated based on -> for each mole of NaCl we put in we got 1 mole of Na⁺ AND 1 mole of Cl⁻ – in terms of particles, we have twice as many, so 1 mole of NaCl

And that’s important because it means it’ll have 2X the effect on COLLIGATIVE PROPERTIES (remember these depend ONLY on the # of particles) as 1 mole of sucrose. 

To account for this, instead of just using the formula unit concentration when calculating colligative properties, we adjust that concentration with that unit’s Van’t Hoff factor (i). For NON-ELECTROLYTES, “no” adjustment needed, so i = 1. BUT for ELECTROLYTES, i depends on the # of ions it breaks into. So NaCl would have an i of 2.

In general, multiplying by the Van’t Hoff factor converts the number of formula units we put in into the number of dissolved particles we get. Well, in ideal solutions… f we were to measure it experimentally, these numbers would actually be lower. This is because, in concentrated solutions, oppositely-charged ions may be close enough together that they pair back up – so ION PAIRING *Impairs* our ability to predict particles.

We have several different ways we can report on concentration using moles. 

  • Molarity is a measure of concentration which tells you about how many of a thing is in a volume of solvent (usually water). MOLARITY is moles per liter (mol/L) & we represent it w/capital M (e.g. a 1M solution has 1 mol/L so 1 L has 1 mol, 2L has 2 mol, 0.5L has 0.5 mol etc.)
  • The mole fraction (aka molar fraction) is the relative amount of 1 component of a mixture compared to the whole mixture. 

These might sound really similar, BUT there’s a key difference Molarity is the moles of something compared to the VOLUME of the solvent. Whereas, mole fraction is the moles of something compared to the TOTAL MOLES of EVERYTHING! more here:

The MOLARITY of one chemical won’t change if I add another chemical, but the MOLE FRACTION will!

And speaking of changing, the volume of a liquid can change w/changing temperature. At a higher temp, molecules can move around more, so they take up more space. To account for this, we can use a different way of reporting: molaLity 

  •  molaLity is moles per kg solvent & we represent it with a lowercase m 

Helpfully, at room temperature, the density of water is 1.00 kg/L so the molarity & molality for water-based (aqueous) solutions at room temp are basically the same 

There’s another reporting method we can use when we’re dealing with gases: partial pressure. We can do cool shortcuts with gases because gas molecules are so far apart that they don’t interact with one another and they don’t take up much space or anything, so different gases act basically the same. The ideal gas law says that, when it comes to pressure, it’s the # of particles, not their identity, that matters. Dalton tells us we that if we have a mixture of gases, can add together the pressure that would be generated by each gas separately and that would tell us the total pressure. And we can go the other way too – if we know what proportion of a mixture is a certain gas we can calculate what the pressure would be if we removed all of the other gases in there – and we call that the partial pressure.

Law of Partial Pressures: Ptotal = P1 + P2 + P3 ….. 

Each of those P’s is the partial pressure coming from one of the components and each can be calculated with P = (nRT)/V. And the only thing different between them will be the n (# of molecules of gas). So there’s a “shortcut” if we know what proportion of the gas mixture is that gas, and we call that value the “mole fraction” We can multiply the mole fraction of the component we’re interested in by the total pressure to get the partial pressure.  

For example, if we had a gas mixture that was 1/2 A & 1/2 B, 1/2 of the gas molecules would be A and half would be B (each would have a mole fraction of 1/2) – so if we had 1 mol total we’d have 0.5 of each, if we had 2 mol total, we’d have 1 mol each, etc. 

And 1/2 of the total pressure would come from A & half from B – each would have a partial pressure of 1/2 the total pressure (e.g. if the total pressure was 1 atm, the partial pressure of each would be 0.5 atm)

If we were to actually remove B, the A molecules could move out more, so there’d be fewer collisions and lower pressure. How much lower? The new pressure would be half what it is.

And the proportions don’t have to be equal – for example, we could have a mixture of 1/4 A & 3/4 B – A would have a mole fraction of 1/4, a partial pressure of 1/4 the total pressure – and B would have a mole fraction of 3/4 & partial pressure of 3/4 the total pressure. 

And it doesn’t matter how many different gasses there are – If our mixture was 1/3 A, 1/3 B, & 1/3 C, each would have a mole fraction of 1/3 and the partial pressure of each would be 1/3 of the total pressure. 

more on topics mentioned (& others) #365DaysOfScience All (with topics listed) 👉⠀

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