our next topic is concentration and solution stoichiometry because so many of the reactions that we will deal with are in solution which means that the components are dissolved usually in water for general chemistry and because of this it will be hugely important in lab it's a good topic for us to talk about at this point so most solutions are made dissolved in water for the purpose of general chemistry as you do other chemistries the solution the solvent of the solution might change but for us it's mostly going to be water which we will call an aqueous solution this is usually designated by having parentheses aq next to the formula you'll also see this when we get into writing reactions so if i had a solution of sodium nitrate i would communicate that by writing nano3 and then aq in parentheses after it when we make solutions the amount of stuff that is dissolved in the solvent is referred to as the concentration now we could refer to the concentration in a qualitative way by calling it dilute or concentrated which is also a very relative term um because there are no numbers here to tell us what does dilute mean what does concentrated mean well it ends up being relative to what we normally use or even just relative to what you happened to be using so we're gonna mostly stick with quantitative measurements of concentration unless rate the number doesn't matter like if you just needed to know that it was sodium nitrate in the solution we might throw in the word dilute or concentrated just to say like hey yeah there was a little bit in here because we needed it or yeah we used the concentrated form because we felt like it but you wouldn't need to know exactly what the number is when you need to know what the number is what we're using most commonly is molarity which we represent with a capital m molarity is the moles of solute divided by the liters of solution so liters of solution means absolutely everything that is in that container being the solution in many cases the volume of the solvent and the volume of the solution are the same but not in every case so we do explicitly state that here now also molarity is not the only concentration unit but it is the most common that we use in general chemistry at this point so this is what we're going to use for our main concentration unit now just to give you a really explicit example of what this looks like if i had an aqueous solution of sodium chloride when i give you a number with an m after it saying this is the molarity of the solution what i'm telling you is that this is the number of moles of sodium chloride per liter of solution and the leader of solution means the volume of the sodium chloride and the water when you make a solution which might seem like okay well this is a lecture class why do i care about making a solution well technically i could ask you how to make a solution but if you take lab you will make solutions in lab and if you understand how the solution was made you can maybe better glean what was going on in that solution and understand what the molarity is trying to tell us so you use something typically called a volumetric flask to make a solution with a known concentration it has one line on it which is this calibrated volume so you will learn how to use these in lab you i don't know may never use one if you don't take lab but this is the type of glassware that you would use because when the solution is filled to that one specific line it means that we know the volume really well usually to two decimal places so the volume of the solution is very well known so to make this solution of a specific molarity we would measure out some number of moles of the solute which would mean in the sodium chloride example weighing out a specific mass of sodium chloride we would put that in the volumetric flask and then add some water to dissolve it now if you're in a lab situation you're going to use this fancy stuff called deionized water where all of the extra ions have been taken out of it so it's just super pure water and we would even like the container that we used to weigh the sodium chloride like rinse it off so every bit of sodium chloride is in the flask we'd add some water and stir it or swirl it around to make sure that the sodium chloride is fully dissolved and then add water to the fill line so what this does is it makes sure that you get all of the sodium chloride you weight out and make sure that all of your sodium chloride is fully dissolved before you make the final volume and then the final volume when you make it is really and truly the water plus the sodium chloride so this is how you would set that up and then right there's i drew a little cap here you would shake it up make sure that it's thoroughly mixed and then you would have your known concentration of sodium chloride solution let's do a calculation example with this so we've been asked to calculate the molarity of a solution where 45.4 grams of sodium nitrate is dissolved to make 2.50 liters of solution so concentration molarity we need moles of sodium nitrate and liters of solution we're very nicely just given the liters of solution so the only thing i have to convert first is the grams of sodium nitrate to moles of sodium nitrate which means i need the molar mass so i have that calculated here you should double check this partly to make sure that i'm right and to make sure that you know how to get the molar mass of this and it should be 84.995 grams per mole which means that 45.4 grams would be 0.534 moles of sodium nitrate so the molarity of this solution is 0.534 moles divided by 2.50 liters and the molarity is 0.214 molar now when we have solutions we don't always store them as the concentration that we need so for the example we just did the 0.214 molar that's a fairly dilute solution i may not want my shelves filled with you know hundreds of bottles at that concentration but there's a very nice dilution equation where if i have a solution of a known concentration and i want to dilute it by just adding more water to it i can calculate if i know the final volume what the new concentration would be or actually i can calculate any number of things if i know the molarity i'm starting with and i know enough of the other variables within this calculation i can find anything else so this is i think a pretty well known equation that gets used a lot so m1 v1 equals m2 v2 if you're a biologist you might know c1 v1 equals c2 v2 it's the same thing right we've just written an m for molarity instead of a c for concentration so this means that the molarity times the volume of solution one is equal to the molarity times the volume of solution two the reason that this works is that because we are just diluting the solution or let's say you have a dilute solution and you want to calculate what the concentration the more concentrated version was that you started with the only thing we're doing is adding more solvent so the number of moles of solute isn't changing in this scenario so as always let's look at this with an example so if you have 200 ml of a 15.0 molar sodium hydroxide solution what would the final volume be if you needed to dilute it to a 2.50 molar solution so we have a known volume of a high concentration of sodium hydroxide solution we want to dilute it to a specific concentration let's find out what the final volume would be so my first solution has a molarity of 15 and a volume of 0.2 liters right i was given 200 mils but if we're going to put in the correct units we need molarity in molarity which well it is and we need volume in liters my after version so my second solution i want to dilute this to 2.50 molar so what volume do i need to get to to have that concentration so my m2 is 2.5 and then my v2 is the unknown so v2 when you calculate this comes out to be 1.20 liters now this is maybe helpful right my final volume needs to be 1.20 liters in practical terms what does that mean if you were asked to do this in the lab i mean there there are a bunch of things that go into it but you would not add 1.20 liters of water because then your final volume would be 1.40 if you needed to really do this in person in real life you would have to figure out the difference between the volumes to figure out how much water to add so i want my final volume to be 1.20 liters so what i would do is get one liter of water and then add my 200 ml of the 15 molar solution to that liter of water and the result would be that i would have 1.2 liters of 2.5 molar sodium hydroxide with this we can add a discussion of stoichiometry in solution and we're going to do this with an example of two things dissolving and depending on when you see this and if you are taking lab you might have already seen something similar to this which is great but let's start from the beginning so i'm going to take two things and dissolve them in water the first one is sugar c12h22o11 if i take that as a solid i add it to water the result is that i have sugar dissolved in water and i've just written this as c12h22o11 with an aqueous on it okay the next thing i want to look at is sodium chloride dissolving in water so sodium chloride solid plus liquid h2o the result is sodium cations that are aqueous and chloride anions that are aqueous so this does something very different in solution when it dissolves now the reason that this is happening is because of the type of bonding so let's do a side-by-side comparison the c12h22o11 the sugar all of those elements are nonmetals this is a molecular compound held together by covalent bonds sodium chloride metal and a non-metal this is ionic the sugar we call this a non-electrolyte sometimes that just means that it doesn't split up into ions in solution sodium chloride we would call an electrolyte because it does split up into its component ions in solution both of them dissolve because dissolving just means that each little piece is surrounded by water molecules and you no longer have the solid and that's true for both of them but covalent compounds are still the whole molecule after they dissolve ionic compounds split into their component ions and it's super important to note that that means polyatomic ions the polyatomic ion stays intact but the ionic bonds break of course let's do an example sodium nitrate so this is the polyatomic ion nitrate with a sodium ion so ionic bond will break when it dissolves which means we get the sodium cation and the nitrate anion we still have no3 the nitrogen and oxygens are still together those covalent bonds don't break we have the entire polyatomic ion by itself dissolved in the solution so what this means and with this reaction and with what we know about um the subscripts for components of a molecule and how that relates to number of moles it means that we can do things like talk about the concentration of just sodium ions or just nitrate anions or i mean something that we'll really need going forward is just the hydroxide anions so let's use our solution from earlier the 2.50 molar solution and calculate the number or not the number the concentration of hydroxide ions in that solution so what that means is i'm saying what is the concentration of o h minus and we represent concentration by putting brackets around stuff so these square brackets around an o h minus means what is the concentration sodium hydroxide is an ionic compound it has the components of it are the sodium cation and hydroxide which is a polyatomic anion so when this splits up in solution i get one sodium plus and one o h minus now this is a conversion factor exactly like the number of moles of carbon in a big molecule conversion factor so i have 2.50 molar sodium hydroxide or you could write this out as moles over liters it would be the same thing and for what every one mole of sodium hydroxide i get one mole of hydroxide in solution so the concentration of hydroxide in the solution is also 2.50 molar