Hello everybody welcome back to med school EU my name is Andre and today is a very special day because we're going to be doing another educational video on Solutions and today we're going to talk about the main ways of expressing concentration of solutions so the general structure of today's video we're going to talk about the several ways that Solutions can be expressed in terms of the different units and we're going to go over an example from each of those expressions so first we're going to talk about molarity it is marked by the capital letter M and the units of molarity is going to be moles of solute over the liters of solution so we've talked about solutes solvents and solution a solution is made up of chemicals that are solutes and solvents solvents are typically in higher quantity than the solute so if we have salt and water the salt is the solute the water is the solvent solvents are breaking down the solutes and dissolving them so if you want to learn more about Solutions and how solutes and solvents work watch a video right here now when we're talking about the different ways of expressing concentration all it really means is how we're going to express concentration in different units that's all it is and concentration what is that well that means it is asking about how many solutes or how many things do we have in a solution so if we're talking about um salt for example how many moles of salt do we have in one liter of solution that is what is measured by molarity now there's going to be other measurements like molality normality and things like that that we will discuss in this lecture and they will nothing will change about them they're still expressing concentration except it will be with different units and the um the denominator will typically change from solvent to solution so here we're talking about leaders of the total solution which means that we're talking about the leaders of solute plus the leaders of solvent which makes up the leaders of solution and that's what's in the denominator that's the part that we need to measure and of course we need to know the number of moles of solute that we would have so let's take a look at an example so the question States what is the concentration of NaCl solution that results when the 0.15 liters of 0.556 molar solution is allowed to evaporate until the volume is reduced to 0.105 liters now these questions are typically going to be solved with a formula of M1 V1 equals M2 V2 M represents the concentration V represents the volume in liters and M is the concentration represented as molarity meaning moles per liter so we are given the concentration right here 0.556 molar solution that's the original solution but it's asking us we're going to evaporate meaning some of the solution will be gone some of the water will be gone out of it and what will be the new concentration if the volume is reduced here because of the evaporation so you see the volume is reduced by 0.45 0.045 of a liter here we're given the original molarity which is M1 which is going to be 0.556 molar we're also given the original volume which is 0.150 liters and we're given the final volume so whenever you're given initial data and a bit of the final data you can use this formula in order to find whatever you need to find so in this case V2 is a 0.105 liter so we're going to see how the concentration changes if some of the water has evaporated that's all we're looking at and the final concentration that we're actually looking for is unknown so when we're looking for the unknown in an equation we want to isolate for the unknown so we will divide by V2 on both sides the V2s will cancel on the right and we end up with M2 that is equal to M1 times V1 over V2 and if I plug all the numbers in this is what I should get and the leaders are going to cancel here and our final result is going to be 0.794 molar so the concentration has gone up because we have less of the solvent and are obviously the answer is going to reflect that next a unit of measurement we're going to take a look at is called molality and molality is marked by Little M or lowercase M and the units are moles of solute just like we had in molarity however it will be over kilograms of solvent so we're no longer talking about solution not the total solution volume but we're talking about mass of just the solvent and that will be the part measuring our concentration here so let's take a look at an example of where this would be applied a sulfuric acid solution containing 571.4 grams of h2so4 per liter of solution has the density of 1.329 grams per centimeter cubed calculate the molality of h2so4 in this solution now something to be very careful of is that in the British system I'm not sure why but they love to use centimeters cubed decimeters cubed and things like that now whenever it's cubed you should know that it measures volume so you're always able to translate any cubed metric into volume and this is how it translates one liter will be one thousand milliliters so this is the regular metric system and it also translates to 1 000 centimeters cubed meaning that one centimeter cubed is one milliliter so here our density is measured to be 1.39329 grams per one milliliter or one centimeter cubed so that's something to keep in mind this is expected to know knowledge since the iMat test is made by the British company and they're going to be using some of the things that they use in their own education system now we would also be given that the molar mass of h2so4 is 98.0768 grams per mole so what we have to calculate is we need the moles of our solute we need to determine how many moles of this we have and we would also need to determine the kilograms of the solvent meaning that we will have to determine the mass of the water in the solution so the strategy for this question will be that I'll have to calculate the mass of the solution and then subtract the mass of the solute from the mass of the solution in order to determine the mass of the water that we have present or mass of the solvent and once I have that that is my denominator that I have for molality if I have 1.329 grams per centimeter cubed that's my initial thing here from the density I can multiply that by 1000 centimeters cubed to in order to just get the mass of the solution which is a thousand three hundred and twenty nine grams that's my Mass of the solution and the reason I am multiplying by a thousand is because one thousand centimeters cubed is one liter and we're given that we have a solution that contains this much in per liter of solution so this is why I'm equating it to the leader so in a liter of solution I will have a thousand three hundred and twenty nine grams of the solution in terms of mass so if it takes up one liter of volume it's going to have 1329 grams of mass that's how much it's going to weigh now I already know that 571.4 grams is my solute that's the mass of my solute so all I have to do is just take the solution mass of the solution minus the mass of the solute and you will get the mass of the solvent and since this is an acidic solution the mass of the solvent so the solvent will have to be water so essentially we have here 0.7576 kilograms of solvent now the last part is to determine the numerator of molality which is moles of the solute and for that we can use our molar mass so I know that I we contain 571.4 grams of h2so4 in this solution so I'm going to multiply that by my molar mass so the units cancel from grams and become moles because I want to find moles so one mole of h2so4 over 98.0768 grams where the grams will cancel with the grams and we end up with 5.83 moles of h2so4 and simple step here is going to be to take the 5.83 moles of solute and divide it by 0.7576 kilograms of solvent and here we would get 7.69 of molality as as the concentration of the solution the next unit of measurement we will discuss is called mole fraction the units for mole fraction is going to be moles of solute just like we had for the previous two over total moles of the solution so let's take a look at an example here a solution is prepared by mixing 25 grams of water and 25 grams of ethanol determine the mole fraction of each substance so the first thing to do is to determine the number of moles that we have for each of the substances so we're going to use molar mass in order to determine that and this will typically be given to you on the test so if we've got 25 grams of water the molar mass for water is 18.015 grams now the grams will cancel in the grams and we would end up with moles of water which is 1.388 moles of H2O and next we're going to take a look at and find the moles of ethanol now in order to determine the total molarity of the solution we just have to add the two numbers so 1.388 moles add 0.543 moles and we should get 1.931 moles of the solution so when we're calculating mole fraction you're just going to take the moles of your solute or moles of each substance and divided by the total moles of the solution and that's how you will find your fraction 1.388 moles of water divided by 1.931 moles of the total solution and we're going to have a mole fraction of 0.719 and if we're looking for the mole fraction of ethanol that would be 0.543 moles all divided by 1.931 moles and we get 0.281 as the mole fraction of ethanol so if you're really wondering what mole fraction means it's simply a comparison of how many moles do you have of the of of the solute versus the solvent so if we're considering water as the solvent then obviously here we have way more water in moles compared to our ethanol and that that's how you can make that comparison using mole fraction another way to express concentration is going to be percent by mass and of course this will be marked by percentage so the units for this will be Mass of the solute typically in grams over the mass of the solution and also in grams multiplied by 100 so we're going to find out the ratio between the mass of solute to the mass of the entire solution so let's see how this works out in an example this is a pretty simple question here a saline solution with a mass of 3.55 grams as 36.5 grams of NaCl dissolved in it what is the mass to mass percent concentration of the solution so when I when I ask you that when I ask you the mass to mass you know that you're doing percent by mass concentration and here you're already given your numbers 36.5 grams of NaCl that's your solute and 3.55 grams as the mass of the entire solution so that's pretty simple there 36.5 grams of NaCl over three five five grams of the entire solution multiplied by 100 percent and you should get 10.3 percent as the mass to mass percent concentration and the last method of expressing concentration that we're going to discuss is going to be percent by volume and of course this will also be marked by percentage the units for this will be volume of solute and whichever one you choose milliliters liters and volume of solution as long as they match in the numerator and denominator multiplied by 100 so very similar to mass except you're using volume instead of mass here for example determine the volume to volume percent solution made by combining 25 milliliters of ethanol with enough water to produce 200 milliliters of the solution so you're already given all the numbers 25 milliliters of ethanol and that will be over 200 milliliters of the entire solution so ethanol added water you're going to have this much volume multiplied by 100 and the answer should be 12.5 percent as your concentration in terms of volume this concludes our lecture for today click on the next video to learn more about equilibrium and aqueous Solutions [Music]