hey guys welcome to this lesson so this is going to be quite a good lesson because we're going to be looking at this formula and there's quite a lot that they can ask you about this formula like in tests and exams there's quite a bit with this one okay so let's quickly talk about it so C stands for concentration concentration n is mole that we've seen before and V is volume okay and volume is measured in let's write that a bit better volume is measured in decimeters decimeters oh concentration by the way concentration is measured in moles Dot decimeters minus three okay that is the units of concentration now this formula is only used when we are busy with um Solutions which is when you have like something mixed in a liquid for example you're not going to use this formula when you're busy with gas okay this for gases we rather use this formula over here because some Learners confuse this volume and this volume this formula is for gas this one is more when you're mixing things together and you've got like Solutions and things like that okay now there are different ways of writing this formula not I don't mean like using a triangle what I'm saying is your teacher might have showed your formula that goes something like this okay now you can use that if you want but you don't have to let me show you where your teacher got that formula from we've learned some earlier lessons that to work out the number of moles you could use this formula okay now what would happen if I just take to to replace this with because I know that um I know that n is the same as M of M so I could say M over M but then the way that this works mathematically is that you could actually just put this m down here and so what you actually end up with is M over m v so that's where your teacher was getting that formula from so you could either use this formula and this formula individually or you could just use it all together in one formula I'll show you how that all works in this lesson with some examples okay now just want to quickly show you something quite interesting and then I'm going to show you one of the most important things in this um for this formula that gets like it's really important that you understand that part to be able to easily do these types of questions it has something to do with this formula which maybe your teacher has showed you but I'm going to show you um I'm going to show you how we do all that but first um you know how we usually take these letters and then we make a triangle where you always put the letter at the top over here um that one always goes at the top and then the other two letters can just go like that so you could make different formulas now for example if you wanted to calculate n you would say n is equal to C multiplied by V because these two are next to each other if you wanted to calculate V you would say the top over the bottom okay so those are different formulas we also need to know now here comes the most important thing you need to understand let's say we have a gloss okay and in that class we are going to pour oros you know the oros that you drink let's say but there's no water in the oros yet we've just poured pure oros and let's say there are seven oros molecules one two three four five six seven seven oros molecules now we're going to add a little bit of water okay so let's add a little bit of water and then we can mix everything together and we're still gonna have seven particles or seven uh seven oros molecules one two three four five six seven okay because all that we did was we just added water that doesn't add more oros or take oros away okay so let's call this solution number one then what we're gonna do is we are now gonna see what happens and you've probably done this before in your own life um if you add more water to this uh to this solution is it going to make the oros less sweet or more sweet well it's going to make it less sweet we say that it becomes less concentrated so the water volume is going to go up to here now but can we all agree that there's still going to be seven oras molecules we did not add more oros and so if you look at the distances between the molecules in the first container and then if you look at the distance between the oros molecules in the second container we can see that in the second container they are a little bit more spread out so the distance between them has increased and so we say that their concentration um has become less the further away they are from each other the less concentrated they are and the less you know like when you drink oros the less sweet it will be because maybe if you take a sip of water um up to here or a sip of oros you're only going to get two oros molecules but if you had to take a sip over here you're going to end up getting three oros molecules and so you're gonna taste more oros and it's going to be more sweet for example okay but that's not the real thing I want to explain what I want you to understand is that the amount of oros is the same in both containers so what we'll say is that the moles in the moles of oros in solution one is the same as the number of moles of oros in solution two so then what I want us to do is to think about how would you calculate the moles in number one well you would use this formula so you would need to know the concentration of solution number one and the volume you see how I just used that formula to calculate moles okay and then in number two you would also use you would calculate using its concentration and its volume but what I've just told you is that the number of moles in the solution um you know in solution number one is the same as the number of moles in solution number two so what we can say then is that N1 is the same as N2 and so from that we could then say that C1 V1 must be the same as c2v2 and this becomes a really nice formula to use when you have a situation like this and we're going to do examples on this lesson where they either add more water or they take water away but the number of moles stays the same and so you could just say you could use this formula and it makes our life really easy so we have some excellent questions coming up now that are going to test you on all of the different formulas that we've uh that I showed you on the previous slide and it's going to use a few formulas from previous lessons so I'll just show you we've got ones like that we've got ones where we're gonna have to use a periodic table um some really interesting things coming up okay so let's get started it says that determine the concentration of solution containing six moles and a volume of two decimeters okay so that's a pretty easy one to start off with we've just learned that C stands for concentration tration and that's measured in moles decimeter minus three V is the volume which is measured in decimeters and then n is moles okay so to determine the concentration of a solution containing six moles so we've got the number of moles as six and the volume is two so that's the easy one you just go plug in 6 divided by two and that's going to give you three but now remember to put the units three mole dot DM minus three remember that that is concentration mole dot DM minus three this one says determine the concentration of a solution that has 60 grams of NaOH in a volume of two decimeters okay so here they're talking about Mass so you have two options now you could either go and use that other formula or one of the old formulas from a previous lesson which goes like this okay you could go use this formula and then once you work out the number of moles you could just go plug that over there but what some teachers do I don't do this but a lot of teachers do this is they just take the spot and they replace it over there so they end up with a formula that goes like this over V but that's the same as just saying M over capital m v so if you use this formula then you just do one step but what I like to do is I use this formula and then I take the answer and I plug it into there it's up to you though okay so I'm going to go use this formula and so you end up with working out the number of moles which is going to be 60 because that's the mat remember that in that formula the small m is the given mass measured in grams and then uh the capital M is molar mass and that's on your periodic table periodic table so that's going to be n a now N A has a mass of 23. whoopsie 23 oxygen has a mass of 16. and hydrogen has a mass of one okay now if you had to go work this a lot you end up with 60 over 40. and that's going to give you 1.5 MO now we have the number of moles so we can come back to this formula so we could say C is equal to n over V now remember that n is your moles and V is your volume and C is your concentration concentration so they want us to work out the concentration so we can just say the number of moles which is 1.5 divided by V which is the volume which is 2 and if you work that out you end up with zero comma seven five now remember concentration is mole dot DM minus 3. and then as I said if you wanted to use that other formula that a lot of teachers like to use I've got nothing against this formula I just I think when I started teaching I just got into the habit of not using it and so these days I just don't use it that much but I do have or I used to have a lot of Learners um that loved using that formula okay so you give it a try it will work out um I'll quickly show you it would sort of go something like um let's just write it over here so you would say C equals to the mass which is 60. now the capital M which is from the periodic table was 40 so you'd say 40 multiplied by the volume which is two and that would end up giving you 60 over 80 which if you simplify that is also 0.75 so you get the same answer so you do whatever you're comfortable with still got a lot of really good questions coming up this question says that we have a solution containing CaCO3 calcium carbonate and it has a concentration of 5 moles per decimeter and a volume of 20. determine the new solution concentration if 40 decimeters of water is added ah so this is exactly like what I was telling you earlier about the oros when you add water what we said was that when you have a solution that has for example let's say you've got this much solution and you've got seven oros particles for example or seven moles of oros is a better way to say it actually then if you add more water if you add more water the amount of oros is still going to be exactly the same the particles because then you're going to mix it with a spoon or whatever and the particles they're still going to be if there were seven moles of a year then there's still going to be seven moles of a year and this is where we say that the amount of moles so the moles in solution one is equal to the moles in solution two and then I showed you that special formula that you could use which is c1v1 equals to C2 V2 because remember from this formula over here if you had to make a triangle the N would be at the top so to calculate the number of moles it's C multiplied by V so to calculate the moles in solution one you would use Solution One concentration multiplied by solution one's volume and then to calculate the moles in this solution you would say that but what we've just said is that the number of moles in solution one is the same as the number of moles in solution two and so you could just say that these two formulas are equal to each other and so this is a Formula that your teacher will definitely show you like that and this formula you use whenever you have a question like this where you have a solution and then you either add or take water away but there's something very important coming up that a lot of Learners make mistakes with so just please check what I do now so in the first solution we have told that we have CaCO3 okay that's not that important but let's say we have CaCO3 and it has a concentration of five okay so the concentration of the first solution is five moles per decimeter and a volume so the volume of solution one is 20. so that is solution one now what they do is they're going to add now listen up carefully it says determine the new solution concentration if 40 decimeters of water is added so they're going to add 40 decimeters of water okay so you've got this original solution which was up to there and now we're going to add another 40 decimeters of water then if you had to go mix everything um together if you had to mix everything together you've got to think about what would the total volume of the solution be well it originally had 20 decimeters there was originally 20 decimeters then you add 40 decimeters so the total volume is now 60. you mustn't say 40 you must say the total volume which is now 60. okay and that's the volume of the second solution but we don't know what the concentration is you can't say that the concentration is the same you know like if you have oros and then you add more water well it becomes less sweet right so the concentration changes so we use this formula now so we say um C1 V1 equals C2 V2 now you just go fill everything in so this is five for concentration of first one and the volume is 20. then for the second solution we don't know what its concentration is but the volume is 60. there we go now on the left hand side you can just multiply those two numbers together which is a hundred and then if you just multiply these two together you just end up with 60 C2 which is concentration of solution number two to get the C by itself you are going to say a hundred divided by 60. and if you had to work that out if you round to two decimals you end up with 1.67 and then you're going to say the concentration is measured in mole per decimeter whoa I just lost the whole container but let's just go 1.67 more per decimeter with a minus three now this next one's a little bit different it's not exactly the same this one says that we have a solution that contains two moles of CaCO3 okay so two moles um two mole of CA CO3 and a volume of 20 decimeters so the volume is 20 decimeters okay so we have the moles and we have the volume now it is determine the new solution concentration if 40 decimeters of water is added okay so they're going to add 40 decimeters of water now this looks like it's the same as the previous question but it's different information that was given okay so that's the original volume and then they're going to add another 40 decimeters so this was originally 20 decimeters then they added another 40 decimeters of water so if you put everything together there's going to be 60 decimeters of a solution the volume will be 60. decimeters right because it was 20 and then the add 40. so now you have 60 decimeters now we said that when you have a question like this where you're adding water the amount of moles stays the same so we know the moles over here whereas in this previous question we did not know the moles so we rather used this formula but we can just use this formula now we can just know that um the amount of moles in this container was two moles so that means the amount of moles over here is also going to be two moles because we've learned that the moles in the first solution will be the same as the moles in the second solution it's like having the same amount of oros particles in both Solutions so the amount of moles on this one is going to be two mole okay so then you can just go use the concentration formula which is then just to say C is equal to n over V and so you could then just say that the number of moles is 2 the volume is 60 and if you had to work that out you end up with zero comma zero three three and then the units for concentration is mole per decimeter like that okay so we still have three very good examples coming up some of them are going to have mass like this one and so let's carry on this one says that a three mole per decimeter now a lot of Learners look at that and they think that it's moles but it's moles decimeter that is the units of concentration remember concentration is measured in mole decimeter volume is measured in decimeter and and then n is just moles so we know the concentration has a volume of six now it is determine the concentration if the volume is changed to 15 oh now this is a little bit different so here we have a solution which I'll call number one and it has a concentration of three and it has a volume of six okay then what they do is they change the new volume they don't add 15. now you've got to read that carefully in these previous two examples they said that they added 40 so we said 20 plus 40 gave us 60. in this example they also added 40. but now they're just saying that the new determine the concentration if the new if the volume is changed to 15 so that means that they're just changing this volume to 15. they're not saying that they're adding 15 they're just changing at 215 okay and then they say determine the new concentration okay so when it's like this when it's a question like this then this formula over here works really nicely and so you just go for everything in so C1 V1 is six C two we don't know and then V2 is 15. okay so multiplied by 15. so 3 times 6 is 18. 15 C2 now to calculate C2 you're just going to say you're just going to divide by 15. and so C2 is going to end up being 1.2 but remember the units 1.2 mole per decimeter this question uses Mass okay so it says that 73 grams of HCL is dissolved in 10 decimeters that's a volume determine the concentration okay so here's where you might want to use um this formula like that or some Learners like to just combine all of it into one formula which looks like that it's up to you okay I'll use this one this time because in the previous example I used this one and this one together okay so that's what you have to do you either use this one by itself or you use this one and then you use this one okay so let's have a look so remember that small m is the given Mass and that's measured in grams capital M is the molar mass that's molar mass and that's on the periodic table periodic table okay so we would go C equals to the given mass of 73. now to find the mass of HCL on the periodic table it's got one hydrogen so that's one and then one chlorine so chlorine is 35.5 35.5 and that's going to give you 36.5 grams per mole remember the units of capital M is grams per mole so I could now put that over here into the formula 36.5 and then the volume is 10. you see how I'm using this formula over here so the volume is 10 and then if you had to go calculate this you end up with 0 comma two now remember the units for concentration is mole per decimeter last question says here determine the mass of CaCO3 dissolved in four decimeters so that's a volume with a concentration of that so we've got a concentration okay so you could use this formula over here if you wanted to um or you could just use this one so I'm actually going to use this one and this one over here so we already know the concentration and we know the volume so we could use this formula to calculate n so you know how you make a triangle where n goes at the top then how would you get n by itself well n is at the top so you'll say n is equal to and then these two are at the bottom so you'd multiply them together like that so you could say n is equal to C multiplied by V so n is equal to the concentration which is 2 multiplied by the volume which is 4 and that would give us 8. moles or eight moles okay now we could use this formula over here because they want us to calculate the mass so they want they're looking for this Mass because we know that this mass is on the periodic table but we need this Mass so you could make a triangle over here the number the thing at the top always goes at the top of the triangle and then you could say n and capital M so let's just make this a capital so to calculate this m you would say n multiplied by capital M and so let's have a look so we'll say m is equal to the number of moles which is eight multiplied now we have to go get the molar mass of calcium carbonate on the periodic table so let's go have a look at that so that's going to be one calcium atom which is this one over here so that's 40. one carbon which is 12. and then three oxygens which is 16 okay and if you had to go calculate all of that you would end up with 100 grams per mole remember that the units of capital M is grams per moles you'd say like that and that's going to give you 800 grams