when certain ionic compounds are formed so for example copper sulfate water molecules can become trapped within the crystal when this happens we form something called a hydrate or a hydrated formula unit or compound these water molecules are trapped within the Crystal and they are attached to the formula units according to a very specific ratio this water is called water Of crystallization and you do need to know how to work with this when it comes to chemistry and stoichiometric calculations here are some examples of some hydrated crystals they're called hydrates they can we can say that they are hydrated meaning they contain water they are hydrous compounds they contain a water Of crystallization and as you can see when we represent the formula the molecular formula the number of moles of water the number of water molecules is represented over here after the dots so for example copper sulfate here we have five molecules of water within this formula unit trapped within this compound so essentially we've got a one to five ratio over here now we can ask you questions such as calculate the percentage of water by mass in a hydrated compound we can also ask you the following calculate the number of moles of water of crystallization and as you can see over here on the screen we can represent this by an X we can represent the spine in essentially you have to find out the number of moles over here and we can do this in the following way practically or experimentally we can weigh say for example a certain math 100 grams of a hydrated Crystal we can put that in a test tube then we heat the test tube and in this diagram over here they are heating the test tube they are heating the hydrated compound over a Bunsen burner this is my heat source so over here they say copper sulfate crystals this will essentially remove the water the water will be evaporated so we heated over a period of time until all the water is removed we will know that this is the case when the mass no longer decreases and water droplets are no longer forming on the side of the test tube if you see over here they indicate that water droplets form this is when the evaporation of the water is taking place we are then able to weigh the crystals again now remember now they no longer contain the water molecules trapped inside and that is how we can determine the number of moles of H2O that was removed so in this video we're going to be doing exactly that we're going to be looking at how to calculate the number of moles of water Of crystallization as well as the percentage of water crystallization by Mass let's first look at how to calculate the percentage of water and this is by mass in cucl2.2 H2O now this too means that I have two water molecules trapped within this formula unit so it's a one to two ratio now how we do this how to calculate the percentage of water is basically how we calculate percentage composition so to calculate the percentage of water the percentage of H2O what we're essentially going to do is we're going to look at the mass of H2O within this particular compound or formula unit divided by the total mass of the compound and when I say the total mass of the compound or the formula units I mean the entire thing including the water and because we're looking for a percentage we're multiplying it by a hundred now this is percentage this is percentage by mass and essentially we're looking at the molar mass we need our periodic table to help us with this now the first thing that I'm going to do is I'm going to look for the total mass I always do percentage composition by looking for the total mass of the compound first now when I say total mass I'm looking at CU cl2 dot 2 H2O when looking for this Mass what we're going to do is we're going to take the atomic mass of copper you look at your periodic table in order to find this the atomic mass numbers are the big numbers so for copper it's 63 comma 5. and if you look at your compound you only have one copper atom in this compound so it's just 63 comma 5 and then we're going to add the atomic mass number of chlorine however we have two chlorine atoms in this compound so we look at chlorine we still C chlorine is 35 comma five so we're going to say 35 comma 5 times 2. y times 2 because there's two chlorine atoms then we do the same thing for the hydrogens and the oxygens the very important thing and where people often go wrong in this question is they think that the dot means multiply it does not mean multiply in math a DOT or a point does represent multiply but in this context it doesn't so we just need to continue adding the atomic mass numbers for each element like normal so hydrogen over here we've got 2 times 2. this 2 over here represents two water molecules so it covers both the hydrogen and the oxygen so 2 times 2 we have four hydrogens and we have two oxygens now the atomic mass for hydrogen is one and as I said we have four hydrogens then we add the atomic mass number for oxygen is 16 we have two oxygens because the big two applies to the oxygen as well let me just add up all of that together and we get the total mass and remember that's the denominator of the fraction so let's do that we're going to get our denominator over there we get 170 comma 5 grams per mole 170 comma five so at the bottom the total mass is 170 comma 5. Now the top is the mass of the water just the mass of the water when I say the water I mean the water within this compound so it's this piece and we kind of already worked that out it's part of our first calculation remember we had four hydrogens add the two oxygens so it's this part over here that is basically my numerator over there let's work that out quickly that is the T6 grams per mole 36 and we multiply this entire thing by 100 because we remember we're looking for the percentage of water and my answer is 21 comma one one percent so 21.11 of this compound is water when the water molecules are obviously attached when I heat it and remove the water then obviously it's no longer there then it's zero percent let's look at how we calculate the number of moles of water Of crystallization so finding X or finding n in something like this in this question they say that we have a hundred grams of hydrated alcl3 crystals so hydrated means that it contains molecules of water Okay cool so we know there's water within the crystal the crystal was heated until no further change in mass was observed now remember when we heat the hydrated or hydrous compound that causes the water to evaporate therefore no more water molecules present in the formula unit anymore just leaving alcl3 they say the mass of the anhydrous crystal in other words the one that has no more water is 55 comma two eight grams calculate the number of moles of water Of crystallization they can call this in they can call this x another way that they can represent this question is they can say for example they can give you alcl3 they can put a n or a x over here in H2O they can give you the above information and they can say calculate n or calculate X and that's the number of moles of water Of crystallization the how do you approach a question like this let's take a look now remember in order to find the number of moles of water Of crystallization what we're essentially doing is finding the ratio between this alcl3 and the number of water molecules so we're basically trying to find this part of the ratio and that represents the number of moles of water Of crystallization so if I can work out the moles of the anhydrous compound the number of moles of the anhydrous compound and the number of moles of H2O and I simplify that ratio I can then work out the number of moles of water Of crystallization but how do I do that my first step is to calculate the mass of the water that was lost now remember we started off with a hundred we ended with 55 comma 2 8. this represented the hydrated crystal in other words the stuff with water 55 comma 2 8 represented the anhydrous compound in other words the stuff without water so if a hundred contains water and 55 comma 2 8 does not contain water the difference between these two numbers must be the mass of the water so if I say 100 minus 55 comma 2 8 I'm going to get the mass of the water that was lost or evaporated so I've got 44 comma 7 2 grams of H2O now how does that help me I now have the mass in grams of H2O 44 comma 72 grams I also have the mass in grams of the anhydrous Crystal basically just the alcl3 so just this left part over here of my formula that is 55 comma 2 8 grams now remember in stoichiometry moles is absolutely everything I'm looking for the number of moles of water of crystallization so if I convert this to moles and if I convert this to moles I can put these two in a ratio and if I simplify that ratio remember what we're trying to do is we're trying to get the ratio between our anhydrous Crystal over here and our water what this basically is it's a one to something ratio it's a 1 to X or 1 to n ratio so if I can simplify this moles to this moles in a ratio simplify that ratio to get one to something then I've got my answer so First Step work out the mass of the water that was evaporated 44 comma 72 grams convert both of them to moles which we know how to do we're going to use this formula n is equal to mass divided by molar mass let's do that for alcl3 and let's do that for H2O so I write my formula once remember I'm using this formula because I have the mass of the water that was lost or evaporated and the mass of the anhydrous Crystal are divided by the molar mass which I've done on the side here I got these values from the periodic table and then I work out the number of moles remember we're not going to round off Yates they have worked out the moles of my anhydrous Crystal so in other words using the 55 comma 2 8 grams because that does not contain the water therefore I divided it by the molar mass of just alcl3 got the moles of that worked at the moles of just the water got that mass remember earlier and I got zero comma 1 for 41408 and then two comma four eight four four four four four four okay the four is recurring remember I want to work out n it's a ratio between the anhydrous part of the crystal and my number of moles of water at the moment the ratio is like this it's a 1 to n ratio I need to work out what n is so how do I get this ratio so so far I've got zero comma four one four and so on to 2 comma 4 8 4 recurring how do I get that ratio to be one to something how do I get this number over here to become one well I divide this left part of the ratio the zero comma four and four I divide that by itself 0 comma four one four zero eight if I divide 0 comma four one four zero eight by itself I get one what I do to the left hand side of the ratio I have to do to the other side of the ratio as well if I divide the 2 comma 4 8 4 by that same number I get 5 comma nine nine nine and five common nine nine nine is basically six I can round that up to six and we needed to be in a one to something ratio because as you can see over here the big number in front of this is one one to n we figured out that in the right side of this ratio over here is six therefore my number of moles of water of crystallization is six moles he has a past paper version of this question pause it see if you can do it and then do it with me Mark your work with me so they say we've got 14 comma 2 grams of hydrated sodium carbonate remember hydrated means that this 14 comma 2 grams includes the water it Heats it until there's no further changes in Mass on heating the water evaporates they give me the little formula over here or the little equation and they want the number of moles of water of crystallization so they want in in this case they're calling it X doesn't matter we want X the number of moles of water Of crystallization in the sodium carbonate sample if five comma 3 grams of solid remained after the heating now remember the solid that remains is the sodium carbonate na2co3 so what we need to do first is we need to work out the mass of the water that was lost so we take the hydrated Mass so that's the mass that contains the water so this contains the sodium carbonate and the water it represents this part of the equation that's 14 comma 2 grams and we minus what was left over after the water evaporated five comma three grams that corresponds to this part over here that's five comma three grams the difference between those two numbers will give me the mass of the water that is eight comma 9 grams of H2O so I'm just going to write you a comma 9 grams of H2O 8 comma 9 grams but I need to work out the number of moles I need to work on X now after we've worked out the mass of water what we're going to do is remember we want to work up this in our ratio so if we take a look at any two CO3 X H2O this can essentially the moles of both can be represented as a ratio and the ratio or the part of the ratio over here is one so so far we've got 1 to X so if I work out the number of moles of sodium carbonate just the sodium carbonate without the water using this Mass over here the five comma 3 and I work out the mass of just the water using this eight comma 9 over here I convert them to moles I simplify that ratio so that so that it is one to something I can work out X so let's convert to moles to do this I'm going to use this formula my mass over here is 5 comma 3 divided by my molar mass of sodium carbonate you get this by using the periodic table the atomic mass numbers and I get 106 grams per mole using my periodic table to work out the number of moles for five comma 3 divided by 106. and that is zero comma zero five moles and that is of just the sodium carbonate there's that we do the same for water remember the mass over here is eight common nine grams the molar mass of water it's one times two because that's of the hydrogen plus 16. that is 18. we get number of moles of water as being zero comma four nine four four four that four is recurring moles of water now remember we write that in a ratio zero comma zero five to zero comma four nine four recurring and we want to simplify that ratio so that it is one to X the one must be on the left hand side because if we look at our hydrated formula a hydrated compounds formula over here we've got na2co3 dot X H2O this na2203 the number of moles of na2co3 is one so we need a one on the left hand side of our ratio and we're looking for X so how do I make or how do I simplify my ratio so that I have one on the left hand side I need a 1 over here in order to get that to one I need to divide this by zero comma zero five what I do to the left hand side I do to the right hand side divide by zero comma zero five and you get 9 comma 8 9 which is essentially 10. don't forget to check the links in the description for more Stoichiometry videos more chemistry more physics more math I can't wait to see you in another video