hey everybody uh welcome to our lecture on the ends of chapter six and seven uh we're going to touch back on these chapters even though we've already gone through them we just had a little bit at the end section six and seven from each of these two chapters now we're going to start off covering the end of chapter six this is going to cover mass percent composition or mass percent when we look to calculate mass percent because it's a percentage it's going to be out of 100 total so we're going to be multiplying by a hundred and we're looking at the mass of interest really just the mass of whatever we're interested in divided by the total mass now how do we apply this idea of mass percent we're looking at a ratio of the part to the whole and this mass percent is a percentage because we're multiplying that ratio by 100. now let's look at the mass percent of a chromium compound so this problem says we've got 0.358 grams of chromium so let's not try to write out a full fledged chemical reaction instead let's just say we've got some chromium i'm not even going to worry about the symbols it says it reacts with oxygen so here i'm going to say chromium plus some oxygen is going to make because it says it forms metal oxide so i'm not trying to get overly complicated because i don't want to get lost in the weeds but the whole process is we take some chromium metal we react it with some oxygen and it forms metal oxide so we're drawing ourselves something to work with i've got .358 grams of chromium tells me that right here and it says reacts with oxygen so it's just going to react with some oxygen and i'm going to make 0.523 grams of metal oxide now law of conservation of mass we could figure this out if we needed to because this .523 grams didn't come from nowhere so if we took this metal oxide and we subtracted off the mass of the chromium we could get the oxygen but we don't actually need it because we said when we're trying to calculate a mass percent then we take 100 times the mass of what we're interested in and the problem says what's the mass percent of chromium well they gave us that mass of chromium so i'm going to put the mass of what we're interested in 0.035 grams of chromium i'm going to divide that by the mass of the total compound well what it made the chromium and the oxygen came together to make the metal oxide so this is going to be the total mass that goes on the bottom so .523 grams is going to go on the bottom so we're going to take 100 times 0.358 divided by 0.523 and that's going to give us our mass percent and that works out to 68.5 percent now what should a mass percent for every component add up to well it should add up to 100 percent so if this chromium was 68.5 and we wanted to know the mass percent of the oxygen we could just say whatever's left has to be the oxygen so 100 minus 68.5 is going to give me the mass percent of my oxygen which works out to 31.5 percent by mass of oxygen so the problem didn't ask for that but good to keep in mind you don't have to go through a whole other calculation you can just keep in mind if i have uh all my components all my components should add up to 100 wow that was close and i said 1 000 we get a cross out here and percentage all right let's keep going what does mass percent really mean uh so we said it's going to be a ratio it's looking at what we're interested compared to the total it's expressed as a percentage so we can also use it not just as an equation though we can use it as a conversion factor so this compound over here is nacl we've seen it a few times at this point this is a crystal lattice it's an ionic compound so it takes this crystalline lattice where we have a negative and positive ions that alternate that's what holds this lattice together we've got the large chloride and the sit and the smaller sodium ions making up the structure so of this structure 39 of the mass is sodium so it says the mass percent of sodium in sodium chloride is 39 so what's the rest of this compound the rest of it is chloride so what would get us up to 100 percent would be 61. so 61 percent has to be cl so how could we write this as a conversion factor let's focus on the sodium if i know that sodium is 39 of the mass of this crystal lattice what a percentage means is it's out of a hundred right so we could say 39 grams out of every 100 grams of nacl is going to be just sodium 100 being that percentage so out of 100 or out of 100 grams of the whole compound 39 grams of that is going to be just the sodium so we could flip it we could also say for every 100 grams of nacl we get 39 grams sodium like any conversion factor these can be flip flop top and bottom depending on what we need to cancel now just taking a quick look here we could do the same thing with chlorine we could say 61 grams of chlorine for every 100 grams of nacl so these mass percents just give us relationships they don't just give us ways to use equations again these are going to be relationships that prove useful we're going to work a couple of practice problems where we use these as conversion factors so let's work through a sodium problem on fda recommendations the fd fda recommends that we consume less than 2.4 grams of sodium and notice it doesn't say sodium chloride it just says sodium so it's just talking about the n a in the nacl so to less than 2.4 grams per day and it says how many grams of sodium chloride can you consume so that's the whole compound that's nacl and still be within the fda guidelines and it gives us the mass percent of sodium and sodium chloride now let's start with what they gave us they gave me 2.4 grams of sodium and i need to be able to relate that to grams of nacl the way i'm going to do that is i can use that mass percent as a conversion factor we could say 39 grams of n a we're putting it on the bottom so grams of n a cancel and on the top we would say for every 100 grams of sodium chloride and we'll set this up as a conversion so i've got 2.4 grams of n a and for every 100 gram or excuse me for every 39 grams of n a of sodium i'm going to have 100 grams of nacl so 2.4 times 100 divided by 39 my grams of na cancel that gives me 6.2 grams of nacl or think maybe a four to five m m's worth of sodium chloride which isn't a lot and we tend to overshoot that pretty quick on the american diet all right let's try another one of these we want to calculate the mass percent of just the cl in c2 cl4 f2 which another name for that is freon 114 so we're going to go by the chemical formula that they gave us this isn't something that i would expect you to pull out of your memory because we haven't seen it so far this semester so we're going to base our calculation off of the chemical formula and find the mass percent of chlorine so just a recap of mass percent it's going to be equal to the mass of interest in this case it's cl divided by the total mass and times 100. so let's get started this is going to be our cl this is going to be our c2 cl4 f2 but we have to be careful we're interested in the chlorine but how many chlorines show that show up in this formula this total mass is going to be the mass of this whole formula but in this formula i have four chlorines so i have to have the mass of four chlorines in the top of this formula so let's work this out so my mass percent is going to be equal to the mass of four chlorines so it's going to be four times this 35.453 and then on the bottom here i'm going to put the mass of the whole compound so i've got two of my carbons that show up in this formula so that's going to be 2 times 12.011 plus i'm going to have four chlorines so that's going to be four times 35.453 plus i've got the mass of my two fluorines so fluorines are each 18.998 so i'm going to tack on to this 2 times 18.998 and then all of this we're going to multiply by 100 to get a percentage now when we work this out this mass percent is going to work out to 69.58 percent now if you wanted to you don't have to do this all in one go in your calculator you could do this in chunks so for example i could do just this chunk 4 times 35.453 that would give me 141.812 so i can calculate the chunks and put them together and then find my final answer or we could put this on the calculator once if you're comfortable but either way we looked at the mass of just what we were interested in our four chlorines divided by the mass of the whole compound times 100 percent and that gave us the mass percent of chlorine all right so this is a classic example that you can have too much of a good thing so fluoride ask any dentist great for teeth strengthens your enamel prevents uh tooth decay uh decomposition of your enamel so too much of a good thing though can result in damage to your bones to your teeth uh skeletal fluorosis over here the pressure on weakened bones cause cause these to bend out of shape can cause fractures when we look at dental fluorosis over here on the right mild dental fluorosis uh too much fluoride uh but not too too much we get a mild case here uh yellowing that yellowing gets worse and even more discoloration of the teeth as we get more and more exposure to fluoride beyond the normal recommended limits now what are the normal recommended limits one to four milligrams a day so uh that's ideal for an adult a typical adult drinking one to two liters of water a day so hopefully adults are drinking one to two liters of water today per day and not uh diet dr pepper doesn't count as water intake so the way we typically do this we would fluoridate the water with something like sodium fluoride so we would take this ionic compound this salt and when we add it to the water we would get that trivial amount of sodium but we would also get that fluoride that we would need for our teeth so let's calculate the mass percent of fluoride in sodium fluoride so in naf i've got a single sodium i've got a single fluoride so if i'm trying to calculate mass percent that's going to equal 100 percent times the mass of what we're interested here it's fluoride and i've just got one of these in the formula so i'm going to put one on top so the mass of a single fluoride is 18.998 we're going to divide that by the mass of the entire compound which is going to be 22.990 and that's the mass of a single sodium because i have a single sodium in my formula plus the mass of a single fluoride 18.998 now when we work this out this is going to work out to 45.24 and this is going to be the percent of fluoride so the percent of f minus in naf and remember we said another way to express this was as a fraction a conversion factor what it really means is in sodium fluoride we've got 45.24 grams of fluoride for every 100 grams of sodium fluoride so always keep in mind what this mass percent actually means okay so let's kick this up a notch we want to find how much sodium fluoride should be added to 1500 liters of water to fluoridate it to one milligram of fluoride for every liter so let's start out here with our 1500 liters so if i have liters and i want to go to milligrams of fluoride they give me a relationship i can go from liters of water to milligrams of fluoride because the relationship is one milligram of fluoride for every one liter and i put liters on the bottom so they would cancel now that puts it puts me at milligrams of fluoride if i want to go from milligrams to grams then i've got to say for every one gram this is a definition back from chapter two i've got 1 000 milligrams milligrams on bottom so it cancels that leaves me at grams of fluoride the problem wants to know not grams of fluoride but grams of sodium fluoride so i need the relationship between grams of fluoride and grams of sodium fluoride and that's a mass percent that's where we use it as a conversion factor so i could say for every 100 grams of naf 45.24 of those grams is going to be sodium uh okay i'm not interested in the sodium though i'm interested in the fluoride so we've got to do one extra step here they give me the mass percent of sodium so how about we say if it's not sodium in the compound it has to be fluoride and these mass percents have to add up to 100 percent so whatever is left over if i take 100 and subtract off that sodium which was 45.24 percent that's going to be my mass percent for fluoride 100 minus 45.24 works out to 54.76 so i would say that 54.76 grams of fluoride for every 100 grams of sodium fluoride so let's uh go ahead and set this up and we'll see where the answer takes us we've got 1500 liters of water and then our first conversion factor says for every one liter i'm going to have one milligram of fluoride that was our target liters cancel our second conversion factor takes us from milligrams to grams so i want milligrams on the bottom to cancel one thousand milligrams for every one gram and then our third conversion factor was our mass percent and these were just to label it a little more clearly this was still grams of fluoride so i need to cancel grams of fluoride so i would put 54 54.76 grams of fluoride for every 100 grams of naf sodium fluoride grams of fluoride cancel that leaves me with the the grams of sodium fluoride that the problem is asking for now the answer is a little bit off down here this works out to about 2.74 grams of naf sodium fluoride we would dissolve this amount of sodium fluoride into 1500 liters to get that target of one milligram of fluoride for every liter