We know from the information given that we have an equal mass of each compound, but no real numbers to plug in and find moles. So what can we do?


 Kristopher Cobb
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1 How do we figure this out? We know that: 1) the number of oxygen atoms can be found by using Avogadro s number, if we know the moles of oxygen atoms; 2) the number of moles of oxygen atoms can be found if we know the number of moles of each molecule; 3) the number of moles of each molecule can be found if we know the mass of each compound We know from the information given that we have an equal mass of each compound, but no real numbers to plug in and find moles. So what can we do? Since we have an equal mass of each compound, if we calculate the percent by mass of oxygen in each compound, we could just compare their ratios, since we know that the mass is directly related to number of moles (which is directly related to the number of atoms). So let s start by finding the % by mass of oxygen in H 2 SO 4 : To find % mass, we use the equation:
2 As we did with the first example we worked in class, we assume we have 1 mole of the compound, which has a molar mass of g/mol (mass of the whole): For every mole of H 2 SO 4 molecules, there are 4 moles of oxygen atoms, which has a molar mass of g/mol (mass of the part): Now we just punch in the numbers and find: Now we can do the same for the other two compounds! Assuming 1 mole of sugar (mass of the whole: g/mol), we have 11 moles of oxygen atoms per mole of sugar molecules:
3 And for potassium chlorate, assuming 1 mole of the compound, we have 3 moles of oxygen atoms per mole of KClO 3 molecules: Now that we have the % by mass of each compound, we can just compare the ratios: Compound % by mass oxygen H 2 SO % C 12 H 22 O % KClO %
4 So we can see that H 2 SO 4 has the greatest percent oxygen by mass, so if we had an equal mass of each compound, the mass of oxygen in H 2 SO 4 would be the greatest, meaning that it has the greatest number of oxygen atoms. ***Also note that subscript does NOT indicate which compound has the greater % by mass of oxygen! Sugar has 11 moles of oxygen atoms per mole of compound, but has less % mass of oxygen than H 2 SO 4, which has only 4 moles of oxygen atoms per mole of compound!*** Now, what would happen if we were told the mass of each compound in the initial problem? Say we have 50.0 grams of each of the compound in the table above. How many atoms of oxygen are in each? So how do we get from grams of a compound to atoms of oxygen? In any problem where I need to convert one type of unit to another unit, I like to set up my dimensional analysis with units only so I can figure out where I m going, kind of like a road map. Then, once I plot my route, I go back and fill in the numbers for my conversion factors. In this problem, I m starting with grams, and I want to get to number of atoms of oxygen: I know that to get number of atoms, I will have to use Avogadro s number at some point in the calculation, and to be able to use Avogadro s number, I need to know moles. But I have grams! So I ll need to convert my grams to moles and I can do that with molar mass (g/mol):
5 Now I have moles, but since it is moles of the compound, not just oxygen. I ll need to convert the moles of the compound to moles of oxygen atoms: Well, I have moles of oxygen atoms, so I can figure out the number of moles of oxygen atoms with Avogadro s number, which is number of things per mole: So now all of my units should cancel out correctly, leaving me with the number of oxygen atoms! So all I have to do is plug in the numbers and solve Note that the starting amount given only has three significant figures, so your answer should have the same. Now we can do the same calculation for the other two compounds:
6 For sugar (C 12 H 22 O 11 ): For potassium chlorate (KClO 3 ):
7 So we want to find the formula and name of some iron oxide compound. What do we do? Well, we know that the new compound is some iron oxide meaning that it must be composed of X moles of iron and Y moles of oxygen: Fe x O y So if we want to write a formula, we need to figure out the molar ratios of iron and oxygen in the new compound so we can figure out the subscripts. But how can we even know how much of each element there is in the new compound? Remember that we learned about the Law of Conservation of Mass earlier this semester, which means that whatever amount of matter we start with before the reaction will be the amount of matter we end up with after the reaction. Since we start with grams of iron, that means that the new compound contains g of iron as well (assuming all of the iron is in the new compound now). So the moles of iron in the new compound should be:
8 So we have moles of iron, but what about the oxygen? We know from the problem that the mass of the new compound is17.16 grams. If grams of the compound is iron, then the remainder must be oxygen: Now that we have the mass of oxygen in the new compound, we can find moles of oxygen: Molecular formulas are always ratios of whole numbers, since they represent the number of atoms in a molecule (you can t have half an atom!), so we have to figure out the whole number ratio by dividing by the smaller of the two numbers: We still don t have whole numbers, though, so we ll need to multiply by some factor to get them to the closest whole number ratio. I see that if I multiply 1.5 by 2, I will have 3; so multiplying both numbers by 2 gives me:
9 So now I see that my molecular formula is: Fe 2 O 3
10 So here we have another problem in which we have to find the molecular formula, but this time we do not know how much we started with, or how much we ended up with, we are only given the mass of carbon in propane and its molar mass. So what can t do what we did on the previous problem. What can we do? Another way we can figure out ratios of substances in a compound is to find their percent composition by mass. First, we ll start by calculating the % by mass of carbon, since we are given the amount of carbon (mass of part) and the molar mass (mass of whole): If propane is 81.71% carbon, then the % hydrogen must be: In order to find the molecular formula of propane, though, we need to find the moles of each particle to figure out the ratios. As I talked about in lecture, percent composition is independent of the amount of a substance. So we can choose any
11 amount to calculate the moles. And since percents are out of 100%, it s easiest to just set our amount to 100 grams. So if we have 100 grams of propane, then there are grams of carbon and grams of hydrogen. Using molar masses, we can find moles of each: Then we find the ratio of the two: And finally we find the closest whole number ratio: So we have found the formula: C 3 H 8 But is this the empirical formula or the molecular formula? Well, we know the molar mass of propane should be g/mol, so let s check what the molar mass of C 3 H 8 would be: It checks out! So C 3 H 8 is the molecular formula, but since it is the smallest whole number ratio, it is also the empirical formula!
12 This problem is very similar to the one we just did, but this problem was really nice and gave us two of the three % compositions we need! To find % by mass of oxygen, we just have to subtract the % by mass of carbon and hydrogen from 100%: Now that we have all three % compositions, we can find the moles of each particle as we did before by assuming that we have 100 grams of the compound, which means we have: grams of carbon, 6.71 grams of hydrogen and grams of oxygen. Using molar mass to find moles, we get:
13 Then we divide by the smallest number to get the ratios: Well, that was nice, we got whole number ratios! So the molecular formula is CH 2 O then? Well, we know our compound s molar mass is 120 g/mol, so let s check: That doesn t add up to 120 g/mol at all! So this must be our empirical formula. How do we come up with the molecular formula then? Well, let s look at the ratio of the molar mass of our compound versus the molar mass of the empirical formula, CH 2 O:
14 It looks like the molar mass of the compound is 4 times larger than the molar mass of the empirical formula. So if we were to multiply all of the molar ratios by 4, we would have a formula of: C 4 H 8 O 4 Does that check out? Yes it does! So our molecular formula is C 4 H 8 O 4.
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