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Worked example: Determining an empirical formula from percent composition data

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We can use percent composition data to determine a compound's empirical formula, which is the simplest whole-number ratio of elements in the compound. Created by Sal Khan.

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  • purple pi purple style avatar for user Junno Martinez
    how is there more chlorine than mercury if there is .73% and 200 moles of Hg and only .27% and 36 moles of Cl?
    (5 votes)
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    • mr pink red style avatar for user Jim Kennedy
      OK, first some corrections. That was 73% by mass (not .73%) Hg and 27% by mass (not .27%) Cl. But more importantly, you have mistaken the number of moles (a measure of the number of atoms) of Hg & Cl for their atomic weights (a measure of the average weight of a collection of atoms of that element). But if you are still confused, and you like to reason by analogy, think of it this way....
      Imagine you have a bag. In the bag, you are told, are nothing but feathers from a dove and fishing sinkers. Each feather weighs 1.0g; each sinker weighs 10.0g. The total mass of all the contents is 150g, and you are told that 2/3 of the mass is made up of sinkers, and only 1/3 of the mass is feathers. So there is twice as much mass of sinkers are there are of feathers. But how many (quantity) of each are there? 2/3 of 150g is 100g, so there are 100g of sinkers, or ten (10) fishing sinkers total. 1/3 of 150g is 50g, so there are 50g of feathers, or fifty (50) feathers total. So, while there is twice as much mass of sinkers, there are five times as many (quantity) of feathers.
      (63 votes)
  • hopper jumping style avatar for user Gabriel
    Why is Cl₂ called Chloride? And why does Sal say Hg "2" Chloride? What does the 2 mean?
    (3 votes)
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    • leaf green style avatar for user Robby358
      And the 2 denotes the charge of the cation, because transition metals have multiple oxidation states (which is essentially the charge of the atom within the molecule) (i.e. Fe can be Fe+3 or Fe+5), so in this case the oxidation number/charge of the mercury needs to be specified. If it were Hg 1 Chloride [not sure if this exists], the compound would be HgCl, versus Hg 2 Chloride which must be HgCl2 to balance.
      (34 votes)
  • male robot hal style avatar for user Greg L
    Why do we assume that the percent compositions are in given in mass rather than in volume or numerically? Why can't the percents be saying that we have a mole ratio just over 3:1?
    (12 votes)
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    • piceratops ultimate style avatar for user Quinn McLeish
      Because atoms tend to differ widely in terms of mass.
      If all atoms weighed the same then we could indeed use weight percentages to determine empirical formulas (formulae?), but, as Sal showed us in this video, there are two Cl atoms for each Hg atom, instead of the one Cl atom to each three Hg atoms that the percentages seemed to indicate.
      In other words: There are six times fewer Cl atoms than it seemed. This is because Cl atoms are about six times LIGHTER than Hg atoms.
      (7 votes)
  • leafers ultimate style avatar for user Kyle Raubenheimer
    This may have been answered in another video, but if you got a ratio of let's say exactly 1:1.5, would you round up or round down in the empirical formula?
    (5 votes)
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  • blobby green style avatar for user daisyanam2
    So there are 2 Cl for every Hg, but if there's 73% Hg and 27% Cl, doesn't that mean there's more Hg than Cl in the bag, because 73% is larger than 27%?
    (3 votes)
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    • piceratops ultimate style avatar for user Just Keith
      There are two kinds of percents here: the mass fraction and the mole fraction. So what the percentage is depends on what kind of percent you're talking about.
      HgCl₂ has one atom of Hg per 2 atoms of Cl. Thus by moles it is ⅓ Hg and ⅔ Cl.

      By mass, since Hg is heavier the percentages are:
      Hg: 1 mol × 200.59 g/mol = 200.59 g
      Cl: 2 mol × 35.45 g/mol = 70.90 g
      HgCl₂: 1 mol × 271.49 g/mol = 271.49 g
      Thus, by mass:
      Hg: 200.59 g / 271.49 g = 0.7388
      Cl: 70.90 g / 271.49 g = 0.2612
      So, by mass HgCl₂ is 73.88% Hg and 26.12% Cl.
      (13 votes)
  • starky tree style avatar for user biancadonk
    When I paused the video, I didn't look at moles, but just used the fraction of the weight divided by the atomic mass to get the relative amount of each, which came out to close to the same answer (a 2.1 to 1 ratio of Cl to Hg). Is it just a coincidence that I got it right, or is this an acceptable way to do this kind of problem?
    (4 votes)
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    • piceratops ultimate style avatar for user Just Keith
      If I follow what you meant by that, then it is no coincidence at all. However, you need to use very clearly stated units. If you get unclear about units, even if the numerical portion of your math is correct, your chemistry teach will most likely mark the problem wrong.

      Incidentally, you cannot round off as much as Sal does in his videos. You have to respect the number of significant digits.
      (5 votes)
  • leaf yellow style avatar for user Maya Lynch
    Why was Carbon decided as the basis of the atomic mass unit measurement?
    (5 votes)
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    • aqualine ultimate style avatar for user Cole B
      Oxygen-16 use to be the basic of amu. But since Oxygen-16,17,18 are often found in nature, they decided up Carbon-12 to be the basic of the amu instead.

      Basically physicists and chemists had different standards, and universally sat in the middle using C-12 as the basis.
      (2 votes)
  • hopper jumping style avatar for user Yuya Fujikawa
    Is there a rule of the order of a molecule? if we have a non metal and a metal, we write the metal first, but what if a molecule contains 5 C, 4 H, 2 N and 1 O? Is it arbitrary? Is it C5H4N2O or..? (It seems like C tends to be written first?)
    (3 votes)
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  • female robot amelia style avatar for user Zhanna Berridge
    Why hydrargyrum"s name is mercury in this video? Thanks
    (2 votes)
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  • male robot donald style avatar for user Prashanth
    why do we use empirical formula ? why don't we get the exact ratio of elements?
    (1 vote)
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    • piceratops ultimate style avatar for user Just Keith
      Because in ionic compounds there are no discrete molecules, just ions bound to each other in a repeating pattern, thus there is no molecular formula possible.

      For covalent compounds, we use the empirical formula as an intermediate step toward finding the molecular formula. So, until we have enough information to find the molecular formula, we have to make due with the empirical formula.

      Also, particularly for extremely large organic molecules we may be more interested in the ratio of the different elements to each other rather than how many are in each molecule -- it just depends on what purpose we have in using the compound. After all, if we have say a protein with 25000 atoms in it, and all we are interested in is how much hydrogen we can extract from it by decomposing it, then we don't need to know exactly how many atoms are in each molecule, just the ratios will do quite fine.
      (6 votes)

Video transcript

- [Instructor] Let's say that we have some type of a container that has some type of mystery molecule in it. So that's my mystery molecule there, and we're able to measure the composition of the mystery molecule by mass. We're able to see that it is 73% by mass mercury, and by mass it is 27% chlorine, so the remainder is chlorine by mass. So pause this video and see if you can come up with what is likely the empirical formula for our mystery molecule in here, and as a little bit of a hint, a periodic table of elements might be useful. All right, now let's work through this together, and to help us make things a little bit more tangible, I'm just going to assume a mass for this entire bag. Let's just assume it is, or this entire container is 100 grams. I could have assumed 1,000 grams or 5 grams, but 100 grams will make the math easy because our whole goal is to say, hey, what's the ratio between the number of moles we have of mercury and the number of the moles we have of chlorine and then that will inform the likely empirical formula. So if we assume 100 grams, well then we are dealing with a situation that our mercury, we have 73 grams of mercury, and we can figure out how many moles this is by looking at the average atomic mass of mercury. That's why that periodic table of elements is useful. We see that one mole of mercury is 200.59 grams on average, so we could multiply this times one over 200.59 moles per gram. So when we multiply this out, the grams will cancel out and we're just going to be left with a certain number of moles. So I'll take 73 and we're just going to divide it by 200.59, divided by 200.59 is going to be equal to 0.36, and I'll just say 0.36 because this is going to be a little bit of an estimation game, and significant digits, I only have two significant digits on the original mass of mercury, so 0.36 moles, roughly. I'll even say roughly right over there, and I can do the same thing with chlorine. Chlorine, if I have 27% by mass, 27% of 100, which I'm assuming, is 27 grams. And then how many grams per mole? If I have one mole for chlorine, on average on earth the average atomic mass is 35.45 grams. And so this is going to approximate how many moles because the grams are going to cancel out, and it makes sense that this is going to be a fraction of a mole because 27 grams is less than 35.45. We take 27 divided by 35.45. It gets us to 0.76, roughly, 0.76. And remember, we're talking about moles. This is how many moles of chlorine we have, or this is how many moles of mercury, that's a number. You can view that as the number of atoms of mercury or the number of atoms of chlorine. Moles are just the quantity specified by Avogadro's number, so this is 0.76 times Avogadro's number of chlorine atoms. So what's the ratio here? Well, it looks like for every one mercury atom, there is roughly two chlorine atoms. If I take two times 0.36, it is 0.72, which is roughly close, it's not exact, but when you're doing this type of empirical analysis, you're not going to get exact results, and it's best to assume the simplest ratio that gets you pretty close. So if we assume a ratio of two chlorine atoms for every one mercury atom, the likely empirical formula is for every mercury atom we will have two chlorines. And so this could be the likely empirical formula. The name of this molecule happens to be mercury two chloride, and I won't go in depth why it's called mercury two chloride, but that's actually what we likely had in our container.