In this module, we're going to look at the percent composition by mass. Our objective is to calculate the percent by mass of each element in a compound. Before we can do any calculations, we need to define what we mean by percent composition. Basically, this is the mass percent of each element in a compound. Remember the general definition for percent is part over the whole times 100. We're going to take the same approach as we calculate the mass percent of elements in a compound. When we want to calculate the mass percent of an element, what we need to look at is the formula for that particular compound, and look at the subscripts and the identity of the element. For a particular element, we're going to look at the value of n, such as an oxygen in CO2 would have an n equal to 2. We're going to multiply that by the molar mass of the element. And we're going to divide it by the complete molar mass of the entire compound, and then multiply it by 100. So now, what we'll have is the mass percent of each element. And if we do this for both carbon, so we have the percent of carbon, plus the percent of oxygen, this should be equal to 100% because those are the only two elements that are found in this particular compound. Let's look at an example of how we would do this for another compound. This is C4H10, which is known as butane. What we are looking at is the mass percent of carbon and hydrogen in this compound. We are given the molar mass of the entire compound, but we could easily find that if it was not provided. So the first thing we're going to look at is the percent of carbon by mass. And that's going to be equal to 4 times the mass of the carbon, divided by the mass of the entire compound, the molar mass of the entire compound. And then I'm going to multiple by 100. Now I can solve the problem by taking 4 times 12.01, dividing by 58.12, and multiplying by 100. The result I get is 82.66% carbon by mass. Note that I can keep four significant figures in this value because both the molar mass of the carbon, as well as the molar mass of the compound, contain four significant digits. Now I can do the same thing, determining the percent of hydrogen by mass. And what I find is that I have 10 times 1.008, which is the molar mass of hydrogen, divided again by 58.12, which is the molar mass of the entire compound, and multiplying by 100. And I get 17.34% hydrogen by mass. Now I can check to see if I've done the calculations correctly by simply adding up these two percentages. The values should be equal to 100 or very nearly 100. And in this case, I find they are actually equal to 100%. You try finding the mass percent of potassium in potassium phosphate. Our correct answer is 55.26. To set up this problem, we need to look at the formula of the potassium phosphate. We need to find the molar mass of the compound, and we also need to find the mass of just one potassium so that we can multiply it by 3 because we have percent of potassium by mass. It's going to be equal to 3 times 39.10 for the molar mass of the potassium, and then I have to divide it by the molar mass of the compound. As I did before, I'm going to look at the molar mass of each individual element on the periodic table and add up the values, and I find that the molar mass of the compound is 212.27. And then I need to multiply the result of that by 100. So I take 3 times 39.10 divided by 212.27 times 100, and what I find is that I get 55.26% of potassium by mass. Now, if we are already given the mass percent or if we need to use that mass percent in the calculation, we can write a relationship from that. For this example, we have calcium carbonate, and we're told that it has 40.04% calcium by mass. That means I can write a relationship showing I have 40.04 grams of calcium for every 100 grams of the compound. Now note I used 100 here because a percent is based on 100. I could have assumed any value, but that would have required further mathematical calculations to know what value would go on top. For example, if I divided this by 2 and put a 50 on the bottom, then my relationship, or my value on top, would then be 20.02 grams of calcium per 50 grams of calcium carbonate. And I could do that with any value, but because it's a percent, we want to keep it easy for ourselves and always base it on 100. Now that we have this relationship, we can actually use this in calculations. So let's figure out how much calcium we have in 225 grams of calcium carbonate. So we know we're starting with 225 grams of calcium carbonate. I know that when I set up my calculation, my grams of calcium carbonate is going to have to go on the bottom and something else is going to have to go on the top. Since I'm worried about the mass of calcium, that's the value I'll use on the top of the equation. So I'm going to put my percent in there, 40.04 grams of calcium over 100 grams of calcium carbonate. Notice that I have grams in both the numerator and the denominator, so I have to be careful to set up the problem correctly. I can only cancel out grams of calcium carbonate with grams of calcium carbonate. It's not enough just to have grams and grams in the numerator and denominator. It has to be the same substance as well. Now we can actually do the calculation to find out how many grams of calcium we have in our sample. So we take 225 times 40.04 and divide by 100, and we get the value 90.1 grams of calcium in our 225 gram sample. This value is reasonable. We noticed that it was 40%, so it was a little less than half. We noticed that the mass of calcium we get out is a little less the half of the mass of the compound. Now, using what you did to determine the mass percent of the potassium in potassium phosphate, determine the mass of potassium in 75 grams of potassium phosphate. In this case, we get 41.4 grams of potassium. Remember, on the earlier problem, we found that we had 55.26% of potassium by mass in potassium phosphate. Now we can write a relationship with that percentage and say 55.26 grams of potassium in 100 grams of K3PO4. Now that we have this information, we can use this to actually figure out the grams of just the potassium. So we have 75.0 grams of K3PO4, and I need to make sure grams of K3PO4 is in the numer, in the denominator. So, we have 100 grams of K3PO4 on the bottom, and we have 55.26 grams of potassium on top. Now, our grams of potassium phosphate cancelled with our grams of potassium phosphate. The value we're left with is the 41.4 grams of potassium. Here we saw the percentage was a little more then half, and we see that the mass we get, the 41.4, is a little more then half of our original 75 gram sample, so this seems to be a reasonable answer. In the next module, we're going to look at the different relationships that we can get from chemical formulas.
