In this video, we're going to talk about the law of multiple proportions. And basically, this law states that when two elements form a series of compounds, the ratio of the masses of the second element that combine with one gram of the first element can always be reduced to small whole numbers. Okay, so what does that mean? Well, let me give you an example. First, we need to use two elements that combine to form multiple compounds. So, let's use carbon monoxide and carbon dioxide. So, both of these compounds contain the same two elements, carbon and oxygen, but the way they're combined is different. These are completely different compounds. Now the atomic mass of carbon is 12 and the atomic mass of oxygen is 16. So in carbon monoxide 12 g of carbon combined with 16 g of oxygen. The first element is carbon. The second element is oxygen. We want the first element to have a mass of 1. So I'm going to divide both of these numbers by 12. 12 / 12 is 1 and 16 / 12 is 1.33. So 1 g of carbon combines with 1.33 g of oxygen in carbon monoxide. Now let's focus on carbon dioxide. We have one atom of carbon in that compound. So that's going to correspond to 12 g based on the periodic table. But notice that we have two oxygen atoms in that same compound. The atomic mass for one oxygen atom is 16. So for two of them is going to be 2 * 16 or 32 g. Now let's divide this by 12. And let's divide 32 by 12. 32 / 12 is 2.67. So now let's focus on the statement. The ratio of the masses of the second element can always be reduced to small whole numbers. So this is the second element oxygen. That's how much oxygen is present. If we have one gram of the first element. So what is the ratio between these two numbers? Well, if you take 2.67 and divide it by 1.33, this is going to be about two. And the reason for that is there's twice as many oxygen atoms compared to this compound. And so that's the main idea behind the law of multiple proportions. Whenever you have two elements that could form a series of compounds in the case of CO and CO2, the ratio of the masses of the second element that combine with 1 g of the first element can always be reduced to small whole numbers. So these two you can divide them and then you could reduce them to a whole number. The mass of oxygen that combines with 1 g of nitrogen to form three different compounds are 1.142 g, 2.284 g, and 2.855 g respectively. Show how these data illustrate the law of multiple proportions. So how can we do this? So we have 1 g of the first element nitrogen and we have the different masses of the second element oxygen. We need to show that the masses of the second element can be reduced to small whole numbers. So for example, let's say this is compound A, compound B and compound C. Compound A has a mass of 1.142 g. That's the mass of oxygen in compound A. The mass of oxygen in compound B, let's say it's 2.284. And the mass of oxygen in compound C is 2.855 g. Now let's see if we can reduce B to A. If we can get a ratio and reduce it to small whole numbers. So 2.28 284 / 1.142. Notice that 1.142 is exactly half of 2.284. If you take 2.284 and divided by 1.142 as a decimal, you get exactly 2. So we show that the ratio to from the ratio of B to A is a whole number. Now let's try C to A. C has 2.855 g of oxygen and A is 1.142. So this is about 2.5. or 2.5 over 1. Now we need to get a whole number. So let's multiply the top and the bottom by two. So the ratio of C to A is 5 to 2. Now what about the ratio between C and B? Let's put the larger number on top. So let's divide 2.855 by 2.284. So this will give you 1.25 which is not a whole number but we're going to make it into a whole number by multiplying by 4. 1.25 * 4 is 5. 1 * 4 is 4. So the ratio between uh the ratio of C to B is 5 to 4. So as you can see the ratio between any of these compounds the ratio of the masses of the second element which is oxygen can now be reduced to a whole number. That's how we can show that this data illustrates the law of multiple proportions. Here's another problem that you could try. There are 100 g of two different compounds that are composed of sulfur and oxygen. The first compound contains 50 g of sulfur and the second compound contains 40 g of sulfur. Show how these data illustrate the law of multiple proportions. So let's call the first compound compound A and the second one compound B. Compound A contains 50 g of sulfur. Compound B contains 40 g of sulfur. Now the total mass of each of these compounds, even though they're different, the total mass is 100. So for compound A, if we have 100 g of the compound and 50 g is sulfur, the other 50 g is oxygen. These two have to add up to 100. Now for compound B, we have 40 g of sulfur, which means we have 60 g of oxygen. 40 + 60 is 100. Now, in order to show that these data illustrate the law of multiple proportions, we need to get one gram of one of the elements. It really doesn't matter which one because you can choose sulfur to be the first element and oxygen to be the second or you could choose oxygen to be the first and sulfur to be the second. So, let's choose sulfur to be the first element and oxygen to be the second one. Therefore, we need to get 1 g of sulfur. So, for compound A, let's divide both numbers by 50. So, 1 g of sulfur will combine with 1 g of oxygen. For compound B, let's divide both numbers by 40. 1 g of sulfur will correspond to 60 / 40, which is 1.5. So 1.5 g of oxygen. Now that we have one gram of the first element, we can now find the ratio of the second elements and reduce it to a whole number. So let's divide this number by this one. 1.5 / 1 is not going to change. It's going to be 1.5. Now let's reduce it to a whole number. So 1.5 over 1. Let's multiply the top and the bottom by two. So this will give us a ratio of 3 to 2. So that's the ratio of the masses of oxygen in the second compound relative to the first. So the ratio of B to A is 3:2. So for every two grams of oxygen in the first compound, there's going to be three grams of oxygen in the second. assuming we have the same mass of sulfur. So that's how you can illustrate the law of multiple proportions. What you want to do is you want to get one gram of one of the elements. And then once you have one gram of the first element, then at that point you could divide the grams of the second element and reduce it to a whole number. So that's it for this video. Hopefully you understand how to apply the law of multiple proportions. If you want to find more of my other chemistry videos, you can go to my channel and just look for my chemistry playlist and you can access more of these videos in order. So thanks again for watching and have a good day.