###### Jacqueline Spivey

Ph.D.,U.C.Santa Cruz
Teaching at a top-ranked high school in SF

She teaches general and chemistry at a top-ranked high school in San Francisco. Prior to that, she lead and published a number of research studies and lectured at SF State University.

Concept

# Law of Definite Proportions - Law of Multiple Proportions - Concept

Jacqueline Spivey
###### Jacqueline Spivey

Ph.D.,U.C.Santa Cruz
Teaching at a top-ranked high school in SF

She teaches general and chemistry at a top-ranked high school in San Francisco. Prior to that, she lead and published a number of research studies and lectured at SF State University.

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The law of definite proportions, also known law of definite composition, states that regardless of the amount, a pure compound always contains the same elements in the same proportions by mass. Law of multiple proportions, also known as Dalton s Law, states that when one element combines with another to form more than one compound, the mass rations of the elements in the compounds are simple whole numbers of each other.

This segment let's discuss the law of definite and multiple proportions. But before we do that let's have a quick review briefly just to remind us of why this is important.

So we need to remember that matter is anything that occupies space and has mass and also that the law of conservation of mass tells us that the mass of the reactants equals the mass of the products because matter is neither created nor destroyed. So that being said we can jump right into the law of definite proportions which is also sometimes called the law of definite composition depending on what you're looking at. So what it states is that regardless of the amount a pure compound always contains the same elements in the same proportions by mass and so just hearing those words probably doesn't really mean a whole lot and so we'll do an example which hopefully will shed a little light on what that means exactly.

So again a reminder is that the law of the conservation of mass is applied to compounds and the mass of the compound is equal to the sum of the masses of the elements that make up the compound. So remember a compound is just two elements together. So water is a compound that's composed of hydrogen and oxygen. So if we're going to, let's apply the law of conservation here based on the mass for water and let's kind of work that out. So we have one water molecule that's composed of two hydrogen atoms and one oxygen atom. So if we recall from the periodic table, hydrogen weighs about 1.008 grams, oxygen weighs about 16 grams. So if we have two hydrogen atoms it means there the mass is one gram each, so we have a total of two grams of hydrogen and then we have one oxygen atom, its mass is 16 grams. So we've got 16 grams of oxygen. So that means the molar mass of water is 18 grams. So then the ratio of hydrogen to oxygen is then 1:8.

So let's move on and talk about the law of multiple proportions, which is a little more difficult maybe and it's also known as Dalton's Law and so this comes into play a lot when you're doing stoichiometry so that's when you're balancing equations, and trying to figure out molar masses of different compounds that are involved in a reaction. So this states that when one element combines with another to form more than one compound, the mass ratios of the elements in the compounds are simple whole members of each other. Again, the words probably don't mean a whole lot, but let's work through a couple of examples and see if that sheds some light.

So here, let's look at carbon monoxide and carbon dioxide. So both of these compounds are composed of the same elements. Carbon monoxide is composed of carbon and oxygen, carbon dioxide is composed of carbon and oxygen, but clearly, they have different properties. Because we know that carbon dioxide is something that's in our air and in our bodies and we breathe it and it's fine. However, carbon monoxide even in pretty small concentrations can actually cause you to to IB] and kill you. So clearly they have different properties. So maybe one of the reasons why that is what we're going to see here. So in carbon monoxide, the oxygen to carbon ratio is 1:1. So again the molar mass of oxygen is 16 grams and the mass of carbon is 12 grams. So then if we look at carbon dioxide, the carbon oxygen to carbon ratio is 2:1, so that means that there are two oxygens for every one carbon so the mass of oxygen is 32 grams and the mass of carbon is still 12 grams. So you see here, that the ratios here, it's exactly two times what it was for carbon monoxide. So we can apply the same logic to the difference between water and hydrogen peroxide, H2O2. So again water and hydrogen peroxide are both composed of the same elements, so compounds of the same elements hydrogen and oxygen in water and hydrogen and oxygen in hydrogen peroxide.

And so let's look at the hydrogen to oxygen ratio in water is 2:1 and in peroxide it's 2:2 or you could say 1:1 but for these purposes it's just a little bit easier to think of it as 2:2. So then the mass of hydrogen again is one gram per hydrogen and you've got two of them. So the mass here is two grams to 16 grams of oxygen and then for the peroxide, it's two grams of hydrogen for the same reason and oxygen is 16 each so it makes the mass here 32. Again you see that the ratios, the mass ratios work out, that H2O2 is exactly twice that of water.

So this is the basics of proportions and go ahead and work through some more practice problems that you can get up to speed on that.