Video: Percentage Composition

In this video, we will learn how to calculate the percentage composition of a material using chemical formulas or the masses of constituent elements.

16:15

Video Transcript

In this video, we will look at percentage composition, the percentage by mass of each element in a substance. The percentage composition of a substance is the percentage by mass of each element in the substance. The mass percentage of an element in a substance is the percentage mass of that element in a sample of that substance. We can calculate the mass percentage by taking the mass of the element and dividing it by the mass of the substance and multiplying by 100 percent.

Let’s have a look at water as an example. Water is a substance made up of the elements hydrogen and oxygen. We know that water is composed of molecules made of hydrogen and oxygen atoms and that a single molecule of water consists of two hydrogen atoms and one oxygen atom. The percentage composition of water is about eleven percent hydrogen and 89 percent oxygen. Remember that the mass percentages must sum to 100 percent. So why is it that even though we have twice as many hydrogen atoms oxygen makes up so much more of the mass? Well, an oxygen atom has a much greater mass per atom than hydrogen. So even though there’re twice as many atoms of hydrogen in the molecule of water, the element oxygen makes up a much greater proportion of the mass.

We can see the relative masses of an average atom of each element by going to the periodic table. We can see that oxygen has a relative atomic mass of 15.999. And hydrogen has a relative atomic mass of 1.008. So an oxygen atom clearly has about 16 times the mass of a hydrogen atom. Now, we need to know the contribution to the mass of the molecule of each element. For that, we take the relative atomic mass of each atom and multiply it by the number of atoms per molecule. This means that oxygen contributes 15.999 to the mass of the water molecule. And hydrogen contributes 2.016.

If we add up these contributions, we’re going to get the relative formula mass of a water molecule which is 18.015. The last thing to do is calculate the mass percentage for each element. To do that we take the mass contribution of the element and divide it by the formula mass of the molecule. This will tell us the proportion of mass that that element is responsible for. And then we multiply it by 100 percent. So we get a value for the mass percentage of oxygen in a water molecule of 88.8 percent and the value for the mass percentage of hydrogen of 11.2 percent.

You can see that these numbers were rounded to give 89 percent and 11 percent originally. This information is useful when we’re thinking about separating compounds into elements. We know that all the mass in the water will be converted into the mass of the hydrogen and the oxygen. And 11.2 percent of that mass will be hydrogen and 88.8 percent of that mass will be oxygen. Percentage compositions are generally used in two ways, either they are used to determine the ratio of elements in a compound to help us find the formula or they are used to determine the mass of an element present in a compound.

Of course, percentage compositions need to be determined from one of these two things in the first place. So you can think of percentage composition as a bridge between the elemental composition of a single sample and the chemical formula. In this case, we say the percentage composition of water is 88.8 percent oxygen and 11.2 percent hydrogen. Now, let’s move on and think about how we calculate percentage composition when we know the formula.

Let’s say you have a compound like sodium chloride and you’re going to separate it into its elements. I’ve chosen sodium chloride here because sodium chloride is actually separated into its elements in industry. Sodium chloride has the formula NaCl. This means we have one sodium Ion for every chloride ion. When calculating percentage compositions, ions are treated like atoms. We don’t pay attention to the mass differences from having more or fewer electrons. In the case of sodium chloride, we can identify our elements as sodium and chlorine. The next step is to find the relative atomic masses of the elements. For sodium, that’s 22.990. And for chlorine. that’s 34.45. If you wanted to, you could also use the atomic masses in unified atomic mass units, as long as you calculate the formula mass in the same units.

In the next step, we need to work out the number of ions in the formula. We have one sodium ion and one chloride ion per sodium chloride formula. That makes it easy because it means that the contribution for each element to the mass is the same as the relative atomic mass. If we sum these together, we’ll end up with a relative formula mass of sodium chloride which is 58.44. Then we calculate the mass percentage for each element by dividing the contribution by the relative formula mass and multiply by 100 percent. This gives us a mass percentage for sodium of 39.3 percent and a mass percentage for chlorine of 60.7 percent. If we sum these two percentages together, we get 100 percent as we should.

This means that if we have a sample of 500 grams of sodium chloride, we can work out the mass of sodium and the mass of chlorine we get from it. We multiply the mass of our sample by the mass percentage to get 197 grams for sodium and 303 grams for chlorine. If we started with a different compound like iron(III) oxide, we would go through exactly the same procedure. For a sample of iron(III) oxide, iron is responsible for 69.9 percent of the mass. And oxygen is responsible for the remaining 30.1. The key thing to remember is to include the number of each element in the mass contribution.

Now that we’ve looked at how to calculate percentage composition from the formula, let’s have a look at calculating it from masses. Calculating the percentage composition of a substance from the masses of each element is actually a lot easier than doing it from the formula. Let’s imagine we have a sample of methane with a mass of 120 grams. And let’s for the moment imagine that we don’t know the formula for methane. All you’ve been told is that the mass due to hydrogen is 30 grams and the mass due to carbon is 90 grams. So at this point, we haven’t yet demonstrated whether there are any other elements present. However, if we add up the masses for each element, we can see that it equals 120 grams. The compound must only contain hydrogen and carbon because the sum of the individual masses equals the mass of the sample.

We work out the mass percentage of each element by dividing the element mass by the sample mass and multiplying by 100 percent. 30 grams divided by 120 grams times 100 percent is 25 percent. And 90 grams divided by 120 grams times 100 percent is 75 percent. So the percentage composition of methane is hydrogen 25 percent and carbon 75 percent. So we’ve looked at percentage composition and different ways to calculate it. Now, let’s have some practice.

A compound contains only the elements 𝑋 and 𝑌. A sample of the compound with a mass of 12.5 grams is found to contain 6.50 grams of 𝑋. What is the percentage composition of the compound?

Percentage composition is a list of mass percentages for each element in the compound. So we’re looking for an answer with this kind of format where we have the mass percentage of 𝑋 and the mass percentage of 𝑌. We start off knowing that we have a sample mass of 12.5 grams and knowing that the only elements in our compound are 𝑋 and 𝑌. Thankfully, we’ve also been told that the mass of 𝑋 in the sample is 6.50 grams. But we don’t know the mass of 𝑌. However, that won’t stop us calculating the mass percentage of 𝑋 which is the mass of element 𝑋 divided by the mass of sample multiplied by 100 percent. This means we take 6.50 grams divided by 12.5 grams and then multiplied by 100 percent giving us 52.0 percent.

But we still don’t know the mass percentage for 𝑌. We can get the mass percentage in one of two ways. We know the mass percentages must sum to 100 percent. So we can take away the mass percentage of 𝑋 to get the mass percentage of 𝑌. Or we can work out the mass of 𝑌 by taking away the mass of 𝑋 from the mass of the sample and then dividing by the mass of the sample and multiplying by 100 percent. For this question, it isn’t actually necessary to work out the mass of 𝑌. So I’ve skipped it. Instead, we’ve worked out the mass percentage of 𝑌 by taking away the mass percentage of 𝑋 from 100 percent.

However, just in case you’re interested, it should be six grams. All that remains for our answer is to write the percentage composition which is a list of the elements and their mass percentages. A compound containing only the elements 𝑋 and 𝑌 having a sample mass of 12.5 grams will have a percentage composition of 52 percent 𝑋 and 48 percent 𝑌 if 6.50 grams of the sample is 𝑋. So our first example dealt with calculating mass percentages from sample masses and element masses.

Now, let’s do a question that uses a chemical formula.

Ethanol has the formula C₂H₅OH. a) As a percentage by mass, what is the oxygen content of the ethanol molecule to two significant figures? b) As a percentage by mass, what is the carbon content of the ethanol molecule to two significant figures? And c) As a percentage by mass, what is the hydrogen content of the ethanol molecule to two significant figures?

On the surface, it looks like this question isn’t looking for percentage composition. But it does ask for the mass percentage of all the elements in our formula. The first thing we should do is condense down the formula into its chemical formula listing the number of atoms of each element only. From the formula, we can see that an ethanol molecule contains only carbon, hydrogen, and oxygen. And each molecule contains two carbon atoms, six hydrogen atoms, and one oxygen atom. The percentage by mass or mass percentage is equal to the mass of the element divided by the mass of the sample all multiplied by 100 percent.

In this case, the sample is one molecule of ethanol. And the mass of the element is the mass of either two carbon atoms, six hydrogen atoms, or one oxygen atom. We can work out the mass of an atom of each element by looking up the relative atomic mass on our periodic table. The relative atomic mass of carbon is 12.011. The relative atomic mass of hydrogen is 1.008. And the relative atomic mass of oxygen is 15.999. By multiplying the number of atoms of each element per molecule by the relative atomic mass of that element, we’ll get the mass of each element in the molecule. This means that for a molecule of ethanol, carbon contributes 24.022 to the mass, hydrogen contributes 6.048, and oxygen contributes 15.999. If we sum all these contributions together, we’ll get the relative formula mass of an ethanol molecule.

We now have all the information we need to answer all three questions. For part a), we take the contribution for oxygen per molecule of ethanol as 15.999 and divide it by the relative formula mass of ethanol 46.069 and then multiply everything by 100 percent. This gets us 34.7283 percent which we round to 35 percent as our answer to two significant figures. Doing the same working for carbon where we use it’s mass contribution of 24.022, we get a mass percentage of 52 percent to two significant figures. And lastly for hydrogen, we get a mass percentage of 13 percent. To find the mass percentage for hydrogen, we could’ve taken away the percentage for oxygen and carbon from 100 percent. However, that would mean that any mistake in our oxygen or carbon calculation would make our hydrogen calculation incorrect. Doing it this way gives us better odds of a correct answer.

So using the process for figuring out the percentage composition of ethanol, we’ve demonstrated that oxygen has a mass percentage of 35 percent. Carbon has a mass percentage of 52 percent. And hydrogen has a mass percentage of 13 percent in the ethanol molecule.

Since we’ve learned all about percentage composition and done a couple of practice questions, let’s look at the key points. Percentage composition is a list of the mass percentages of all the elements in a substance. The mass percentage of an element in a substance is the percentage of the mass of that substance that particular element is responsible for. Percentage compositions can be determined from chemical formulas and atomic masses or from masses of samples and the elements inside.

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