Video Transcript
A 10-gram sample of silicon carbide, SiC, is found to contain 3.0 grams of carbon. What is the percentage composition of silicon carbide?
Percentage composition is the percentage by mass of each element in a compound or sample. We may recall that a percentage is calculated by dividing the part in question by the whole and multiplying by 100 percent. With this in mind, let’s construct an equation for percentage composition. We know that compounds are made up of elements. So an element is just a part of a compound which represents the whole. We also know that percentage composition is a percentage by mass. So we’ll need to use the mass of the element and the mass of the compound. So the part of our percentage composition equation is the mass of the element in the compound or sample and the whole is the total mass of the compound or sample.
In the question, we are told that a sample of silicon carbide has a mass of 10 grams. This is the total mass. We are also told that this sample contains three grams of carbon. This is the mass of the element carbon in the sample. We can substitute both of the masses into the equation to solve for the percentage composition of carbon in silicon carbide. The gram units will cancel, and we’ll get an answer of 30 percent. This is the percentage of carbon in silicon carbide.
But we’ve not finished calculating the percentage composition. This is because percentage composition tells us the percentage by mass of each element in the compound. Silicon carbide is composed of carbon and silicon. So we need to calculate the percentage composition of silicon and silicon carbide. We know the total mass of the sample is 10 grams, but we weren’t explicitly given the mass of silicon in the sample. As the sample only contains silicon and carbon and three of the 10 grams are carbon, the remaining seven grams of the sample must be silicon.
Now we can perform the calculation. Once again, the gram unit will cancel, and we’ll get an answer of 70 percent. One quick way to check our answers is to verify that the sum of the percentages is equal to 100 percent. We have therefore determined that the percentage composition of silicon carbide is 30 percent carbon and 70 percent silicon.
