Vinaigrette salad dressing consists mainly of oil and vinegar. The density of olive oil is 0.918 g/cm3, the density of vinegar is 1.006 g/cm3, and the two do not mix. If a certain mixture of olive oil and vinegar has a total mass of 397.8 g and a total volume of 422.8 cm3, what is the volume of oil and what is the volume of vinegar in the mixture?

Video transcript

Hi everyone. This problem reads in an experiment, you combine water with a density of one g per mil liter and hexane with a density of 10.66 g per milliliter in a beaker to make a mixture with a total volume of 354.4 mL and a total mass of 312.9 g. Water and hexane. Do not mix, calculate the volume of water and hexane in the mixture. Okay. So we want to calculate volume and then the problem we're given density and were given math. So let's go ahead and write out our density equation. Our density equation is density is equal to mass over volume. And our goal here is to calculate the volume of water and hexane in the mixture. Okay, so one thing we know And this problem is the total mass. Okay, we're told that the total mass is 312.9 g. So if we rearrange this density equation to set mass equal to density times volume, will be able to solve this problem but we need to define some variables so that we can do that. So let's go ahead and say let X equal volume of water. And the we're going to say 354.4 middle leaders minus X equals the volume of hexane. Okay. And the reason for that is because we know that the total volume is 354.4 mil leaders. So that minus X is going to give us the volume of hexane. Alright, so we have mass is equal to density times volume. So we know the total mass is 312. g and it's going to equal density times volume for both. Water and hexane. Okay, we're taking the some of both. So our density of water is one gram per middle leader. This is our density and our volume we're going to say is X. Okay, so remember mass is equal to density times volume And this is for water. So now we're going to say plus the density times volume of hexane. So our density of hexane is 0.66 g per mil leader times the volume of hexane. And we define that as 354.4 mL minus X. Okay, so we have mass is equal to density times volume, this is for water and then density times volume. This is for hex ng. So hopefully you can see what we're doing here. Once we solve for X, we'll be able to figure out the volume of water and then we'll be able to subtract our value of X from 354.4 mL to find the volume of hex ng. Alright, so let's go ahead and clean this up a little bit. So we have 312.9 g is going to equal so to simplify this we need to foil this part. Okay, so we're going to foil that out. So the one for water stays the same. So we have one g per mil liter times X. Plus. So our 10.66 g per millimeter times 354.4 mL are foiling that out. We get plus 233. grams minus. Okay, 0.66 g per mil leader times X. So we just foiled out the hexane part and that's what we got. So let's go ahead and clean this up some more and we'll do that by adding Our one g per mil leader. And our excuse me, hold on. So we're going to simplify by Yes. So we're going to add our we're going to subtract Our one g per mil leader and this point This .66 g per mil leader times X. Ok, And we're going to move it over to the left side. So we're going to get 0. g per mil leader times X is equal to 78. g. Okay, in the 78.996g we took the 312.9 and subtracted 233.904. Alright, So with that this is what we get simplified and then we're going to go ahead and divide both sides by 0.34. Okay, because we want to solve for X. Okay, So once we do that we get X is equal to 232.3 ml and this is our volume of water. And remember we said that the volume of hexane is going to be 354.4 mL minus X. So that means it's going to be minus 232. mL, which gives us a volume of 122.1 mill leaders, which is the volume of hexen. Okay, so these are two final answers here. So 230 2.3 Mil leaders is our volume of water 122.1 mill leaders is the volume of Hexane. Alright, so that is it for this problem. I hope this was helpful.