In this example problem, we'll use dimensional analysis to convert from the mass of an element in a compound to the volume of that compound. The question is: What is the volume, in milliliters, of hexane (C6H14) if the sample contains 1.00 x 10^24 atoms of carbon? The density of hexane is 0.658 g/cm^3. We can start dimensional analysis with the number of atoms of carbon given in the problem. Our first step will be to convert from atoms of carbon to moles of carbon, and we can do this using Avogadro's number. One mole of carbon is equal to 6.022 x 10^23 atoms of carbon. Now we can convert from moles of carbon to moles of hexane using the chemical formula. We know that there are 6 moles of carbon for every 1 mole of C6H14. Next, we want to convert from moles of hexane into grams of hexane using the molar mass. Calculating the molar mass of hexane, we have 6 moles of carbon plus 14 moles of hydrogen. Putting it into our calculator, we should get 86.178 g/mol. So, in our dimensional analysis, 1 mole of hexane equals 86.178 grams of hexane. Next, we can convert from grams to cubic centimeters (cm^3) using the given density of 0.658 g/cm^3. One cubic centimeter of hexane is equal to 0.658 grams of hexane. The problem asks for the volume in milliliters, so we can convert from cubic centimeters to milliliters using the conversion factor: 1 milliliter equals 1 cubic centimeter. Now the units should cancel, and we end up with milliliters of hexane. Putting this into our calculators, we should get 36.4 milliliters of hexane.