hello everyone this video will cover information in chapter two section seven which is the final section in chapter two so uh section seven is all about density and so density is defined as mass over volume so the mass of the substance divided by the volume that it occupies and generally density is a property that we can go to literature and look up and it's usually reported in units of grams per milliliter so grams mass milliliter for volume and we can also utilize density not only to be able to help us identify different substances but we can also use density as a conversion factor so let's go ahead and work through these examples so for 2.78 solve each of the following problems a a glucose solution has a density of 1.02 grams per milliliter what is its specific gravity so let's first define specific gravity and so that is defined as the density of some substance divided by the density of water and the density of water is 1.00 grams per milliliter so essentially we are just dividing the density of the subs of some substance by one but specific gravity is a unitless quantity right if we have some density of a substance reported in grams per milliliter and we divide that by one gram per milliliter the units cancel out and we're left with a unitless quantity so if we want to figure out the specific gravity of this glucose solution we would take 1.02 grams per milliliter for the density of the glucose and divide that by 1.00 grams per mil again our units cancel out and we get a specific gravity of 1.022 okay there you go now for b we have a zero point two zero zero milliliter sample of a very low density uh lipoprotein the vldl another typo which has a mass of 190 milligrams what is the density of this eodl so in order to determine the density we need the mass 190 milligrams of vl dl and we need to divide that by the volume 0.200 milliliters so we have one more step that we need to take before we can report our final answer and that is that we have been provided a mass in milligrams and as i mentioned we generally report density in terms of grams per mill so we're just going to go ahead and put in our conversion factor to convert from milligrams to grams right and then milligrams and milligrams will cancel out and we will be left with grams per mil so that is 190 divided by 0.200 okay times 0.001 and let's see two sig figs three sig figs so we're going to report this number to two significant figures and i get 0.95 grams per milliliter this is less dense than water okay for c butter has a specific gravity of 0.86 what is the mass in grams of 2.15 liters of butter so we've got a couple steps that we need to take here to solve this one first off we've been given the specific gravity of butter um but we're going to need to figure out what the density of butter is and then once we have that value we can use density as a conversion factor to get us from volume of butter in liters and convert that to grams of butter so 0.86 is equal to the density of butter divided by the density of water and so if we rearrange this equation we get 1 gram per ml times 0.86 which means that the density of butter is 0.86 grams per milliliter density of butter and now we can move on to step two so our known beginning 2.15 liters of butter 2.15 liters of butter and before we can use density as a conversion factor we see that we have some um unit inconsistencies because we have our density reported in grams per milliliter and our initial volume of butter reported in liters so we're going to want to go ahead and put in the conversion factor to get us from liters to milliliters there are 1000 milliliters per liter or 10 to the power of 3. now liters and liters cancel out and now we know we need to cancel out the units of milliliters so that will need to go on the bottom and we can put 0.86 grams mils and mils cancel out we have 2.15 times 0.86 and let's do a sig fig check so it's three sig figs these are exact numbers and two sig figs so we can report our final answer to two sig figs so if i put down what i get from my calculator i get 1 849 but here are our two significant figures so we look immediately to the right and we see that it's four so that is less than five which means that our final significant digit will remain unchanged and so um just a little um a quick tutorial for rearranging right if we have density equals mass over volume right we can rearrange this depending on um which of these properties that we want to solve for so if we wanted to solve for mass that would look like density times volume equals mass or if we wanted to solve for volume and volume would come up here and switch places with density and that would look like volume equals mass divided by density so we just have one more example problem that i want to work through so d a 5 milliliter urine sample has a mass of 5.025 grams if the normal range for the specific gravity of urine is 1.003 to 1.030 with the specific gravity of this urine sample indicate that the patient could have type 2 diabetes so we are given the volume of urine and the mass of urine but this range is given as specific gravity so that tells us that first we have to figure out what the density of this urine sample is and then from there we'll figure out what its specific gravity is and then make a determination as to whether or not it is likely um that this patient may have type 2 diabetes so if density is mass over volume and we know that that's grams per mil so no need to do any conversion factors because we're given a mass in grams and a volume in milliliters so we'll just plug that in 5.025 grams divided by 5.000 milliliters and we get 1.005 grams per mil and then we need the specific gravity which means we just need to take this density and divide it by the density of water grams per mil density of water and we get our unitless quantity for specific gravity of the urine sample of 1.005 and so if we compare that to the range 1.003 to 1.030 we see that this value does in fact lie within the bounds of this range um albeit on the low end but that would be an indication that this patient could have type 2 diabetes so that's going to wrap up my coverage of section 7 so seeing that if provided information about the mass and the volume of a sample that we can determine the density or if we know the density we can use density as a conversion factor to convert between mass and volume and then also how to determine what the specific gravity of your particular substance is by comparing the density of that sample to the density of water so i do encourage you all to take a look at the phet simulation for density where you'll be able to get some experience seeing how we can measure the density of different substances through water displacement okay all right you