density okay so before we start discussing density we need to talk a little bit about units and the idea of mass and volume okay so mass is generally defined as the amount of matter contained in an object So that's its mass now you can kind of think of it as weight although it's not technically the same now I've uh put a little link about Mass versus weight at the bottom of this slide but we will not go over this information it it won't be you know important to our discussion so if you'd like to think about mass as weight just go ahead and the SI unit or the standard unit for mass is the kilogram and in this course we're off I'm going to use grams and so 1,000 gr is equal to 1 kilogram Now volume is the 3D space occupied by an object so liters is the SI unit for volume so now we're ready to talk about density so density is basically the amount of mass per unit volume of a certain substance and so masses are generally given in grams and volumes can either be milliliters or cubic centim or CC's and 1 milliliter is equal to 1 cm cubed which is equal to 1 cc so remember CC's and centimet cubed are the same thing and and the equation for density is the mass divided by the volume and of course we're going to have our mass in grams and then our volume in either milliliters or CC's so density is going to have units of grams per Cc or grams per milliliter and so I've put this little triangle here I actually like this guy so here's density here's mass and here's volume so you can get all the different Arrangements so like let's say we want to calculate density then we would take mass divided by volume let's say we wanted to get the volume contained by a certain substance given its mass and its density then we would say volume is equal to mass divided by density or if we want mass then we say mass is equal to density multiplied by volume okay so using that triangle you can get anything you want nice little easy way to rearrange it okay so let's do a little practice problem so we're going to calculate the density of a piece of graphite with a mass of 50 gr and a volume of 22.4 cm cubed and be sure to include the units so how do we do this so the first thing we're going to do is identify what information we are given in the problem all right so the problem tells us that we have a mass of 50 g all right so we're going to write that down and a volume of 22 2.4 cm cubed okay so we have identified important information and so we've identified the mass and the volume okay so the next thing we have to do is just plug these guys in okay so there's our mass and we're going to know it's the mass because we know the units for Mass are grams all right and then we're going to divide it by our volume 22.4 and we're going to get 2.23 gam per cubic centimeter or CC now just a little note just to remind you about fractions you take the top number divided by the bottom number okay and then you're going to get your 2.23 Gram per centimeter cubed okay so you try one so go ahead and take a few seconds and go through step by step and identify the important information and then do the math all right so what information do we have well we were given the density this time okay so that's here and we were given the volume which is here here so we're left with mass we want Mass okay now this one we can actually use our handy dandy Little Triangle okay so we have density and volume and we want the mass okay so mass is equal to density time volume okay now on the next slide we're just going to plug that in all right so we're going to plug in our values density times volume so 78 85 G per milliliter multiplied by 150 milliliters and if we remember our dimensional analysis the milliliters will go away okay then we're going to end up with 117.5 Gram now we need to determine how many sigfigs we need Okay so let's go up here so 0.785 this zero is before the decimal point this is not significant so 1 two three sigfigs this uh 150 M does not have a deal point right here so this zero is not significant so one two nonzero unit numbers and so that is two sigfigs so our final answer needs to have two sigfigs so we're going to round this all right so rounding we want to go 117 so we're just going to round up to two sigfigs giving us 120 gram okay so try it again so here's another here's another little mini quiz this time you have have the density of a 1.40 g per cubic centimeter of an aspirin tablet and we don't care about the temperature that's just given in the problem because that's its density at that temperature and we want to know what is the volume of this 3.90 G aspirin tablet so go ahead and try it okay so again we're going to identify the important information okay so we are looking we have the density and we have the mass and we're looking for the volume okay using our triangle so here we have our volume that we're looking for we can see that that's mass divided by density okay so here's our rearranged equation and now we're going to plug everything in so 3.90 G divided 1.40 G per cenm cubed so both the grams are going to go away and we're going to be left with centimet cubed or CC's and the last step we need to go up here and look at our sigfigs so 1.40 this Zer is after this decimal point so that is significant so three sigfigs here same deal here with 3.90 gram so three sig figs there so we want to round this to three sig figs we're going to so one two three so we had would have 2.78 but this number is a five so that means we have to round this up so it's going to be 2.79 cm cubed