# Very Common Mole Questions

in this video I want to talk about two

types of

## questions

#### mole

s these two types of

## questions

don't really fit into the other categories we've talked about do they show up all the time on homework in textbooks on quizzes and particularly on tests and exams ok here's the first one what is the mass in grams of a single atom of oxygen ok this is a type of question it asks us to calculate the mass of a single atom of some element here we're going to use oxygen as the
example now in order to solve problems like this we've got to pull in a few different pieces of information about

#### mole

s ok the first one is going to be about maths right we're talking about the mass of a single atom of oxygen what do we know about the mass of oxygen well we can look up oxygen on the periodic table and we can zoom in to this number 16.00 which tells us the molar mass of oxygen it tells us how much a

#### mole

of oxygen ways in grams so we can say that from this information on
the periodic table 1

#### mole

of oxygen atoms ways 16.00 grams ok but we're not talking about a

#### mole

of oxygen atoms we're talking about a single ad of oxygen one oxygen atom so what do we know about say like the number of oxygen atoms in a bowl well you may know that one

#### mole

of oxygen atoms contains 602 hex fillion oxygen atoms which we often abbreviate is six point 0 2 times 10 to the 23rd now we want to combine these two pieces of information to make a third piece of information ok check
this out we know two things here on the one hand we know that one

#### mole

of oxygen atom of oxygen atoms ways 16.00 grams and we also know that one

#### mole

of oxygen atoms contains 602 hex fillion oxygen atoms so we can combine these two pieces of information to say that 602 xilion oxygen atoms way 16.00 grams ok we can even take this and express it kind of as an equation kind of as relationship here we can say six point 0 2 times 10 to the 23rd oxygen atoms equals or is equivalent to 16 grams now
check out this last thing that I drew okay this thing here is an equation a relationship that we can turn into a conversion factor that will let us go from the number of oxygen atoms we have two grams okay so I'm going to use this equation as a conversion factor to go from one oxygen atom to a certain number of grams here's how I'm going to do it let's start here I'm going to do one oxygen atom and now i'm going to multiply that by a conversion factor made from this
relationship i want to get rid of oxygen atoms which is on top here so i'm going to write this relationship as a conversion factor with oxygen atoms on the bottom okay so i'm going to take this part here 6.02 times 10 to the 23rd oxygen atoms put that on the bottom and make my fraction here a little bit longer and then I'm going to put the other side of the relationship 16.00 grams on top and now when I work through the math here oxygen atoms on the top oxygen atoms on the bottom
they're going to cancel out and that's going to leave me with grams which is exactly what I want just going to rearrange this so we can go through the math okay so you write this out you probably want to solve it by putting it into the calculator you can type it in like this although you don't really have to multiply by one here because multiplying something by one doesn't change its value but it's totally up to you you put this in your going to get this out as an answer this
e- 23 and calculator language just means this times 10 to the negative twenty third and then we're going to want to take this number and round it to three significant figures we don't worry about the significant figures in one here because this is a counting number we're saying one oxygen atom it's not a measurement so this has an infinite number of significant figures we're gonna round this to three significant figures because there are three and six point 0 2 which has a
fewer number so you can configures so we round this to two points we have the five here we round it up because the 72.6 six times ten to the negative twenty third and what are our units they are grams that's what we were left over with after the conversion factors here is our final answer in scientific notation and if we write this out in regular decimal notation we can see that it is a tiny tiny tiny number two point six six times ten to the negative 23rd grams then the the mass of a single
atom of oxygen okay so the key to solving that problem is being able to take this information and write conversion factors with it okay we knew that one

#### mole

of oxygen wait this much and we know how many oxygen atoms are in one

#### mole

so we could take that information and write these two conversion factors it could let us go from number of oxygen atoms to grams and back and forth what mass of mercury has the same number of atoms at 64.2 grams of calcium I don't know about you but i find the
wording in this question really confusing so I want to try to explain like what they're actually trying to ask here so you can understand how to solve okay so we got mercury and we got calcium we can look them up on the periodic table and this number here the molar mass tells us how much a

#### mole

of each of these types of atoms would wet okay so mercury here we know that one

#### mole

of mercury atoms 602 xilion mercury atoms would weigh 200 point 6 grams and for calcium here one

#### mole

of calcium
atoms 602 heck silicon calcium atoms weighs forty point zero eight grams okay so here's the main point the main point is that 200 point six grams of mercury and forty point zero eight grams of calcium both have the same number of atoms okay the masses are different this weighs a whole lot more this is a lot lighter but the point is even though the masses are different the number of atoms is the same to 602 hexylene mercury atoms weigh this much and 602 xilion calcium atoms weigh this much
okay so we can say this amount of mercury and this amount of calcium have the same number of atoms in okay what the question is really asking it's sort of like X grams of mercury and 64.2 grams of calcium have the same number of atoms right that's not really a question but it's a statement okay it's like what amount of mercury has the same number of atoms 64.2 grams of counts okay this amount of mercury and this amount of calcium have the same number of atoms this amount of
calcium and how much mercury have the same number of atoms okay so here's how we're going to solve it we can do two steps step one we're going to ask how many atoms are in 64.2 grams of calcium and then we're going to take that number of atoms that are in this amount of calcium and we're going to ask if we had that number of mercury atoms how much would that way so let's start here with part one okay so i'm going to start here with 64 points 2 grams of calcium and now
i want to figure out how many atoms are in so i'm going to multiply it by a conversion factor that i can make from this information here i want to get rid of grams so i'm going to put grams on the bottom i'm going to do 40 points 08 grams of calcium and then on the top i'm going to put 6.02 times 10 to the 23rd atoms okay so now we got grams calcium here grams calcium here they're going to cancel out I'm going to be left with atoms atoms of calcium can put this into the
calculator i get this out as my answer i'm going to round it to three significant figures so i'm going at nine point six four times 10 to the 23rd okay 9.64 times 10 to the 23rd calcium out of it this how many calcium atoms aren't this much calcium now the next thing that I want to do here is asked if we had that number if we had this number of mercury atoms how much would that way okay so we have this many calcium atoms if we had that much of mercury how much would that way okay so
here's how we do that we're going to take this and we're going to multiply it by a conversion factor that we can write from this information that tells us about how much a certain number of mercury atoms fine okay so we're going to multiply that by six point 0 2 times 10 to the 23rd and do hg mercury atoms on the bottom and then multiply it by 200 point six grams of mercury on top and now mercury atoms on the top mercury atoms on the bottoms cancel that I'm left with grams of
mercury the math I'm going to do is this I get this out of the calculator and my final answer rounded to three significant figures is 321 grams of mercury and that tells us how much mercury what massive mercury would have the same number of atoms as 64.2 grams of calcium