# Calculate the Mass of a Single Atom or Molecule

in this video we're going to learn how to

## calculate

the#### mass

of a### single

#### atom

or### molecule

what is the#### mass

in grams of a### single

#### atom

of silver to solve this problem we're going to have to pull in a few different pieces of information about moles the first is going to be about#### mass

because we're talking about the#### mass

of silver#### atom

s here so what do we know about the#### mass

of silver well we can look it up on the periodic table in this number here 107.9 tells us the molar#### mass

of silverit tells us how much one mole of silver weighs in grams so we can say that one mole of silver

#### atom

s weighs a hundred and seven point nine grams okay so that's what we know about the#### mass

of silver we're not talking about a mole of silver here though we're talking about a### single

#### atom

of silver so what do we know about say like the relationship between moles and the number of things in a mole well we know that one mole of silver#### atom

s contains 602 hexillion sulfur#### atom

s and this isoften abbreviated as 6.02 times 10 to the 23rd silver

#### atom

s now to solve this problem we want to take these two pieces of information and combine them to make a third piece it's going to be the most useful force okay here are the two things we know right we know that one mole of silver#### atom

s weighs this much and we also know how many silver#### atom

s 602 hexillion are in one mole so from these two pieces of information we can say that 602 hexillion silver#### atom

s 1 mol way 107.9 grams okay so nowwe know how much this number of silver

#### atom

s weigh okay we can even write this as kind of an equation a relationship and equivalence and from this relationship we can write two conversion factors one of these has grams on the top one of these has grams on the bottom but both of them can let us convert back and forth between the number of silver#### atom

s we have and their#### mass

in grams so we work through these pieces of information we're able to write this equation that then lets us write twoconversion factors that let us go from the number of silver

#### atom

s to grams we will use one of these conversion factors to go from one### single

#### atom

of silver to how much it would weigh in grams so let's see how we'll start that out okay we're going to do a conversion factor problem where we start with one silver#### atom

one silver app and we're going to want to multiply one silver#### atom

by one of these two conversion factors and the one we're going to choose is going to be the onethat's going to cancel out silver

#### atom

s which is on the top on this side of the equation okay so it's on the top here we're going to want it on the bottom so this one's not going to work because silver#### atom

s is on the top but this one is when we want okay so silver#### atom

s on the top cancels out silver#### atom

s on the bottom cancels out there and it's going to leave us with grams now that we've written this out we can solve it with a calculator you can type it in like this wewill get this out as our answer which is just the calculators way of saying this number times 10 to the negative 22nd and all we have to do now is just round this using significant figures because calculators don't do around it we're going to round this to three significant figures we don't worry about the number of significant figures in the one because it's a counting number it's not a measurement so we're going to do one point seven nine times ten to the negative

twenty second what are the units here they are grams and that is our final answer for the

#### mass

of a### single

#### atom

of silver and just to show you this not an exponential notation here is a decimal point and all the way over here one seven nine grams this is a tiny tiny tiny number it is how much a### single

#### atom

of silver weighs now let's look how to do this with### molecule

s instead of just#### atom

s what is the#### mass

in grams of a### single

### molecule

of water this is a lot like calculating the#### mass

of a### single

#### atom

except they're just a couple extra things to keep in okay so here's a water### molecule

h2o it's made up of two hydrogen#### atom

s and one oxygen#### atom

the first thing we want to do is figure out the molar#### mass

of h2o okay we want to know how much a mole of h2o### molecule

s would weigh in grams okay so to do that it's made up of hydrogen and oxygen so we look up hydrogen and oxygen on the periodic table here's a molar#### mass

of hydrogen here's the molar#### mass

of oxygen andwe're going to add them up okay so there are two hydrogen

#### atom

s in water so we do two times the molar#### mass

of hydrogen and then there's one oxygen#### atom

so we do one times the molar#### mass

of oxygen we add this up and we get eighteen point zero two which tells us the molar#### mass

and it tells us that one mole of h2o### molecule

s weighs eighteen point zero two grams now we know how much mole of h2o### molecule

s weighs in order to convert back and forth between number of### molecule

s and#### mass

we need toknow a little bit about the number of things in a mol which is 602 hexillion h2o

### molecule

s in one mole of h2o### molecule

s and as we did before with silver we can combine these two pieces of information to say that 602 hexillion h2o### molecule

s is one mole and it weighs eighteen point zero two grams we can express this as a relationship and we can use this to write two conversion factors both of these are based on this equation it's just one is the flipped version of the other okay so we gotthese two conversion factors that we can write from this information here and here's how we'll use it okay we're starting with one h2o

### molecule

and what I want to do is multiply that by the conversion factor that's going to get rid of h2o### molecule

s so I'm going to want to use the one that's with h2o here on the bottom so h2o### molecule

s cancels out h2o### molecule

s cancels out there it's going to leave me with grams and when I go through and do the math rounding to threesignificant figures I'm going to end up with two point nine nine times ten to the negative twenty-third grams here's just how you'd plug it into your calculator and the answer that you'd get and finally I always just like to emphasize that this number here isn't just some like weird Martian number with this 10 to the negative 23rd but it is actually a very very tiny number that if you have the time could be written out with lots and lots and lots and lots of zeros a tiny tiny

amount in grams the