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Calculate the Mass of a Single Atom or Molecule

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 silver
calculate the mass of a single atom or molecule
it 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 is
often 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 now
we 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 two
conversion 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 one
calculate the mass of a single atom or molecule
that'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 we
will 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 and
calculate the mass of a single atom or molecule
we'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 to
know 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 got
these 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 three
significant 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

mass

of a

single

molecule

of water h2o