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in this example problem

we have chlorine which has two isotopes

shown in the table below

chlorine 35 and chlorine 37

we're given the percent abundance of

each isotope

and also

the atomic mass of those two isotopes

so using that data

how can we calculate the average

atomic mass of chlorine

now it turns out that there's a simple

formula that we need to use

so the average atomic mass

will be equal to the mass of the isotope

times the percentage in its decimal form

plus

the mass of the second isotope

times the percentage

and if you have multiple isotopes this

formula can continue

but since we only have two we're going

to stop here

so the mass of the first isotope

is 34.96

amu atomic mass units

now the percentage is 75.76

we need to divide that number by a

hundred

or you can move the decimal point

two units to the left

so it becomes point

seven five

seven six

now the mass of the second isotope

chlorine 35 i mean not that one but

chlorine 37

it's

36

times the percentage as a decimal which

is 0.2424

so go ahead and type this in your

calculator

34.969 times 0.7576

and then plus

36.966 times

0.2424 should get this answer

35.453

and so this

is the average atomic mass

of chlorine

so this is the basic formula that you

need to use in order to get the answer

now let's move on to the next problem

magnesium

has three stable isotopes

magnesium 24 magnesium 25 and magnesium

26.

given the average atomic mass of

magnesium

it's uh 24.305

which isotope is most abundant

would it be mg24 mg25 or mg26

now keep in mind this number

is an average

it's the average atomic mass

of

the masses of these elements

so which number is closest to 24.305

the answer is 24.

so because this particular isotope

is closest to the average atomic mass

this one

is most likely to be

the most abundant isotope of magnesium

and it's just as simple as that

the isotope whose mass is closest to the

average is usually the one that's going

to be the most abundant isotope

now here we have a longer problem

iron metal has four stable isotopes as

shown in the table below

determine the average atomic mass of

iron

feel free to pause the video if you want

to try this so i'm going to give you a

few minutes to work on it

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so now let's get back to this lesson

so to calculate the average

we need to use this formula

so we have four stable isotopes

so we need to go up to m4 p4

now the mass of the first isotope that's

53.9396

and then we're going to multiply it by

the percentage that corresponds to it

and don't forget to divide that number

by a hundred

so that's going to be .05845

now the mass of the second isotope

is 55.9349

and let's multiply that by

if we divide that by 100 that becomes

point nine one

seven

five four

now for the next one

m3 it's going to be 56.9354

times the percentage which is 0.02119

and finally for the last one it's 57.933

and then if we divide this by 100

that's going to be

0.00282

so go ahead and type

all of that into your scientific device

this might take me a while so

just uh bear with me for one moment

and just be careful not to uh mistype a

number because if you make a little

mistake here that changes the entire

problem

so the answer that i got

is 55.845

so that is the average atomic mass

for iron metal

in atomic mass units which is equivalent

to

grams per mole

now let's think about the number that we

have

in the last example we saw that

the element

or isotope that is most abundant is the

one whose mass is closest to the average

so fe 56

is the most abundant

isotope

91.754

of iron metal consists of this isotope

and notice that the average

is very close to fe 56

because it's the most abundant one there

and so you can see how that makes sense

particularly with this example

and uh the other example

so i'm going to stop here that's it for

this video so now you know how to

calculate the average atomic mass of an

element

simply by using this formula so thanks

for watching