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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
