In this video you're finally gonna
understand what an isotope is and how to
calculate percent abundance. All right
let's do this.
Hello hello Melissa Maribel here
and I help students like you understand
what you just learned in class so you
stress less and you graduate faster.
Before we get started let's take a deep
breath. It's gonna be a lot easier than
you think.
Starting with our first example let's
just talk about the concept of isotopes.
So back in 2009 I weighed a hundred and
twenty pounds. Then in 2012 I weighed a
hundred and thirty pounds and then in
2015 when I discovered my love for sushi
I weighed a hundred and forty pounds. So
even though there were different weights
or different versions of myself, I am
still the same person. Isotopes are
different versions of the same element.
So how does this relate back to
chemistry. Let's talk about gold. The
chemical symbol for gold is Au. Take
this gold bar, it weighs 196 amu. Our
second gold bar weighs 197 amu and our
third gold bar weighs 198 amu. All of
these gold bars have different weights
but are made out of the same element
which is gold. These are three different
types of isotopes of gold. If we were to
look at the periodic table and look for
where Au is or Gold, we'd see it has a
bottom number, right? That atomic mass.
That atomic mass is actually the average
of all the different types of isotopes
of that element. Isotopes have the same
atomic number, the same protons and
electrons.
However, they do not have the same masses.
So they have different masses and a
different number of neutrons. Let's go
into our first example talking about
percent abundance. A certain element X
has four isotopes 0.5600% of X
has a mass of 83.91343 amu. Second
isotope, 9.860% of X has a mass of
85.90927 amu. our
third isotope,
7.000% of X has a mass of 86.90890 amu and
our last isotope 82.58% of X has a mass of
87.90562 amu. Find the average atomic mass of
element X. You have four different
isotopes, those are our givens. That
0.5600% of our certain
amount of mass. So this is what we refer
to as percent abundance, where we have a
certain amount of percent of our first
isotope of a mass. So you see it changes
for every single isotope, however, if we
were to add up all the percentages, it's
always out of a hundred percent. In this
example, you are finding your average
atomic mass. Step one is to convert all
percentages to decimals by dividing by 100. Your first given 0.5600.
We'll divide that by 100.
And you get 0.005600
There's a trick for this.
What we can instead do is move the
decimal place over twice to the left
for every single percentage to get our
decimal form and we'll see we keep doing
this and it gives us our answer. Moving
on we'll jump to our actual percent
abundance formula where our atomic mass
is equal to the percentage converted to
a decimal, times, the mass of that
specific isotope and we'll keep adding
every different type of isotope. Since we
have four isotopes,
I went ahead and added our first decimal
form of that percentage multiplied by
the mass of that first isotope and kept
doing that for every single isotope
since we have four. Looking at this first
portion we'll multiply 0.005600,
times the mass
of 83.91343
and that gives us 0.469915. We would
then do this for every single isotope
and you'll get this. We'll add them all
together,
that'll give us
87.616626 amu. The reason why
we're going to round to only four sig
figs is because going back to our given
we actually only had four significant
figures, 82.58 is
four sig figs, same with 7.000
and you'll see that every
single one actually has four sig figs. So
we'll round up and our final atomic mass
is 87.62 amu.
In the second example we are solving for
percent composition or percent abundance
we're no longer solving for the average
atomic mass.
Naturally occurring copper consists of Cu at 63, this is just the
isotope notation, where our mass is equal
to 62.9296 amu and our second isotope, copper at 65,
which our mass is 64.9278 amu, quick note, they're just
rounding here. This is the mass number
but they do give us the exact mass
amount. Continuing with this question,
with an average atomic mass of
63.546 amu. What is
the percent abundance of copper in terms
of these two isotopes? You're given, are
the two different types of isotopes so
we're really just focusing on our masses
that are exact in this case. This is just
the proper notation that they typically
have it, but as mentioned we're just
focusing on these masses. We're also
given the average atomic mass of
63.546 amu and we're
asked to find the percent composition of
copper. What they're actually referring
to here is, they're saying how much of
this isotope, what percentage, is within
our atomic mass? So we're really looking
for two different percentages for our
two different isotopes. Using our percent
abundance formula once more, our atomic
mass is equal to that percentage however
we don't know what the percentage is of
our first isotope. So in that case we're
actually just going to refer to this as
X. I also went ahead and placed what we
do know which was that atomic mass. So
referring to this percentage as X, it's
just a way to be able to figure out what
X is towards the end. Our mass of our
first isotope was this. And next we once
again do not know what the second
percentage of our isotope is. So what
we'll do is we'll subtract it from 1.
What 1 refers to is really saying, it's
out of a hundred percent so if we don't
know what X is, we'll then subtract it
from 1 or a hundred percent and that
would then give us our second percentage
of our isotope. We'll multiply this by
our mass of our second isotope. Next,
going back to math,
let's go ahead and actually distribute
this mass to both the one and that
negative X. When we do this we end up
getting this, and you want to group your
X's together so we'll combine these two
X values. We're actually subtracting
since this is a negative 64.9278. When we do that we end
up getting negative 1.9982x. From there we want to
isolate our x value. So we'll subtract
over that 64.9278
to both sides.
These would then cancel and subtracting
these two we get a negative 1.3818.
 And we want to
isolate that X by itself, so we'll get
rid of that negative 1.9982
by dividing it for both sides.
Those would then cancel and our x value
gives us a positive value of 0.6915. That was just for our
first isotope which was that copper at
63. For our second isotope what
we'll do is, taking that 1 minus X,
we're actually going to subtract this x
value from the 1 and that would then
give us 0.30847.
The next step is to multiply both
of these decimals by 100. The
reason is because we want this to be a
percentage, so multiplying this by
100 turns it into our percentages.
We'll see that our first isotope, that
copper 63, has a percentage of 69.15%. Our second isotope,
where copper 65, has a percentage of
30.85%. These
are our percent compositions of our
isotopes. Now that we've worked on two
possible exam questions,
hint hint, it's your turn to see if
you're ready for your exam. Musica maestro!
So are you ready for your exam? As a
tutor, I always tell my students to do
these practice problems, to get them down,
because I do see them on exams over and
over again. Teachers like to reuse their
exam questions, so if you feel like
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