Hello and welcome to NinetyEast. In this video, we'll be looking at how to calculate the relative atomic mass for a sample, and comparing
that to the standard atomic weight for the chemical element.
You'll remember from our previous video that the relative atomic mass is the average mass of an atom within that sample, irrespective of where
that sample comes from. So it could be from our planet, or from outer space; say for instance from another planet,
like Uranus.
The standard atomic weight on the other hand is the average atomic mass of an atom that's from a normal sample - and by normal we mean
something that you'd probably find in your science lab, or in industry - something that hasn't been significantly changed.
In this video, we'll work through three different examples, but you'll find in the description box below, a worksheet of exercises
that you can work through in your own time to consolidate your understanding.
Without further ado, let's get started. So our first example
is quite similar to what we used in our last video, but with with larger numbers.
We've got a given sample of 20,000 chlorine atoms, with two isotopes: chlorine-35 and chlorine-37.
If you remember from our last video, there's three things we need to know about a sample to work out the relative atomic mass:
the # of isotopes, their relative abundance and the atomic mass of each isotope.
Let's put in the numbers here. We've got the two chlorine atoms,
their relative abundance (the number of atoms of each),
and their atomic mass.
You probably also remember from our previous video, this equation here.
N1 = # atoms of isotope 1, or its relative abundance.
Ma1 is that isotope's atomic mass.
The 'number of atoms' is the number of total atoms - in this sample that's 20,000 chlorine atoms.
To make the most of this video, we suggest you press 'pause' and actually put these numbers into the equation to calculate the relative atomic
mass, and then compare it to what we've calculated.
So the numbers we've put into the equation look like this.
If you calculate that a little further along, it looks like this.
And the final numbers,
will look something like this;
where the relative atomic mass
is 35.459, or when reduced to four significant figures, 35.46.
Now let's compare that to the standard atomic weight of chlorine (35.45).
The numbers are almost identical which means that the sample here is pretty much a sample of normal chlorine atoms.
Let's look at our second example, and work out how to calculate the relative atomic mass when the abundance is expressed not as
'number of atoms', but as a percentage of the sample.
In this one we're looking at bromine atoms, and we've got 20% of atoms are bromine-81,
and 80% are bromine-79.
And this is the atomic mass or isotope mass of each atom.
Now we need to calculate the relative atomic mass.
To ensure that we can do that, we'll just make sure we've got all of the information: # isotopes, their relative abundance and their atomic mass.
Now we just need to look at the formula. It's a slightly different formula to the one we used in the last example.
Rather than N1, we look at F1. F1 is the fraction of an isotope within a sample.
If you'd like to work through the exercise by yourself first,
then pause the video here; otherwise let's get started. Let's plug our numbers in.
It looks like this, where 1/5 of the sample is made up of bromine-81,
and 4/5 is made up of bromine-79.
If we work out the multiplication here, these are the numbers that you should come up with.
And then the final atomic mass is 79.32
or if we reduce it down to two significant figures, 79.
Let's compare that now to the standard atomic weight of bromine, and that is 79.9.
While it looks similar to the value we've calculated for this sample, it's slightly different - that means that the sample is not a 'normal' one.
Ok let's move on to our last example. In this example we are going to be looking at
a sample that has got many different isotopes within it:
titanium-46, -47, -48, -49 and -50.
We've got their relative abundance up here which we can put down there to keep things nice and simple;
and the atomic masses for each isotope.
Because the abundances are given in %, we'll use the same equation that we used in the last example.
But because we've got five different isotopes here,
we need to extend this equation out to include five isotopes.
If you'd like to work through the exercise by yourself, pause here. Otherwise we'll plug in the numbers now.
So if you put the numbers carefully in, this is what you should come up with.
Do the multiplications, and this is what you should come up with.
Do the additions, and then you can work out that the relative atomic mass,
when reduced down to two significant figures, is 48.
The next question is, is this a normal sample? We just need to look at the standard atomic weight to decide that, and that is 47.86.
Compare the two numbers, then yes this is normal sample.
So, to review, the relative atomic mass of a sample is basically the average atomic mass in that sample;
whereas the standard atomic weight is the average atomic mass in a normal sample. And we've worked through three different examples.
As we've already mentioned, there is a worksheet down below that you can download and work through in your own time; if you have any
questions, please directly send us a message through YouTube, or email NinetyEastTV@gmail.com. Thanks everyone.