What I'm about to go over is going to feel very basic
and you may be tempted to skip it but please do not.
Knowing this basic concept will do wonders for your understanding in
Chemistry and will save you from making a lot of
common mistakes. Now let's review two basic math terms.
A multiple is the result we get from multiplying two whole numbers together.
The least common multiple is the smallest multiple that is common to two
or more numbers. For example one we are asked to find the
least common multiple of 2 and 3. To find the least common multiple
start with finding the multiples of each number.
To find the multiples of 2 we would simply multiply 2 times different whole
numbers like these. So two times one is two, two times two is
four, two times three is six ,two times four is
eight and so on. Do the same thing for our other number
which is three. So three times one is three, three times
two is six, three times three is nine, three times
four is twelve and so on. Now that we've found our multiples of
each number we'll look for the smallest number that
both lists of multiples have in common. The smallest number both lists share is
six thus six is our least common multiple. Go ahead
and try this next example out on your own.
Let's go over the answer. We'll start with finding the multiples of each
number so two times one is two, two times two is four, two
times three is six, two times four is eight and so on. We'll
do the same thing for our other number which is four
so four times one is four, four times two is eight,
four times three is twelve, four times four is sixteen and so on.
Both lists have a four and an eight but we are looking for the smallest number
that both lists have in common therefore our least common multiple is
four. There are two main chemistry topics
where knowing how to find the least common multiple will be
very helpful these topics are naming compounds and redox reactions.
Let's start with naming compounds which is also referred to as nomenclature.
You will typically be asked to write the chemical formula from the compound name.
We specifically will use the least common multiple to help balance
charges and you only balance charges for ionic compounds.
An ionic compound consists of a metal and a non-metal,
where metals have positive charges and non-metals have negative charges.
For charges to be balanced they must be the same number but have
opposite signs. Let's find the least common multiple using the charges as our
numbers. We'll start with finding the multiples of each number
so two times one is two, two times two is four, two times three
is six. Do the same thing for the three so
three times one is three, three times two is six and we can stop here
since both lists have a 6 and that is the smallest number that both lists have
in common thus 6 is our least common multiple. This
means that we want both charges to be 6. To balance charges
we add subscripts to the element that needs its charge to change. In this
example we want both charges to change to 6
so the subscript for iron will be 2 because for
this charge of 3 to become 6 it needs to be multiplied by 2.
Same concept goes for the oxygen the subscript for oxygen would be 3 because
for this charge of 2 to become 6 it needs to be multiplied by 3. We
just found our chemical formula and note we do not include charges the charges
are there to help determine the subscripts of the chemical formula.
Here's another example, where we again need to balance the charges to find the
new subscripts of the chemical formula. Let's find the least common multiple
using the charges as our numbers we'll start with finding the multiples
of each number so two times one is two, two times two is four. Do the same thing
for our other number of one so one times one is one, one times two is
two and we can stop here since both lists have a 2 and that is
the smallest number that both lists have in common
thus 2 is our least common multiple. This means we want both charges to be
2. Again to balance charges we add subscripts to the element that needs its
charge to change. In this case only one element needs to
change since the calcium already has a charge of two so the only
element that needs a subscript is the chlorine.
We'll place a two subscript on chlorine because for this
charge of one to become two it needs to be multiplied by two.
This is our chemical formula. Alright how about you try this one
on your own using the same steps we went
over. If you said pb2o4 you just made a common
mistake and this is exactly why finding the least common
multiple will help you avoid making this mistake. So let's find the
least common multiple using the charges as our numbers. We'll
start with finding the multiples of each number so two times one is two, two times
two is four. Do the same thing for our other number of four
so four times one is four and we can stop here
since both lists have a 4. This means we want both
charges to be 4. Again to balance charges we add subscripts to the element
that needs its charge to change in this case only one element needs to
change since the lead already has a charge of
four so the only element that needs a subscript is the
oxygen. We'll place a two subscript on oxygen because for this charge of two to
become four it needs to be multiplied by two and
this is the correct chemical formula. Now do you have to go through these
steps every single time and find the least common multiple?
No. If you do this enough times you will be able to balance these charges
in your head, which should be your goal. The main thing I want you to understand
is how we figure out the subscripts for the chemical formula
but if for any reason you aren't sure then I do recommend
finding the least common multiple first. The second chemistry topic that uses a
least common multiple is in redox reactions. Redox reactions
are a type of reaction where electrons are being gained and
lost between two reactants. A redox reaction undergoes two processes
at the same time. The first process is oxidation
which is the loss of electrons and the second process is reduction which is the
gaining of electrons. We use something known as oxidation
numbers or oxidation states to help us determine which reactant
undergoes oxidation or reduction. Note how to find oxidation numbers will
be explained later in this learning playlist.
When balancing redox reactions there is a step where you need to balance the
electrons of the half reactions. Note a redox reaction can be split apart
to show each process these are called half
reactions. Where we only show the elements or
chemical species involved in oxidation and in reduction.
We find our electrons from the oxidation numbers. We subtract the product's
oxidation number by the reactant's oxidation number of the same element.
That's how we got our three electrons for oxidation and our two electrons for
reduction and it's fine that this is positive
electrons are already negatively charged. We are only looking for the positive
values, we'll place the electrons for oxidation
on the product side of their half reaction,
while the electrons for reduction go on the reactant side.
Now it's time to use the least common multiple to help us balance these half
reactions. We want the electrons to be the same
number. Let's find the least common multiple
using the electrons as our numbers. We'll start with finding the multiples of each
number so three times one is three, three times two
is six. Do the same thing for our other number
of two so two times one is two, two times two is four, two times three is
six and we can stop here since both lists have a six this
means that we want both electrons to be six. To balance the
electrons we will multiply the entire half reaction by
two because for these three electrons to become a six
we need to multiply them by two. Same concept goes for this
other half reaction we will multiply by 3 for these two electrons to become a 6.
We'll distribute the 2 to each coefficient. If there is no coefficient
then assume it is 1. And this is our new half reaction for oxidation.
Do the same thing for reduction, distribute the three to each coefficient
and here's our new half reaction for reduction.
Add both half reactions together to get our balanced redox reaction
and you'll know if you did this correctly if the electrons are the same
on opposite sides and cancel out. This is our balanced redox reaction.
I've seen so many students struggle with this because they simply don't practice
that's why I've made it so much easier for you to practice along with me.
Head over to melissa.help/practice to find practice problems specifically for
what you just learned and once you get through them all come
back for the next video.