### Video Transcript

Which of the following is not equal
to Avogadro’s number? (A) The number of atoms in 4.48
liters of CH4 at STP. (B) The number of molecules in one
mole of CO2. (C) The number of Cl− ions in one
liter of 1.0-molar hydrochloric acid. (D) The number of electrons with a
combined charge of negative 96,500 coulombs. (E) All of the other answers equal
Avogadro’s number.

Avogadro’s number is equal to 6.022
times 10 to the 23. This number is equivalent to the
number of entities that are in one mole of something. So, for example, one mole of
molecules contains 6.022 times 10 to the 23 molecules. In this question, we need to figure
out which answer choice is not equal to Avogadro’s number. And since Avogadro’s number is
equivalent to the number of entities in one mole, we need to figure out which answer
choice does not contain one mole.

So let’s take a look at our first
answer choice, which is the number of atoms in 4.48 liters of CH4, or methane, at
STP. STP stands for standard temperature
and pressure, which is defined as zero degrees Celsius and one bar of pressure. To see if this answer choice
contains one mole, we’re going to use the fact that at STP, all ideal gases have a
molar volume equal to 22.4 liters per mole.

The molar volume is simply the
volume that the gas occupies divided by the amount of gas particles in moles. We need to find the amount of CH4
particles that we have in 4.4 liters in moles, which we can do by dividing the
volume that was given by the molar volume. So we’ll need to divide 4.48 liters
by 22.4 liters per mole. This looks a little bit tricky, but
22.4 divided by 4.48 is equal to five. So we have one-fifth of a mole of
methane molecules in 4.48 liters of methane.

Now, we need to figure out the
number of atoms that are in this amount of methane. And as we can see from methane’s
formula, for every one mole of methane molecules that we have, we would have one
mole of carbon and four moles of hydrogen atoms. Which gives us a total of five
moles of atoms for every one mole of methane molecules.

So now we just have to multiply
one-fifth by five, which gives us one mole of atoms. So there’s one mole of atoms in
4.48 liters of CH4 at STP, which means that answer choice (A) is equal to an
Avogadro’s number of atoms. So answer choice (A) does contain a
mole. So it’s not the answer choice we’re
looking for.

Our next answer choice is the
number of molecules in one mole of CO2, or carbon dioxide. We don’t have to do any math for
this answer choice, since one mole is an Avogadro’s number of molecules. So we would have one mole of carbon
dioxide molecules. So answer choice (B) is equal to an
Avogadro’s number.

Our next answer choice is the
number of Cl− ions in one liter of 1.0-molar hydrochloric acid solution, which has
the chemical formula HCl. When we have a solution of
hydrochloric acid, it will disassociate into H+ ions and Cl− ions. Since molarity is defined as the
amount of the substance in moles per liter of solution, we can find the amount of
HCl that we have in moles by multiplying the concentration by the volume. So we have one mole of HCl in the
solution.

As we can see from the
stochiometric coefficients in our balanced chemical equation, every one mole of HCl
will dissociate into one mole of Cl− ions. So since we have one mole of HCl,
we’re going to end up with one mole of Cl− ions in the solution. So there’s one mole of Cl− ions in
one liter of a 1.0-molar hydrochloric acid solution. Since we have a mole of Cl− ions,
that means we have an Avogadro’s number. So this isn’t the correct answer
choice either.

So, that just leaves us with our
final answer choice, which is the number of electrons with a combined charge of
negative 96,500 coulombs. To think about this statement,
we’ll use Faraday’s constant, which tells us the magnitude of electric charge per
mole of electrons. And it’s equal to 96,485 coulombs
per mole.

Faraday’s constant tells us the
magnitude of electric charge, which is why the constant is a positive value even
though the electron has a negative charge. As we can see, this number is
approximately equal to the negative 96,500 coulombs that we have in statement
(D). Which means that the number of
electrons that have a combined charge of negative 96,500 coulombs must be
approximately one mole of electrons, which again is equal to an Avogadro’s
number. So this statement is not the
correct answer choice either.

Since all of the statements had one
mole of particles, which means they were all equal to an Avogadro’s number, that
means answer choice (E) must be the correct answer.