### Video Transcript

A 500-milligram tablet of
paracetamol, C8H9NO2, was dissolved in 200 milliliters of water. What is the concentration of the
resulting solution? Give your answer in units of moles
per decimeter cubed and to two significant figures.

This question is asking us to work
out the concentration of a solution. In order to do this, we’re going to
need a key equation. Of course, the equation we need is
𝑛 equals 𝑐𝑣, where 𝑛 is the number of moles, 𝑐 is the concentration, and 𝑣 is
the volume. We’re given the value of 𝑣,
volume, in the question as 200 milliliters. However, the question specifically
asks for our answer in units of moles per decimeter cubed. So we’re going to need to do some
unit conversion. Remember that decimeters cubed are
exactly the same as liters. So you can imagine giving our
answer in units of moles per liter.

But the volume we’re given is in
milliliters. So we’re going to need to convert
our milliliters into liters. To convert milliliters to liters,
we need to multiply by one liter per 1000 milliliters. You can remember that there are
1000 milliliters per liter by remembering that the prefix milli- means
thousandth. Performing this conversion gives us
0.2 liters. As a side note, remember that
milliliters are exactly the same as centimeters cubed. Now that we have our volume in the
right units and we know that we’re working out the concentration, we just need to
find the number of moles, 𝑛.

However, in the question, we’re not
given the number of moles. Instead, we’re given a mass in
milligrams. So we’re going to need to convert
our mass into the number of moles. To do this, we need another key
equation. The equation we need is moles
equals the mass divided by molar mass, where our units are moles, grams, and grams
per mole. So the first thing we need to do is
convert our mass from milligrams into grams. Converting from milligrams to grams
is very similar to converting milliliters to liters in that we multiply by one gram
divided by 1000 milligrams. So converting 500 milligrams into
grams, we multiply by one gram per 1000 milligrams, leaving us with 0.5 grams.

Now we can begin to work out the
number of moles. From our second key equation, we
know that the number of moles equals 0.5 grams divided by the molar mass of
paracetamol. To work out our molar mass, we need
the periodic table and the formula for paracetamol given in the question. We can see that it contains eight
carbon atoms, nine hydrogen atoms, one nitrogen atom, and two oxygen atoms. So to get our molar mass, we add
the masses of eight carbons, nine hydrogens, one nitrogen, and two oxygens
altogether, which gives us a molar mass of 151.165 grams per mole.

We can now use this to work out the
number of moles of our paracetamol. So 𝑛 equals 0.5 grams divided by
151.165 grams per mole, which gives us 0.0033076 moles. Now that we have both 𝑛 and 𝑣, we
can use 𝑛 equals 𝑐𝑣 to give us the concentration. Rearranging our equation in terms
of 𝑐, we get 𝑐 equals 𝑛 divided by 𝑣. By inputting our values, we get
concentration equals 0.0033076 moles divided by 0.2 liters. This works out at 0.016538 moles
per liter.

However, we’re not finished
yet. The question asks for our answer to
be given to two significant figures and with units of moles per decimeter cubed. Rounding to two significant figures
gives us 0.017. And since liters are the same as
decimeters cubed, we don’t need to do anything regarding units. We can simply write the units as
moles per decimeter cubed. And this is our final answer.