Video Transcript
How many grams of CaCl2 contain
15.0 grams of chlorine? Give your answer to one decimal
place.
The molar mass of chlorine is 35.5
grams per mole, and calcium, 40 grams per mole. CaCl2 is calcium chloride, so we
want to work out how many grams of calcium chloride contain 15.0 grams of
chlorine. Let’s call the unknown mass of
calcium chloride 𝑥. The ratio between the chlorine mass
and the calcium chloride mass is fixed. The two are directly
proportional. So if the mass of calcium chloride
was doubled to two 𝑥 grams, then the mass of chlorine would also double to 30.0
grams.
This is much like scaling
ingredients when making a cake. If a recipe states that a cake
requires 200 grams of sugar and you want to double the size of the cake, then you
need to double the amount of sugar you put in. So 400 grams of sugar would be
required for a cake twice the size. The ratio between the amount of
sugar used and the cake size is fixed. Let’s assume that the smaller cake
is 1000 grams and the larger cake is 2000 grams. We can represent the mass of sugar
as a fraction of the mass of the entire cake. Since the ratio is the same for the
small cake and the large cake, we can equate these fractions.
We need to work out the ratio
between the mass of chlorine and the mass of calcium chloride. We can do this by using the molar
masses which have been given to us in the question. The molar masses tell us how many
grams of a substance there are in one mole. So we can work out the mass of
chlorine and the mass of calcium chloride in one mole. This will enable us to work out the
ratio between them. The molar mass of chlorine is 35.5
grams per mole, and calcium chloride contains two equivalents of chlorine. So in one mole of calcium chloride,
there are two times 35.5 grams of chlorine. This gives 71 grams.
Now that we know the mass of
chlorine in one mole of calcium chloride, we can work out the mass of calcium
chloride per mole. There is one equivalent of calcium
in calcium chloride, and calcium has a molar mass of 40 grams per mole. So if we add one times 40 grams to
the mass of chlorine, which we’ve already established is 71 grams, then we get 111
grams. So now we know that one mole of
calcium chloride is 111 grams.
Just as with the cakes, we can
write the mass of chlorine as a fraction of the mass of calcium chloride. And since the ratio between
chlorine and calcium chloride is fixed, we can equate these fractions. Now we want to make 𝑥 grams of
calcium chloride the subject. To do this, we need to multiply
both sides by both denominators and then divide both sides by 71 grams. If we do this calculation, we find
that 𝑥, which is the number of grams of calcium chloride, is 23.45.
But the question asks for the
answer to be given to one decimal place. 23.45 to one decimal place is 23.5,
so 23.5 grams of calcium chloride contain 15.0 grams of chlorine. So the answer to the question is
23.5 grams.
