Video Transcript
A sample of cobalt(II) chloride
hydrate CoCl2โ
๐ฅH2O is heated until its mass remains constant. For every 1.00 grams of cobalt(II)
chloride produced, 0.831 grams of water is liberated. What is the value of ๐ฅ, where ๐ฅ is
an integer? And we are given the molar mass of
cobalt, 59 grams per mole; for chlorine, 35.5 grams per mole; for hydrogen, one gram
per mole; and oxygen, 16 grams per mole.
We are told that a hydrated salt,
cobalt(II) chloride, is heated until constant mass. The name cobalt(II) chloride
hydrate and the formula do not tell us how many molecules of water they are per unit
of cobalt chloride. We are only told the number of
moles of water of crystallization in terms of x. Heating a hydrated salt to constant
mass typically involves heating a salt strongly in a crucible with the lid off to
allow the water of crystallization to escape.
The reaction equation for this
process is CoCl2โ
๐ฅH2O solid being heated to give CoCl2 solid plus ๐ฅH2O gas. Over time, all the water of
crystallization is removed. The hydrated salt is converted to
an anhydrous salt. An anhydrous salt contains no water
of crystallization. During cooling and weighing, the
lid of the crucible must be in place, and this is to prevent water vapor from the
air reentering the crucible.
This is important because this
reaction is reversible, and we want to prevent the reverse reaction from
occurring. Otherwise, the masses of each
substance are unknown. We need to ensure that cobalt(II)
chloride is indeed fully anhydrous. To solve this problem, we can put
the data that we are given and that which we need to find into a table. This table is not absolutely
necessary, but sometimes it helps when we are dealing with a lot of information.
We are told that for every 1.00
grams of cobalt(II) chloride produced, so letโs put this mass into the table under
CoCl2, 0.831 grams of water is liberated. And so, this is the mass of
water. The words โfor everyโ tell us that
1.00 grams of cobalt(II) chloride and 0.831 grams of water are not necessarily the
actual masses of these substances produced, but rather the ratio in which they are
produced.
We know that the stoichiometric
coefficients one as to ๐ฅ is the mole ratio of these substances. So first, we need to convert the
masses of these products to moles. We start by calculating the molar
mass of cobalt(II) chloride, which is equal to the molar mass of cobalt plus two
times the molar mass of chlorine since there are two chlorines. Substituting in the molar mass of
cobalt, which was given to us 59 grams per mole, and that of chlorine, 35.5 grams
per mole, we get a molar mass of cobalt(II) chloride of 130 grams per mole. We can put this value into the
table.
The molar mass of water is equal to
two times the molar mass of hydrogen because there are two hydrogens plus the molar
mass of oxygen, and these values are given to us. So, substituting one gram per mole
for hydrogen and 16 grams per mole for oxygen, we get 18 grams per mole, the molar
mass of water, which we can put into the table.
The next step is to calculate the
number of moles of cobalt(II) chloride and water. We can use the key equation number
of moles is mass divided by molar mass. So, for cobalt(II) chloride, taking
its mass and molar mass from the table, we get 1.00 grams divided by 130 grams per
mole, which is equal to 0.00769 moles. For water, the number of moles is
equal to its mass, 0.831 grams, divided by its molar mass, 18 grams per mole, which
gives 0.04616 moles.
Since the ratio of the moles of
cobalt(II) chloride as to water are the same as the stoichiometric ratio one as to
๐ฅ, we can now solve for ๐ฅ. How we do this is we take the moles
of cobalt(II) chloride as to the moles of water and divide each value by the moles
of cobalt(II) chloride. These two values cancel, giving us
one. The moles units cancel on both
sides, and solving this division here, we get 6.00166.
So far, in this calculation, we
have not rounded off, but now it is time to do so. We need to round off to a value
with no decimal places since ๐ฅ cannot be a fraction. We cannot have a fraction of a
water molecule. And we are specifically told that ๐ฅ
is an integer. Finally, we get an answer of one as
to six. And this is the mole ratio of
cobalt chloride as to water. These values are also the
coefficients in the hydrated compound formula. Therefore, the value of ๐ฅ is
six. And the formula of the hydrated
compound is CoCl2โ
6H2O, which is cobalt(II) chloride hexahydrate.
