Video Transcript
A student is attempting to
determine how many water molecules there are in the hydrate CoSO4⋅𝑥H2O, where 𝑥
is an integer. The student weighs a sample of the
compound and heats it until the mass remains constant. Using the experiment results below,
determine the value of 𝑥. The molar mass of cobalt is 59
grams per mole, sulfur is 32 grams per mole, oxygen is 16 grams per mole, and
hydrogen is one gram per mole.
In this question, we are told that
we have a sample of cobalt(II) sulfate hydrate. The word hydrate tells us that we
have a hydrated salt. A hydrated salt is a substance that
contains water of crystallization. Water of crystallization is the
presence of water molecules within the structure of a crystal. We can see from the chemical
formula that for every one unit of cobalt(II) sulfate in the crystal structure,
there are 𝑥 molecules of water associated with it.
Our job in this question is to find
the coefficient of H2O, which is represented by 𝑥. One way to determine the amount of
water of crystallization is through volatilization gravimetry, which is a mass
analysis method that uses thermal or chemical energy to separate substances in order
to measure the masses of their components.
In the question, we are told that
the hydrated salt is heated until its mass remains constant. When looking at the data table, we
can clearly see that the mass of the sample decreased after being heated. The student starts with 4.97 grams
of the hydrated salt. After heating, 2.74 grams of
anhydrous salt remains. The decrease in mass occurs because
water has been removed during heating. The mass of water lost can be
calculated as the difference between the mass of the sample before heating and the
mass of the sample after heating.
After substituting in the mass
values from the table, we get 4.97 grams minus 2.74 grams, which equals 2.23
grams. Therefore, 2.23 grams of water were
lost during heating.
Now in order to determine the value
of 𝑥, we need to find out the ratio between the number of moles of water and the
number of moles of cobalt(II) sulfate, or CoSO4. Let’s start by converting 2.23
grams of water to moles of water. And after that, we can convert 2.74
grams of CoSO4 to moles of CoSO4.
In both of these steps, we can use
the following formula, where 𝑛 is the number of moles, lowercase 𝑚 is the mass in
grams, and uppercase 𝑀 is the molar mass in grams per mole. Let’s begin by calculating the
molar mass of water, which can be found by adding together the average molar mass of
oxygen and two times the average molar mass of hydrogen. The molar mass of water is
therefore 18 grams per mole. We know the mass of the water lost
is 2.23 grams. We need to divide it by 18 grams
per mole. The result is approximately 0.124
moles of water.
Now, let’s repeat this process for
CoSO4. The molar mass of CoSO4 can be
calculated by adding together the average molar mass of cobalt, sulfur, and four
times the average molar mass of oxygen. Therefore, the molar mass of CoSO4
is 155 grams per mole.
Now, we can find the number of
moles of CoSO4 by dividing 2.74 grams by 155 grams per mole. The result is approximately 0.0177
moles of CoSO4. To determine the whole number ratio
of moles of CoSO4 to moles of water, we need to divide both sides of our ratio by
the smaller amount of moles, which is approximately 0.0177 moles. The resulting ratio is one mole of
CoSO4 to approximately 7.0083 moles of water. However, 𝑥 must be an integer. Therefore, since 7.0083 is within
about one-tenth of the whole number seven, the final ratio is one mole of CoSO4 to
seven moles of water.
In conclusion, the ratio of
cobalt(II) sulfate to water in the hydrated salt is one to seven. Therefore, the chemical formula of
the cobalt(II) sulfate hydrate is CoSO4 7H2O, and the value of 𝑥 is seven.
