Video Transcript
An unknown hydrated metal salt has
the chemical formula XBr2⋅6H2O. When a 4.361-gram sample of the
salt is heated, the sample decreases in mass by 1.443 grams. Which of the following is the
identity of metal X? The molar mass of bromine is 80
grams per mole, hydrogen is one gram per mole, and oxygen is 16 grams per mole. (A) Co, M equals 59 grams per
mole. (B) Cu, M equals 63.5 grams per
mole. (C) Fe, M equals 56 grams per
mole. (D) V, M equals 51 grams per
mole. (E) Mn, M equals 55 grams per
mole.
Let’s start by defining a hydrated
metal salt in order to understand what happens when it is heated. When a salt contains molecules of
water as part of its structure, it’s known as a hydrated salt. During a volatilization gravimetry
experiment, if we are able to remove all the water molecules from the hydrated salt
by heating, we would form the anhydrous salt. This is why the mass of the
anhydrous salt is less than the hydrated salt. The mass of the liberated water
molecules is simply calculated as the difference between the mass of the sample
before heating and the mass of the sample after heating.
The mass of the water lost from the
hydrated salt is given in the question as 1.443 grams. And the mass of the sample before
heating is given as 4.361 grams. Therefore, we can calculate the
mass of the anhydrous salt by subtracting 1.443 grams from 4.361 grams. This gives us 2.918 grams. We can now use this information to
help us figure out the identity of X. First, we need to convert 1.443
grams of water to moles. Next, we will find the number of
moles of XBr2. Finally, we will determine the
molar mass of X, which will help us identify the metal.
The number of moles of water can be
calculated by using the following formula. The number of moles equals the mass
in grams divided by the molar mass in grams per mole. The mass of water is 1.443 grams,
and the molar mass of water is 18 grams per mole. The molar mass of water is
calculated by adding together the average molar masses of two hydrogen atoms and one
oxygen atom. Dividing 1.443 grams by 18 grams
per mole gives us the number of moles of water. Now, to determine the number of
moles of XBr2, we need to look at the provided chemical formula of the hydrated
salt. From the formula, we can determine
that there are six moles of water per every one mole of XBr2. We can therefore calculate the
number of moles of XBr2 by dividing the number of moles of water by six.
Now that we have the number of
moles and the mass of the anhydrous salt XBr2, we can calculate its molar mass. The molar mass can be calculated by
dividing the mass in grams by the number of moles. After substituting in the correct
values and dividing, we obtain the molar mass of XBr2. Since we want to know the molar
mass of just X, we need to take the molar mass of XBr2 and subtract the molar mass
of Br2. The average molar mass of Br is 80
grams per mole. So the molar mass of Br2 is 160
grams per mole. After subtracting 160 grams per
mole from the molar mass of XBr2, we finally have the molar mass of X.
When looking at the answer choices,
we can see that the metal that has a molar mass closest to the one we calculated is
cobalt. Therefore, the identity of metal X
is cobalt, which has an average molar mass of 59 grams per mole.
