Hey there!
It is evident that the problem gives the mass of the bottle with the calcite, with water and empty, which will allow us to calculate the masses of both calcite and water. Moreover, with the given density of water, it will be possible to calculate its volume, which turns out equal to that of the calcite.
In this case, it turns out possible to solve this problem by firstly calculating the mass of calcite present into the bottle, by using its mass when empty and the mass when having the calcite:

Now, we calculate the volume of the calcite, which is the same to that had by water when weights 13.5441 g by using its density:

Thus, the density of the calcite sample will be:

This result makes sense, as it sinks in chloroform but floats on bromoform as described on the last part of the problem, because this density is between 1.444 and 2.89. g/mL
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Answer: 69.72 kg of cryolite will be produced.
Explanation:
The balanced chemical equation is:

To calculate the moles, we use the equation:

moles of
= 
moles of
= 
moles of
= 
As 1 mole of
reacts with 6 moles of 
166 moles of
reacts with =
moles of 
As 1 mole of
reacts with 12 moles of 
166 moles of
reacts with =
moles of 
Thus
is the limiting reagent.
As 1 mole of
produces = 2 moles of cryolite
166 moles of
reacts with =
moles of cryolite
Mass of cryolite
= 
Thus 69.72 kg of cryolite will be produced.
Answer:
A and B are not the same substances.
The reason is because they do not have the same density which is a function of their masses and volumes.
For instance, for every Volume of 1mL of each substances, A has a mass of 0.97g which is different from the 0.89g of B.