Question

Calculate the number of moles of $ Ba{F_2} $ present in $ 41g $ of $ Ba{F_2} $ ?

Answer 1

Hint : We must remember that the total number of atoms that are present in a mole is actually one and the same for every substance; we must be clear about this. The relation between a mole and the mass of an element is that: $ 1\;mole\;C - 12\;atoms $ contain $ 6.023 \times {10^{23}}\;atoms $ . The steps would be to find molar mass using the molecular formula of the compound, then find the number of moles in the compound by dividing the mass by the molar mass of the compound in grams.

Complete Step By Step Answer:
Let us write down what all we know:
- For every substance, the total number of atoms inside a mole is equal.
- $ 1\;mole\;C - 12\;atoms $ contain $ 6.023 \times {10^{23}}\;atoms $ .
Now let us write down the formula for calculating the number of moles in a given compound:
 $ Number\;of\;moles = \dfrac{{mass\;of\;compound(g)}}{{molar\;mass(g.mo{l^{ - 1}})}} $
But here we need to know two things: the mass of the compound and the molar mass of that compound. How do we find this?
It is given in the question that we need to find the number of moles in $ 41g $ of $ Ba{F_2} $ ; that is why, clearly the mass of the compound is given to be $ 41g $ .
To find the molar mass we can make use of our molecular formula $ Ba{F_2} $ ;
 $ BaF_2 $ is made up of $ 1\;atoms $ of Barium and $ 2\;atoms $ of Fluorine.
 $ \Rightarrow 1 \times 137.327\; + \;2 \times 18.9984 \\
   \Rightarrow 175.34\;g.mo{l^{ - 1}} \\ $
So the molar mass of $ BaF_2 $ is $ 175.34\;g.mo{l^{ - 1}} $ .
Now substituting the values of mass of compound and molar mass in the formula to find the number of moles, we get;
 $ Number\;of\;moles = \dfrac{{mass\;of\;compound(g)}}{{molar\;mass(g.mo{l^{ - 1}})}} $
 $ = \;\dfrac{{41.0\;g}}{{175.34\;g.mo{l^{ - 1}}}} \\$
 $ = \;0.233\;mol \\ $
 $ \therefore $ The number of moles of $ Ba{F_2} $ present in $ 41g $ of $ Ba{F_2} $ is $ 0.233\;mol $ .

Note :
Barium fluoride is a colorless solid. Even though its molecular weight is $ 175.32\;gmo{l^{ - 1}} $ , its exact mass is said to be $ 175.902\;gmo{l^{ - 1}} $ . It is stable when it is kept in normal conditions of storage but if it comes in contact with any mineral acid, it releases a toxic gas which is hydrogen fluoride. It is also soluble in mineral acids. It is used in the manufacturing of optical glasses, as it is a good detector of X-rays and gamma rays.