Question

How many moles of $M{g_3}{(P{O_4})_2}$ contains $3.011 \times {10^{23}}$ atoms of oxygen?

Answer 1

Hint: Here, we need to find out the number of moles of Magnesium Phosphate, for that we need to first convert atoms of oxygen into a number of moles of oxygen and we know that $1mole$of oxygen contains $6.022X{10^2}^3 atoms$.

Complete step by step answer:
Above it is given $3.011 \times {10^{23}}$ atoms of oxygen and we need to find out the answer in terms of moles, so first we will convert atoms into the number of moles. For that we know:
$1\,mole$ of oxygen consists of $6.022X{10^2}^3$ atoms, which is Avogadro’s number. So, $6.022X{10^2}^3$ atoms are present in $1mole$.
$\therefore $ $1atom$of oxygen is consists of $\dfrac{1}{{6.022 \times {{10}^{23}}}}mol = 0.5mol$
As we can see from the molecular formula of Magnesium Phosphate $M{g_3}{(P{O_4})_2}$, it consists of $3moles$ of Magnesium, $8moles$ of Oxygen, and $2moles$ of Phosphorus. So, it is clear that Magnesium Phosphate consists of $8moles$ of oxygen and we have already converted the given atoms of oxygen into moles of oxygen.
Now, by using unitary method we can do the further calculations:
Since, $1mole$ of $M{g_3}{(P{O_4})_2}$ consists $8moles$ of oxygen
So, $x\,moles$ of $M{g_3}{(P{O_4})_2}$ consists $0.5moles$ of oxygen
Therefore, $x$ can be calculated by using the above values given and by putting together we will calculate the value of x :
$x = \dfrac{{0.5 \times 1\,mole\,of\,oxygen}}{{8\,moles\,of\,oxygen}} = 0.0625$
$\therefore x = 0.0625$
Therefore, $0.03125moles$ of $M{g_3}{(P{O_4})_2}$ contains $3.011 \times {10^{23}}$ atoms of oxygen.

Note:
If we know that how many moles of elements are present in $1mole$ of any compound then we can easily find out the presence of a number of moles of the compound in $n\,moles$ of that compound. Also, with the help of the molecular formula we can find out the composition of it, that is, the number of atoms present in the molecular formula of that compound.