# Question d7115

Dec 22, 2017

Here's what's going on here.

#### Explanation:

The chemical formula of calcium phosphate, "Ca"_ color(red)(3)("PO"_ color(green)(4))_ color(blue)(2), tells you that every mole of this ionic compound contains

• $\textcolor{red}{3}$ moles of calcium cations, $\textcolor{red}{3} \times {\text{Ca}}^{2 +}$
• $\textcolor{b l u e}{2}$ moles of phosphate anions, $\textcolor{b l u e}{2} \times {\text{PO}}_{\textcolor{g r e e n}{4}}^{3 -}$

Now, the subscripts act as multipliers, so in terms of the number of atoms present in $1$ mole of calcium phosphate, you can say that you have

• $\textcolor{red}{3}$ moles of atoms of calcium, $\textcolor{red}{3} \times \text{Ca}$
• $\textcolor{b l u e}{2}$ moles of atoms of phosphorus, $\textcolor{b l u e}{2} \times \text{P}$
• $8$ moles of atoms of oxygen, $\left(\textcolor{b l u e}{2} \times \textcolor{g r e e n}{4}\right) \times \text{O}$

So, for example, if you want to find the percent composition of phosphorus in calcium phosphate, i.e. the mass of phosphorus present in $\text{100 g}$ of calcium phosphate, you can use the fact that $1$ mole of calcium phosphate contains $\textcolor{b l u e}{2}$ moles of phosphorus to say that

"% P" = (color(blue)(2) xx M_ ("M P"))/(M_ ("M Ca"_ 3("PO"_ 4)_ 2)) xx 100%

Here

• ${M}_{\text{M P}}$ is the molar mass of phosphorus
• M_ ("M Ca"_ 3("PO"_ 4)_ 2) is the molar mass of calcium phosphate

Similarly, you can say that the percent composition of oxygen in calcium phosphate is equal to

"% O" = ((color(blue)(2) xx color(green)(4) )xx M_ ("M O"))/(M_ ("M Ca"_ 3("PO"_ 4)_ 2)) xx 100%

Here

• ${M}_{\text{M O}}$ is the molar mass of atomic oxygen

If you want to find the percent composition of calcium in calcium phosphate, you can do

"% Ca" = (color(red)(3) xx M_ ("M Ca"))/(M_ ("M Ca"_ 3("PO"_ 4)_ 2)) xx 100%

Here

• ${M}_{\text{M Ca}}$ is the molar mass of calcium

Now, the empirical formula of an ionic compound is actually the same as its formula unit. This means that, for example, if you analyze a sample of an unknown compound that contains calcium, phosphorus, and oxygen, and find that the smallest whole number ratio that exists between the three elements is

$\text{Ca " : " P " : " O " = " 3 " : " 2 " : " 8 }$

you can say that the empirical formula of the compound is

${\text{Ca"_ 3"P"_ 2 "O}}_{8}$

Using the fact that subscripts are multipliers, you can rewrite this as

"Ca"_ 3 ("P"_ 1 "O"_ 4)_ 2

which gives you

"Ca"_ color(red)(3) ("PO"_ color(green)(4))_ color(blue)(2) -># the chemical formula of calcium phosphate.