Question

Question #d7115

Answer 1

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

• `color(red)(3)` moles of calcium cations, `color(red)(3) xx "Ca"^(2+)`
• `color(blue)(2)` moles of phosphate anions, `color(blue)(2) xx "PO"_ color(green)(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

• `color(red)(3)` moles of atoms of calcium, `color(red)(3) xx "Ca"`
• `color(blue)(2)` moles of atoms of phosphorus, `color(blue)(2) xx "P"`
• `8` moles of atoms of oxygen, `(color(blue)(2) xx color(green)(4)) xx "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 `"100 g"` of calcium phosphate, you can use the fact that `1` mole of calcium phosphate contains `color(blue)(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_ ("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_ ("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_ ("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

`"Ca " : " P " : " O " = " 3 " : " 2 " : " 8 "`

you can say that the empirical formula of the compound is

`"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.