Question #d7115

1 Answer
Dec 22, 2017

Answer:

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.