Question

What mass of calcium phosphate will I need to contain the same number of ions as 14.2 g of sodium phosphate?

Answer 1

You will need 18.6 g of `"Ca"_3("PO"_4)_2`.

Explanation:

Step 1. Calculate the moles of `"Na"_2"SO"_4`

`"Moles of Na"_2"SO"_4 = 14.2 color(red)(cancel(color(black)("g Na"_2"SO"_4))) × ( "1 mol Na"_2"SO"_4)/(142.04 color(red)(cancel(color(black)("g Na"_2"SO"_4)))) = "0.099 97 mol Na"_2"SO"_4`

Step 2. Calculate the moles of ions

`"Na"_2"SO"_4 → "2Na"^"+" + "SO"_4^"2-"`

So, 1 mol of `"Na"_2"SO"_4` produces 3 mol of ions.

`"Moles of ions" = "0.099 97" color(red)(cancel(color(black)("mol Na"_2"SO"_4))) × "3 mol ions"/(1 color(red)(cancel(color(black)("mol Na"_2"SO"_4)))) = "0.2999 mol ions"`

Step 3. Calculate the moles of `"Ca"_3("PO"_4)_2`

`"Ca"_3("PO"_4)_2 → "3Ca"^"2+" + "2PO"_4^"3-"`

∴ 1 mol of `"Ca"_3("PO"_4)_2` produces 5 mol of ions.

`" Moles of Ca"_3("PO"_4)_2 = 0.2999 color(red)(cancel(color(black)("mol ions"))) × (1 "mol Ca"_3("PO"_4)_2)/(5 color(red)(cancel(color(black)("mol ions")))) = "0.059 98 mol Ca"_3("PO"_4)_2`

Step 4. Calculate the mass of `"Ca"_3("PO"_4)_2`

`"Mass of Ca"_3("PO"_4)_2 = "0.059 98" color(red)(cancel(color(black)("mol Ca"_3("PO"_4)_2))) × ("310.18 g Ca"_3("PO"_4)_2)/(1 color(red)(cancel(color(black)("mol Ca"_3("PO"_4)_2)))) = "18.6 g Ca"_3("PO"_4)_2`