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

Sep 5, 2017

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

#### Explanation:

Step 1. Calculate the moles of ${\text{Na"_2"SO}}_{4}$

${\text{Moles of Na"_2"SO"_4 = 14.2 color(red)(cancel(color(black)("g Na"_2"SO"_4))) × ( "1 mol Na"_2"SO"_4)/(142.04 color(red)(cancel(color(black)("g Na"_2"SO"_4)))) = "0.099 97 mol Na"_2"SO}}_{4}$

Step 2. Calculate the moles of ions

$\text{Na"_2"SO"_4 → "2Na"^"+" + "SO"_4^"2-}$

So, 1 mol of ${\text{Na"_2"SO}}_{4}$ produces 3 mol of ions.

$\text{Moles of ions" = "0.099 97" color(red)(cancel(color(black)("mol Na"_2"SO"_4))) × "3 mol ions"/(1 color(red)(cancel(color(black)("mol Na"_2"SO"_4)))) = "0.2999 mol ions}$

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

$\text{Ca"_3("PO"_4)_2 → "3Ca"^"2+" + "2PO"_4^"3-}$

∴ 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