How many grams of magnesium phosphate would you need to dissolve in water to have 8.02 x 10^25 phosphate ions dissolved in solution?
Magnesium phosphate has the formula `Mg_3(PO_4)_(2)`
There are two phosphate ions in every formula unit. Each formula unit of magnesium sulfate that dissolves will produce two phosphate ions. Here are the unit factors that are needed to solve this problem:
1 magnesium phosphate/2 phosphate ions
1 mole / 6.02x10^23 (Avogadro's number for measuring number of particles)
262.9 grams magnesium phosphate/1 mole (molar mass)
Multiply the given quantity of phosphate ions by these factors:
(8.02x10^25 phosphate ions)(1 mole/6.02x10^23) = 133 moles phosphate
(133 moles phosphate ions)(1 magnesium phosphate/2 phosphate ions) = 66.5 moles magnesium phosphate
(66.5 moles magnesium phosphate)(262.9 g/1mole) = 1.75x10^4 grams magnesium phosphate
The first step in solving problems like this one is to write the formula of the compound. The magnesium ion has a charge of 2+ and phosphate has a charge of 3- so they combine in a 3:2 ratio of magnesium ion to phosphate ion to give a neutral compound.
When converting from moles to grams you need to know the molar mass of the substance. You can calculate this by adding the molar masses of the atoms in the formula:
(3xMg) + (2xP) + (8xO) = 3(24.3) +2(30.97) + 8(16.00) = 262.9 grams/mole