We have 2 givens in the question stem and we are solving for mass.
We need to prepare "500 mL"500 mL of LithiumLithium ion solution with a concentration of 0.175 M.0.175M. Well, what does that mean exactly?
You have a given volume with a given number of moles. That basically translates to saying we have "0.175 moles"0.175 moles of LiLi for every "1 liter"1 liter of solution.
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The thing is, we don't have "1 liter"1 liter; we are told to prepare "500 mL"500 mL . If you convert "500 mL"500 mL to LitersLiters first,
(500(cancel(mL)))/(1) * ("1 * "10^-3" L)/(cancel(mL)) = 0.500 L
we get "0.500 Liters".
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Using our conversion factor we can solve for moles.
(0.500 cancel("Liters of solution"))/1 * ("0.175 moles" Li)/(1 cancel("Liter of solution")) = "0.087 moles" Li
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We know that for every 1 mole of Li_3PO_4 will gives us "3 moles of Li ions"
Li_3PO_4 ->3 Li^+ + PO4^-3
This means "0.087 moles of Li" will be released from one-third as many Li_3PO_4 molecules so "0.029 moles" of Li_3PO_4
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Now find the molar mass and convert from moles to mass to figure out the unknown.
Molar mass of Li_3PO_4
Li = 7 g * 3 = 21g
P = 31 g
O = 16 g * 4 = 64g
Total: 116 g
(0.029 cancel("moles" Li_3PO_4))/1 * (116 grams)/(1 cancel("mole" Li_3PO_4)) = "3.364 grams of" Li_3PO_4
Answer: 3.364 grams of Li_3PO_4
