Question

Phosphoric acid (H3PO4) is important in the production of both fertilizers and detergents. It is prođuced in the following process Ca5 (PO4)3F+5H2SO4 -> 3H3PO4 +5 CaSO4 + HF. It is distributed commercially as a solution with a concentration of about 14.8 M. Approximately 2.00 x 109 gallons of this concentrated phosphoric acid solution are produced annually in this country alone. Assuming that all of this H3PO4 is produced in the reaction above, what mass (in g) of the mineral fluoroapatite, Ca5 (PO4)3F, would be required each year?

Answer 1

1.88 × 10¹³ g

Step-by-step explanation:

Phosphoric acid is produced through the following reaction.

Ca₅(PO₄)₃F + 5 H₂SO₄ → 3 H₃PO₄ + 5 CaSO₄ + HF

We can establish the following relations:

• 1 gal = 3.78 L
• Each liter of solution has 14.8 moles of H₃PO₄
• 3 moles of H₃PO₄ are produced per mole of Ca₅(PO₄)₃F
• The molar mass of Ca₅(PO₄)₃F is 504.3 g/mol

Approximately 2.00 × 10⁹ gallons of this concentrated phosphoric acid solution are produced annually in this country alone. The required mass of Ca₅(PO₄)₃F is:

`2.00* 10^(9)gal * (3.78L)/(1gal) * (14.8molH_(3)PO_(4))/(1L) * (1molCa_(5)(PO_(4))_(3)F)/(3mollH_(3)PO_(4)) * (504.3gCa_(5)(PO_(4))_(3)F)/(1molCa_(5)(PO_(4))_(3)F) =1.88 * 10^(13) gCa_(5)(PO_(4))_(3)F`