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molarity and molality of H3PO4

A typical commercial-grade phosphoric acid is 75% H3PO4, by mass, and has density d= 1.57 g/mL. What are the molarity and molality of H3PO4 in this acid?

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Assume there are 1000 g of acid solution, the concentration of phosphoric acid is 75% by mass. so the mass of phosphoric acid is
m = 1000 * 75% = 750 g.

the density of the solution is d = 1.57 g/mL, the volume of 1000 g of solution is
V = m / d = 1000 / 1.57 = 636.94 mL = 0.63694 L.

The molar mass of H3PO4 is 3 * 1 + 31 + 4 * 16 = 98 g/mol
so the moles of 750 grams of H3PO4 is
n = 750 / 98 = 7.65 mol.

therefore, the molarity of the acid is
c = moles of solute / liters of solution
c = 7.65 / 0.63694 = 12.0 M.

the mass of the solvent is
m1 = mass of solution - mass of solute = 1000 - 750 = 250 grams = 0.25 kg.
so the molality of H3PO4 in this acid is
moles of solute / kilograms of solvent = 7.65 / 0.25 = 30.6 ( mol/kg or m)