Calculate the mass of phosphoric acid, which is obtained from 31 kg of calcium phosphate

Calculate the mass of phosphoric acid, which is obtained from 31 kg of calcium phosphate by its interaction with concentrated sulfuric acid. If the yield of the reaction product is 80% of the theoretically possible.

Let’s implement the solution:

In accordance with the condition of the problem, we write down the process equation:
Ca3 (PO4) 2 + 3H2SO4 = 3CaSO4 + 2H3PO4 – ion exchange, phosphoric acid is formed;

Let’s make the calculations:
M Ca3 (PO4) 2 = 309.8 g / mol;

M (H3PO4) = 97.9 g / mol;

m Ca3 (PO4) 2 = 31000 g;

Y Ca3 (PO4) 2 = m / M = 31000 / 309.8 = 100 mol.

Proportion:
100 mol Ca3 (PO4) 2 – X mol (H3PO4);
-1 mol – 2 mol from here, X mol (H3PO4) = 100 * 2/1 = 200 mol.

Find the mass of acid, taking into account the product yield:
m (H3PO4) = Y * M = 200 * 97.9 = 19580 g (theoretical weight);

m (H3PO4) = 19580 * 0.80 = 15664 g = 15 kg 664 g

Answer: received phosphoric acid weighing 15 kg 664 g