100 g of metaphosphoric acid was dissolved by heating in 50 ml of water.

100 g of metaphosphoric acid was dissolved by heating in 50 ml of water. What substance was found in the solution and what is its mass fraction in the solution?

Given:
m (HPO3) = 100 g
V (H2O) = 50 ml
ρ (H2O) = 1 g / ml

To find:
substance -?
ω (substances) -?

Decision:
1) HPO3 + H2O = (tOC) => H3PO4;
orthophosphoric acid;
2) M (HPO3) = Mr (HPO3) = Ar (H) + Ar (P) + Ar (O) * 3 = 1 + 31 + 16 * 3 = 80 g / mol;
M (H3PO4) = Mr (H3PO4) = Ar (H) * 3 + Ar (P) + Ar (O) * 4 = 1 * 3 + 31 + 16 * 4 = 98 g / mol;
3) n (HPO3) = m (HPO3) / M (HPO3) = 100/80 = 1.25 mol;
4) n (H3PO4) = n (HPO3) = 1.25 mol;
5) m (H3PO4) = n (H3PO4) * M (H3PO4) = 1.25 * 98 = 122.5 g;
6) m (H2O) = ρ (H2O) * V (H2O) = 1 * 50 = 50 g;
7) m solution (H3PO4) = m (HPO3) + m (H2O) = 100 + 50 = 150 g;
8) ω (H3PO4) = m (H3PO4) * 100% / m solution (H3PO4) = 122.5 * 100% / 150 = 81.67%.

Answer: H3PO4 – phosphoric acid; the mass fraction of H3PO4 is 81.67%.