Find the formula for the crystalline hydrate of sodium hydroorstophosphate if it is known that the mass fraction

Find the formula for the crystalline hydrate of sodium hydroorstophosphate if it is known that the mass fraction (%) of phosphorus in the crystalline hydrate is 11.56%.

Given:
Na2HPO4 * xH2O
ω (P) = 11.56%

To find:
Na2HPO4 * xH2O -?

1) Mr (Na2HPO4 * xH2O) = N (P) * Ar (P) * 100% / ω (P) = 1 * 31 * 100% / 11.56% = 268.16 ≈ 268;
2) Mr (Na2HPO4) = Ar (Na) * N (Na) + Ar (H) * N (H) + Ar (P) * N (P) + Ar (O) * N (O) = 23 * 2 + 1 * 1 + 31 * 1 + 16 * 4 = 142;
3) Mr (xH2O) = Mr (Na2HPO4 * xH2O) – Mr (Na2HPO4) = 268 – 142 = 126;
4) Mr (H2O) = Ar (H) * N (H) + Ar (O) * N (O) = 1 * 2 + 16 * 1 = 18;
5) x = Mr (xH2O) / Mr (H2O) = 126/18 = 7;
The crystal hydrate formula is Na2HPO4 * 7H2O.

Answer: The formula of the crystalline hydrate is Na2HPO4 * 7H2O.