Make up the formula of manganese oxide if it is known that the mass fraction of manganese is 49.6%.

Given:
MnxOy
ω (Mn in MnxOy) = 49.6%

To find:
MnxOy -?

Decision:
1) Let m (MnxOy) = 100 g;
2) m (Mn in MnxOy) = ω (Mn in MnxOy) * m (MnxOy) / 100% = 49.6% * 100/100% = 49.6 g;
3) n (Mn in MnxOy) = m (Mn in MnxOy) / M (Mn) = 49.6 / 55 = 0.9 mol;
4) m (O in MnxOy) = m (MnxOy) – m (Mn in MnxOy) = 100 – 49.6 = 50.4 g;
5) n (O in MnxOy) = m (O in MnxOy) / M (O) = 50.4 / 16 = 3.15 mol;
6) x: y = n (Mn in MnxOy): n (O in MnxOy) = 0.9: 3.15 = 1: 3.5 = 2: 7;
7) Unknown substance – Mn2O7.

Answer: Unknown substance – Mn2O7.