With the help of chemical analysis, it was found that in a certain compound the mass fractions

With the help of chemical analysis, it was found that in a certain compound the mass fractions of elements are equal: potassium-39.6%, manganese-27.9%, oxygen-32.5%. Find the formula for this compound.

Given:
ω (K) = 39.6%
ω (Mn) = 27.9%
ω (O) = 32.5%

To find:
KxMnyOz -?

Decision:
1) Let m (KxMnyOz) = 100 g;
2) m (K) = ω (K) * m (KxMnyOz) / 100% = 39.6% * 100/100% = 39.6 g;
3) n (K) = m (K) / M (K) = 39.6 / 39 = 1.02 mol;
4) m (Mn) = ω (Mn) * m (KxMnyOz) / 100% = 27.9% * 100/100% = 27.9 g;
5) n (Mn) = m (Mn) / M (Mn) = 27.9 / 55 = 0.51 mol;
6) m (O) = ω (O) * m (KxMnyOz) / 100% = 32.5% * 100/100% = 32.5 g;
7) n (O) = m (O) / M (O) = 32.5 / 16 = 2.03;
8) x: y: z = n (K): n (Mn): n (O) = 1.02: 0.51: 2.03 = 2: 1: 4;
9) Unknown substance – K2MnO4.

Answer: Unknown substance – K2MnO4.