What is the empirical formula of a compound containing 24.56% potassium, 34.81% manganese, and 40.50% oxygen?

Assume a 100g sample to make things easier; so 24.56% of 100g is 24.56g, for example. The empirical formula is simply the ratio of the moles of each substance. So convert each to moles so that you can compare them:

24.56g K * (1 mol/39.10g) =.6281 mol K

34.81g Mn * (1mol/54.94) =.6336 mol Mn

40.50g O * (1mol/16.00g) = 2.531 mol O

Remember that we are trying to find the ratio between them. The easiest way to do that is to divide each by the smallest number:

.6281 mol K /.6281 mol = 1

.6336 mol Mn /.6281mol = 1.0

2.531 mol O /.6281 mol = ~ 4.0

So you have a ratio of 1:1:4 (there is some degree of approximation that you have to make)

So the empirical formula is:

KMnO4