To find the simplest formula of the compound, we need to determine the empirical formula first, which represents the simplest whole-number ratio of the constituent elements in a compound.

Step 1: Calculate the moles of Mn and S in the compound.

- Moles of Mn = (mass of Mn) / (molar mass of Mn)

= (mass of Mn in the oxide - mass of Mn in the sample) / (molar mass of Mn)

= (1.22 g - 0.5 g) / (54.94 g/mol)

= 0.0134 mol

- Moles of S = (mass of S) / (molar mass of S)

= (mass of S in the oxide - mass of S in the sample) / (molar mass of S)

= (1.38 g - 0.5 g) / (32.06 g/mol)

= 0.0274 mol

Step 2: Determine the mole ratio of Mn and S.

- Divide the moles of each element by the smaller number of moles to obtain the simplest whole-number ratio.

- Mn: S = 0.0134 mol / 0.0134 mol : 0.0274 mol / 0.0134 mol

- Mn: S = 1 : 2

Step 3: Write the empirical formula.

- The simplest formula of the compound is MnS, as the mole ratio of Mn to S is 1:2.