Answer :
To find the empirical formula, you first need to determine the moles of each element present. Then, you divide each mole value by the smallest mole value to get the simplest ratio of elements.
1. Calculate the moles of manganese (Mn) and oxygen (O):
- Moles of Mn = mass of Mn / molar mass of Mn = 142.16 g / 54.94 g/mol ≈ 2.587 moles
- Moles of O = mass of O / molar mass of O = 82.85 g / 16.00 g/mol ≈ 5.178 moles
2. Divide the moles by the smallest number of moles (which is approximately 2.587):
- Mn: 2.587 moles / 2.587 ≈ 1
- O: 5.178 moles / 2.587 ≈ 2
So, the empirical formula is MnO₂.
To find the molecular formula, you'll need the molar mass of the empirical formula and the molar mass of the compound. Then, you divide the molar mass of the compound by the molar mass of the empirical formula to find the multiplier.
1. Calculate the molar mass of the empirical formula (MnO₂):
- Molar mass = (mass of Mn) + 2 × (mass of O) = (54.94 g/mol) + 2 × (16.00 g/mol) ≈ 86.94 g/mol
2. Divide the molar mass of the compound (347.6 g/mol) by the molar mass of the empirical formula (86.94 g/mol):
- Multiplier = 347.6 g/mol / 86.94 g/mol ≈ 4
3. Multiply the subscripts in the empirical formula by the multiplier:
- MnO₂ * 4 = Mn₄O₈
So, the molecular formula is Mn₄O₈.
1. Calculate the moles of manganese (Mn) and oxygen (O):
- Moles of Mn = mass of Mn / molar mass of Mn = 142.16 g / 54.94 g/mol ≈ 2.587 moles
- Moles of O = mass of O / molar mass of O = 82.85 g / 16.00 g/mol ≈ 5.178 moles
2. Divide the moles by the smallest number of moles (which is approximately 2.587):
- Mn: 2.587 moles / 2.587 ≈ 1
- O: 5.178 moles / 2.587 ≈ 2
So, the empirical formula is MnO₂.
To find the molecular formula, you'll need the molar mass of the empirical formula and the molar mass of the compound. Then, you divide the molar mass of the compound by the molar mass of the empirical formula to find the multiplier.
1. Calculate the molar mass of the empirical formula (MnO₂):
- Molar mass = (mass of Mn) + 2 × (mass of O) = (54.94 g/mol) + 2 × (16.00 g/mol) ≈ 86.94 g/mol
2. Divide the molar mass of the compound (347.6 g/mol) by the molar mass of the empirical formula (86.94 g/mol):
- Multiplier = 347.6 g/mol / 86.94 g/mol ≈ 4
3. Multiply the subscripts in the empirical formula by the multiplier:
- MnO₂ * 4 = Mn₄O₈
So, the molecular formula is Mn₄O₈.
