Chemical Formula

To determine the chemical formula of the solid waste sample, we need to analyze the elements present in the sample and their respective atomic masses. Based on the given data, we can calculate the mole ratios of the elements and use them to derive the chemical formula.

1. Calculate the moles of each element:
- Carbon (C): 15% of 400 kg = 60 kg = 60,000 g
- Hydrogen (H): 10% of 400 kg = 40 kg = 40,000 g
- Nitrogen (N): 0.8% of 400 kg = 3.2 kg = 3,200 g
- Oxygen (O): 70% of 400 kg = 280 kg = 280,000 g
- Sulfur (S): 0.5% of 400 kg = 2 kg = 2,000 g

2. Convert the mass of each element to moles:
- Moles of Carbon (C) = 60,000 g / 12.01 g/mol = 4,995.84 mol
- Moles of Hydrogen (H) = 40,000 g / 1.01 g/mol = 39,603.96 mol
- Moles of Nitrogen (N) = 3,200 g / 14.01 g/mol = 228.41 mol
- Moles of Oxygen (O) = 280,000 g / 16.00 g/mol = 17,500 mol
- Moles of Sulfur (S) = 2,000 g / 32.07 g/mol = 62.39 mol

3. Determine the empirical formula:
- Divide the moles of each element by the smallest number of moles:
- Carbon (C): 4,995.84 mol / 62.39 mol ≈ 80
- Hydrogen (H): 39,603.96 mol / 62.39 mol ≈ 635
- Nitrogen (N): 228.41 mol / 62.39 mol ≈ 3.66
- Oxygen (O): 17,500 mol / 62.39 mol ≈ 280
- Sulfur (S): 62.39 mol / 62.39 mol = 1

- The empirical formula is C80H635N3O280S.

4. Simplify the empirical formula (optional):
- Since the empirical formula does not have any common factors, the simplified empirical formula is the same as the original empirical formula.

5. Determine the molecular formula:
- To find the molecular formula, we need to know the molar mass of the compound.
- Assuming the molar mass of the compound is 100 g/mol (for simplicity):
- Molecular formula mass = empirical formula mass × n
- 100 g/mol = (12.01 g/mol × 80) + (1.01 g/mol × 635) + (14.01 g/mol × 3) + (16.00 g/mol × 280) + (32.07 g/mol × 1) × n
- n ≈ 1.27

- The molecular formula is approximately C101