Final answer:
The molecular formula of compound X is Al₉Cl₂₇ derived using the given mass percentages and atomic masses.
Step-by-step explanation:
To determine the molecular formula of compound X, we need to find the empirical formula first. The empirical formula gives the simplest whole-number ratio of elements in a compound. To find it, we divide the percentage composition of each element by its molar mass:
Aluminum: 20.24% ÷ 26.98 g/mol ≈ 0.751. Chlorine: 79.76% ÷ 35.45 g/mol ≈ 2.248. Since we cannot have fractional atoms, we multiply both numbers by 4 to get whole numbers: Aluminum: 0.751 × 4 ≈ 3. Chlorine: 2.248 × 4 ≈ 9. The empirical formula of compound X is Al₃Cl₉.
We divide the given molar mass by the empirical formula mass: Molar mass: 266.64 g/mol. Empirical formula mass: (Al: 26.98 g/mol × 3) + (Cl: 35.45 g/mol × 9) = 320.38 g/mol. Dividing the molar mass by the empirical formula mass, we get: 266.64 g/mol ÷ 320.38 g/mol ≈ 0.83. Empirical formula: Al₃Cl₉. Molecular formula: (Al₃Cl₉) × 3 = Al₉Cl₂₇.