This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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To find the molecular formula of caffeine, we will first determine its empirical formula from the given mass percentages and then use the molar mass to find the molecular formula. Step 1: Assume a 100 g sample to convert mass percentages to grams. • Mass of C = 49.47 g • Mass of H = 5.19 g • Mass of N = 28.86 g • Mass of O = 16.48 g Step 2: Convert the mass of each element to moles using their respective atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol, O = 16.00 g/mol). Moles of C = 49.47 g12.01 g/mol = 4.119 mol Moles of H = 5.19 g1.008 g/mol = 5.149 mol Moles of N = 28.86 g14.01 g/mol = 2.060 mol Moles of O = 16.48 g16.00 g/mol = 1.030 mol Step 3: Divide the number of moles of each element by the smallest number of moles (1.030 mol for O) to find the simplest whole-number ratio. Ratio for C = 4.119 mol1.030 mol ≈ 4.00 Ratio for H = 5.149 mol1.030 mol ≈ 5.00 Ratio for N = 2.060 mol1.030 mol ≈ 2.00 Ratio for O = 1.030 mol1.030 mol = 1.00 Step 4: Write the empirical formula based on these ratios. The empirical formula is C_4H_5N_2O. Step 5: Calculate the empirical formula mass. Empirical formula mass = (4 × 12.01) + (5 × 1.008) + (2 × 14.01) + (1 × 16.00) = 48.04 + 5.040 + 28.02 + 16.00 = 97.10 g/mol Step 6: Determine the ratio between the given molar mass and the empirical formula mass. The given molar mass (M) of caffeine is 194.2 g/mol. n = Molar MassEmpirical Formula Mass = 194.2 g/mol97.10 g/mol ≈ 2.00 Step 7: Multiply the subscripts in the empirical formula by this ratio (n=2) to get the molecular formula. Molecular Formula = (C_4H_5N_2O)_2 = C_4 × 2H_5 × 2N_2 × 2O_1 × 2 = C_8H_10N_4O_2 The molecular formula of caffeine is C_8H_10N_4O_2. Send me the next one 📸