The compound ibuprofen, used in some pain relievers, has the molecular formula \(\mathrm{C}_{13} \mathrm{H}_{18} \mathrm{O}_{2}\). If \(0.250 \mathrm{~g}\) of ibuprofen is burned in oxygen, how many grams of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) will be produced?

First, we need to write the balanced chemical equation for the combustion of ibuprofen. When ibuprofen (C₁₃H₁₈O₂) burns in oxygen (O₂), it produces carbon dioxide (CO₂) and water (H₂O). The balanced chemical equation is: \[C_{13}H_{18}O_{2} + 17O_{2} \rightarrow 13CO_{2} + 9H_{2}O\]

In order to perform stoichiometry calculations, we need the molar masses of ibuprofen, CO₂, and H₂O: Ibuprofen: Molar mass = (13 × 12.01 g/mol C) + (18 × 1.01 g/mol H) + (2 × 16.00 g/mol O) = 206.28 g/mol CO₂: Molar mass = (1 × 12.01 g/mol C) + (2 × 16.00 g/mol O) = 44.01 g/mol H₂O: Molar mass = (2 × 1.01 g/mol H) + (1 × 16.00 g/mol O) = 18.02 g/mol

Given 0.250 g of ibuprofen, we can now use stoichiometry to calculate the grams of CO₂ and H₂O produced: 1. Determine the moles of ibuprofen used: moles of ibuprofen = grams of ibuprofen / molar mass of ibuprofen moles of ibuprofen = 0.250 g / 206.28 g/mol = 0.00121 mol ibuprofen 2. Determine the moles of CO₂ and H₂O produced: From the balanced chemical equation, 1 mol ibuprofen forms 13 mol CO₂ and 9 mol H₂O. moles of CO₂ = 0.00121 mol ibuprofen × (13 mol CO₂ / 1 mol ibuprofen) = 0.0157 mol CO₂ moles of H₂O = 0.00121 mol ibuprofen × (9 mol H₂O / 1 mol ibuprofen) = 0.0109 mol H₂O 3. Convert the moles of CO₂ and H₂O to grams: grams of CO₂ = 0.0157 mol CO₂ × 44.01 g/mol = 0.690 g CO₂ grams of H₂O = 0.0109 mol H₂O × 18.02 g/mol = 0.196 g H₂O

The combustion of 0.250 g ibuprofen in oxygen will produce 0.690 g of CO₂ and 0.196 g of H₂O.