- Problem 1: Use Boyle's Law (P₁V₁ = P₂V₂). Given P₁=2.5 mm Hg, V₁=3.5 L, P₂=10 mm Hg. Solve for V₂: V₂ = (P₁V₁)/P₂ = (2.5 * 3.5) / 10 = 0.875 L.
- Problem 2: Use Gay-Lussac's Law (P₁/T₁ = P₂/T₂). Convert temperatures to Kelvin: T₁=100°C+273=373 K, T₂=185°C+273=458 K. Given P₁=4.1 atm. Solve for P₂: P₂ = P₁ * (T₂/T₁) = 4.1 * (458/373) ≈ 5.0 atm.
- Problem 3: Use Charles's Law (V₁/T₁ = V₂/T₂). Convert T₁ to Kelvin: T₁=10°C+273=283 K. Given V₁=25 L, V₂=50 L. Solve for T₂: T₂ = T₁ * (V₂/V₁) = 283 * (50/25) = 566 K. Convert to °C: 566 - 273 = 293°C.
- Problem 4: Use Ideal Gas Law (PV = nRT) to find moles (n), then calculate molar mass. Given P=2 atm, V=6.7 L, T=245 K, R=0.0821 L·atm/(mol·K). n = PV/(RT) = (2 * 6.7) / (0.0821 * 245) ≈ 0.666 mol. Molar mass = mass/n = 34 g / 0.666 mol ≈ 51 g/mol.
- Problem 5: Use Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂). Convert P₁ to atm: 270 mm Hg / 760 = 0.355 atm. Convert T₁ and T₂ to Kelvin: T₁=65°C+273=338 K, T₂=100°C+273=373 K. Given V₁=400 mL, P₂=1.4 atm. Solve for V₂: V₂ = (P₁V₁T₂) / (P₂T₁) = (0.355 * 400 * 373) / (1.4 * 338) ≈ 112 mL.
- Problem 6: Use Ideal Gas Law (PV = nRT). Find moles of neon: n = mass / molar mass = 23 g / 20.18 g/mol ≈ 1.14 mol. Given T=1°C+273=274 K, P=2 atm, R=0.0821 L·atm/(mol·K). Solve for V: V = nRT/P = (1.14 * 0.0821 * 274) / 2 ≈ 12.8 L.
Parent Tip: Review the logic above to help your child master the concept of mixed gas laws worksheet.
