1. Use the ideal gas law: PV = nRT. Convert temperature to Kelvin (40°C = 313 K), pressure to atm (375 mm Hg = 375/760 ≈ 0.493 atm), and volume to liters (125 mL = 0.125 L). R = 0.0821 L·atm/(mol·K). Solve for n: n = PV/(RT) = (0.493 × 0.125)/(0.0821 × 313) ≈ 0.00239 mol.
2. Use PV = nRT. Convert temperature to Kelvin (195°C = 468 K), pressure to atm (795 mm Hg = 795/760 ≈ 1.046 atm), and volume to liters (2.0 L). R = 0.0821 L·atm/(mol·K). Solve for n: n = PV/(RT) = (1.046 × 2.0)/(0.0821 × 468) ≈ 0.0542 mol. Molar mass of N₂ is 28.0 g/mol, so mass = 0.0542 × 28.0 ≈ 1.52 g.
3. Use PV = nRT. Convert temperature to Kelvin (288°C = 561 K), pressure to atm (898 mm Hg = 898/760 ≈ 1.182 atm), and volume to liters (1.25 L). R = 0.0821 L·atm/(mol·K). Solve for n: n = PV/(RT) = (1.182 × 1.25)/(0.0821 × 561) ≈ 0.0254 mol. Molar mass of CH₄ is 16.0 g/mol, so mass = 0.0254 × 16.0 ≈ 0.406 g.
4. Use PV = nRT. Convert temperature to Kelvin (37°C = 310 K), pressure to atm (8750 mm Hg = 8750/760 ≈ 11.51 atm), and volume to liters (1500 L). R = 0.0821 L·atm/(mol·K). Solve for n: n = PV/(RT) = (11.51 × 1500)/(0.0821 × 310) ≈ 678 mol. Molar mass of O₂ is 32.0 g/mol, so mass = 678 × 32.0 ≈ 21,700 g or 21.7 kg.
5. Use PV = nRT. Convert temperature to Kelvin (300 K), pressure to atm (42 L tank at 300 K and 1 atm). Wait — problem says “a container of acetylene has a volume of 42 L” and “temperature of the acetylene is 300 K and pressure is 780 torr”. Convert pressure to atm: 780 torr = 780/760 ≈ 1.026 atm. Volume is 42 L. R = 0.0821 L·atm/(mol·K). Solve for n: n = PV/(RT) = (1.026 × 42)/(0.0821 × 300) ≈ 1.75 mol. Molar mass of C₂H₂ is 26.0 g/mol, so mass = 1.75 × 26.0 ≈ 45.5 g.
6. Use PV = nRT. Convert temperature to Kelvin (27°C = 300 K), pressure to atm (450 torr = 450/760 ≈ 0.592 atm), and volume to liters (2500 L). R = 0.0821 L·atm/(mol·K). Solve for n: n = PV/(RT) = (0.592 × 2500)/(0.0821 × 300) ≈ 60.0 mol. Molar mass of argon is 39.9 g/mol, so mass = 60.0 × 39.9 ≈ 2394 g or 2.39 kg.
7. Use PV = nRT. Convert temperatures to Kelvin (1750 K and 27°C = 300 K), pressure to atm (1750 mm Hg = 1750/760 ≈ 2.303 atm), and volume to liters (2500 L). R = 0.0821 L·atm/(mol·K). First, find moles at high T: n = PV/(RT) = (2.303 × 2500)/(0.0821 × 1750) ≈ 40.0 mol. Since amount of gas is constant, use P₁V₁/T₁ = P₂V₂/T₂ or directly calculate new pressure at same volume and lower T: P₂ = nRT₂/V = (40.0 × 0.0821 × 300)/2500 ≈ 0.394 atm. Convert to mm Hg: 0.394 × 760 ≈ 299 mm Hg.
Parent Tip: Review the logic above to help your child master the concept of ideal gas laws worksheet.
