Ideal Gas Law, Partial Pressures

ideal-gas equation - describes hypothetical gas (ideal gas)

• results not exactly correct for actual gases
• PV = nRT
  • R = gas constant, depends on values of P, V, n, T
  • T = temperature, always expressed as absolute temperature
  • n = number of moles of gas
  • P = pressure, usually given in atm
  • V = volume, usually given in L
• standard temperature and pressure (STP) - 0 C, 1 atm
  • molar volume - 22.41 L/mol
• all gas laws derived from the ideal-gas equation
• P1V1/T1 = P2V2/T2

Find the temperature of gas at which 0.407 mol takes up 3.23 L of space at 118 in Hg 

• Given:
  • PV = nRT
  • P = 118 in = (118 in x 2.54 cm/in x 10 mm/cm) = 2997.2 mm = 3.94 atm
  • V = 3.32 L
  • n = 0.407
  • R = 0.08206 (L-atm/mol-K)
• (3.94)(3.23) = (0.407)(0.08206)T
• T = [(3.94)(3.23)] / [(0.407)(0.08206)]
• T = 381 K

gas density - unit mass per unit volume

• n/V = P/(RT)
• density = n(molar mass)/V = P(molar mass)/(RT)
• higher molar mass/pressure >> higher gas density
• higher temperature >> lower gas density

Find the density of carbon tetrachloride at 714 torr at 125° C  

• Given:
  • molar mass = 12 + 4(35.5) = 154 g/mol
  • P = 714 torr = 714/760 atm
  • R = 0.0821 L-atom/mol-K)
  • T = 125° C = 125 + 273 K = 398 K
• d = [(714/760)(154)] / [(0.0821)(398)]
• d = 4.43 g/L

Dalton ’s law of partial pressures

• total pressure of a mixture of gases equal to sum of pressures of each gas in the mixture
• Pt = P1 + P2 + P3 +…
• at constant temperature/volume, total pressure determined by number of moles of gas
• mole fraction - ratio of moles of 1 substance in mixture to total number of moles
• partial pressure = mole fraction x total pressure

Find the partial pressures and total pressure of a mixture made from 6.00 g O2 and 9.00 g CH4 in a 15.0 L container at 0° C  

• Given:
  • PV = nRT
  • P = nRT/V
  • R = 0.0821 (L-atm/mol-K)
  • T = 273 K
• moles of O2 = 6.00 / 32 = 0.188 mol
• moles of CH4 = 9.00 / 16 = 0.563 mol
• pressure of O2 = (0.188)(0.0821)(273) / 15 = 0.281 atm
• pressure of CH4 = (0.563)(0.0821)(273) / 15 = 0.841 atm
• total pressure = 0.281 + 0.841 = 1.122 atm

collecting gases over water - gases produced by chemical reactions often collected over water

• volume of gas measured by raising/lowering inverted bottle until water level is the same on inside/outside of bottle
• pressure inside bottle equal to atmospheric pressure outside when water level is the same
• Ptotal = Pgas + PH2O