2A combination of laws: Boyle’s Law Charles’ Law Avogadro’s Law k = PV at constant T and nCharles’ LawV = bT at constant P and nAvogadro’s LawV = an at constant P and TThese laws show how the volume of a gas is dependent on the temperature, pressure, and number of moles presentThe ideal gas law can be used to solve almost any gas problem.
3Ideal Gas Law Equation: The Ideal Gas LawDefines the ideal behavior of a gasPressures less than or equal to 1 atmTemperatures greater than or equal to 0 oCUnits must be in L, atm, K, and mol.The Universal Gas Constant:R = L atm/K molIdeal Gas Law Equation:PV = nRT
4Sample Problem #1A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0 oC and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample.Identify the Variables:P = 1.5 atm n = ???V = 8.56 L T = 0 oCSet up the Equation:PV = nRTPV = nRTRT RTn = PVRTConvert units if needed:T = 0 oC = = 273 KSolve:n = (1.5 atm)(8.56 L)( LK atm mol)(273 K)n = 0.57 mol
5Sample Problem #2Suppose we have a mol sample of ammonia gas at 25 oC with a volume of 3.5 L at a pressure of 1.68 atm. The gas is compressed to a volume of 1.35 L at 25 oC. Use the ideal gas law to calculate the final pressureSet up the Equation: PV = nRT*Set it up so that the variables that change are on one side and the constants are on the other.P1V1 = nRT and P2V2 = nRTBecause nRT is constant, we can write:P1V1 = P2V2 or P2 = P1V1V2Identify the Variables:P1 = 1.68 atm P2 = ?V1 = 3.5 L V2 = 1.35 Ln1 = mol n2 = molT1 = 25 oC T2 = 25 oC*n and T are constantConvert units if needed:T = 25 oC = = 298 KSolve:P2 = (1.68 x 3.5) ÷ (1.35)P2 = 4.4 atm
6Ideal Gas Practice Problems Given the following sets of variables, calculate the unknown quantity using the Ideal Gas Law:P = mm Hg; V = ?; n = mol; T = 26.2 oCP = ? mm Hg; V = 27.5 mL; n = mol; T = 16.6 oCP = atm; V = 45.2 mL; n = mol; T = ? oCCalculate the mass (g) of argon gas required to fill a L container to a pressure of 1.09 atm at 25 oC.What volume does 2.25 g of nitrogen gas, N2, occupy at 273 oC and 1.02 atm?What mass of helium gas is needed to pressurize a L tank to 255 atm at 25 oC?What mass of oxygen gas would be needed to pressurize the same gas tank?At what temperature will a 1.0-g sample of neon gas exert a pressure of 500 torr in a 5.0-L container?