Gases

Properties of Gases Pressure Barometric Pressure Gases uniformly fill any container Gases are easily compressed Mix completely with any other gas Exert pressure on their surroundings Pressure = force/area Barometric Pressure mm Hg (torr) Newtons/meter2 = pascal (Pa) Atmospheres (atm) Standard Pressure 760 torr 101,325 Pa 1.0 atm 760 mm Hg

Gas Stoichiometry Standard temperature and pressure (STP) Molar volume 0˚C, 273 K 1 atm, 760 torr Molar volume One mole of an ideal gas occupies 22.42 L of volume (at STP) True for ANY gas Useful things to remember Density = mass/volume n = grams of substance/molar mass

Dalton’s law of partial pressures The total pressure of a gaseous mixture is the sum of the partial pressure of all the gases. PT = P1 + P2 + P3 + ..... Air is a mixture of gases - each adds it own pressure to the total. Pair = PN2 + PO2 + PAr + PCO2 + PH2O

Partial Pressure Example Mixtures of helium and oxygen are used in scuba diving tanks to help prevent “the bends.” For a particular dive, 46 liters of O2 and 12 liters of He were pumped into a 5 liter tank. Both gases were added at 1.0 atm pressure at 25oC. Determine the partial pressure for both gases in the scuba tank at 25oC.

Partial pressure example First calculate the number of moles of each gas using PV = nRT. Rearrange to solve for n n = P V R T nO2 = = 1.9 mol nHe = = 0.49 mol (1.0 atm) (46 L) (0.08206 L atm K-1 mol-1)(298.15K) (1.0 atm) (12 L) (0.08206 L atm K-1 mol-1)(298.15K)

Partial pressure example Calculate the partial pressures of each. PO2 = = 9.3 atm PHe = = 2.4 atm Total pressure in the tank is 11.7 atm. (1.9 mol) (298.15 K) (0.08206 L atm K-1 mol-1) (5.0 L) (0.49 mol) (298.15 K) (0.08206 L atm K-1 mol-1) (5.0 L)

Mole Fraction XA = nA = PA nT PT Directly related to pressures! If a gas is responsible for 25% of pressure, it is 25% of moles

Butane gas, P1, and water vapor, P2, are in the tube. Experiment Air Pressure, PT PT =P1+P2 Butane lighter

Butane gas is collected by water displacement at 25°C Butane gas is collected by water displacement at 25°C. If the atmospheric pressure is 755mm Hg, what is the pressure of the butane gas? (Given vapor pressure of water is 24 mm Hg)

Patmosphere = Pbutane+ PH2O 755 mm Hg = Pbutane + 24 mm Hg Pbutane = 731 mm Hg

Example of Dalton’s Law O2 gas is collected by water displacement at 15ºC. If the atmospheric pressure is 644 mm Hg, what is the pressure of the O2 gas, given P of water is 13 mm Hg? (631mm )

Avogadro’s law If you have more moles of a gas, it takes up more space at the same temperature and pressure.

Dalton & Avogadro’s Laws 2NH4OH (s) 2N2 (g) + O2 (g) + 4H2O (g) When 10.0 g NH4OH decomposes, the total pressure of the mixture of gaseous products is 800. mm Hg. What is the partial pressure of each gas? Ptotal = PN2 + PO2 + PH2O ntotal = nN2 + nO2 + nH2O PN2 nN2 Ptotal ntotal . =

Dalton & Avogadro’s Laws 2NH4OH (s) 2N2 (g) + O2 (g) + 4H2O (g)

Dalton & Avogadro’s Laws

Kinetic-molecular theory This theory explains the behavior of gases. Gases consist of very small particles (molecules) which are separated by large distances. Gas molecules move at very high speeds - hydrogen molecules travel at almost 4000 mph at 25oC. Pressure is the result of molecules hitting the container. At 25 oC and 1 atm, a molecule hits another molecule and average of 1010 times/sec.

Kinetic-molecular theory No attractive forces exist between ideal gas molecules or the container they are in. Energy of motion is called kinetic energy. Average kinetic energy = mv 2 Because gas molecules hit each other frequently, their speed and direction are constantly changing. The distribution of gas molecule speeds can be calculated for various temperatures. 1 2

Kinetic-molecular theory Fraction having each speed 0 500 1000 1500 2000 2500 3000 Molecular speed (m/s) O2 at 25oC O2 at 700oC H2 at 25oC Average speed

Diffusion versus Effusion The random and spontaneous mixing of molecules. Effusion The escape of molecules through small holes in a barrier.

Graham’s law Rate A MM B Rate B MM A = Relates the rates of effusion of two gases to their molar masses. This law notes that larger molecules move more slowly. Rate A MM B Rate B MM A =

Graham’s law Helium is placed in scuba tanks so it effuses into your blood instead of N2. How much faster is He than nitrogen? Rate He 28 Rate N2 4 = = 2.6 X faster

Graham’s law What is the molar mass of an unknown gas that effuses 2.12 times faster than pentane, C5H12, through a porous barrier? Rate unknown gas = 2.12 = 72 Rate C5H12 x x = 16 g / mole

Graham’s law CH4 and H2 effuse through a porous barrier. How much faster will hydrogen effuse than methane? Rate H2 16 Rate CH4 2.02 = = 2.8 times faster

Ideal Gas Law Limitations Works well at low pressures and high temperatures Most gases do NOT behave ideally above 1 atm pressure Does not work well near the condensation conditions of a gas Assumes: Molecules don’t attract or repel each other Volume of molecules is negligible (volume is a vacuum) Both untrue

Real Gases As pressure approaches zero, all gases approach ideal behavior. At high pressure, gases deviate significantly from ideal behavior. Why? Attractive forces actually do exist between molecules. Molecules are not points -- they have volume.