Gases Pressure Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’s Law Ideal Gas Equation Dalton’s Law Effusion and Diffusion Kinetic-Molecular Theory Real Gases

Elemental states at 25oC Solid Liquid Gas He Rn Xe I Kr Br Se Ar Cl S Ne F O P N C H Li Na Cs Rb K Tl Hg Au Hf Ls Ba Fr Pt Ir Os Re W Ta Po Bi Pb Be Mg Sr Ca Cd Ag Zr Y Pd Rh Ru Tc Mo Nb Ac Ra Zn Cu Ti Sc Ni Co Fe Mn Cr V In Sb Sn Ga Ge Al Gd Cm Tb Bk Sm Pu Eu Am Nd U Pm Np Ce Th Pr Pa Yb No Lu Lr Er Fm Tm Md Dy Cf Ho Es At Te As Si B 5 - 2 Solid Liquid Gas

Observed properties of matter State Property Solid Liquid Gas Density High High Low (like solids) Shape Fixed Takes shape Expands of lower part to fill the of container container Compressibility Small Small Large Thermal Very Small Moderate expansion Small

The gaseous state In this state, the particles have sufficient energy to overcome all forces that attract them to each other. Each particle is completely separated from the others. This results in low densities and the fact that gases completely fill the container that holds them.

Gas pressure Gases exhibit pressure on any container they are in. Pressure is defined as a force per unit of area. Pressure = Force / Area Several common units 1.00 atm = 760 torr 760 mm Hg 29.9 in Hg 14.7 lb/in2 1.01 x 105 Pa force area

Barometer Device used to measure atmospheric pressure. One atm vacuum One atm 760 mmHg 29.9 inHg

The gas laws Since gases are highly compressible and will expand when heated, these properties have been studied extensively. The relationships between volume, pressure, temperature and moles are referred to as the gas laws. To understand the relationships, we must introduce a few concepts.

Units we will be using Volume liters, although other units could be used. Temperature Must use an absolute scale. K - Kelvin is most often used. Pressure Atm, torr, mmHg, lb/in2. - use what is appropriate. Moles We specify the amounts in molar quantities.

Gas laws Laws that show the relationship between volume and various properties of gases Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’s Law The Ideal Gas Equation combines several of these laws into a single relationship.

Temperature and number of moles must be held constant! Boyle’s law The volume of a gas is inversely proportional to its pressure. PV = k or P1 V1 = P2 V2 Temperature and number of moles must be held constant!

Boyle’s law Increasing the pressure on a sample on gas decreases it volume at constant temperature. Note the effect here as weight is added.

Pressure and number of moles Charles’ law The volume of a gas is directly proportional to the absolute temperature (K). V T = k V1 V2 T1 T2 or = Pressure and number of moles must be held constant!

Charles’ law When you heat a sample of a gas, its volume increases. The pressure and number of moles must be held constant.

Charles’ Law Placing an air filled balloon near liquid nitrogen (77 K) will cause the volume to be reduced. Pressure and the number of moles are constant.

Gay-Lussac’s Law Law of of Combining Volumes. At constant temperature and pressure, the volumes of gases involved in a chemical reaction are in the ratios of small whole numbers. Studies by Joseph Gay-Lussac led to a better understanding of molecules and their reactions.

Gay-Lussac’s Law Example. Reaction of hydrogen and oxygen gases. Two ‘volumes’ of hydrogen will combine with one ‘volume’ of oxygen to produce two volumes of water. We now know that the equation is: 2 H2 (g) + O2 (g) 2 H2O (g) + H2 O2 H2O

Avogadro’s law Equal volumes of gas at the same temperature and pressure contain equal numbers of molecules. V = k n V1 V2 n1 n2 =

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

Standard conditions (STP) Remember the following standard conditions. Standard temperature = 273.15 K Standard pressure = 1 atm At these conditions: One mole of a gas has a volume of 22.4 liters.

The ideal gas law A combination of Boyle’s, Charles’ and Avogadro’s Laws PV = nRT P = pressure, atm V = volume, L n = moles T = temperature, K R = 0.082 06 L atm/K mol (gas law constant)

Example What is the volume of 2.00 moles of gas at 3.50 atm and 310.0 K? PV = nRT V = nRT / P = (2.00 mol)(0.08206 L atm K-1mol-1)(310.0 K) (3.50 atm) = 14.5 L

Ideal gas law PV R = nT R = = 0.08206 atm L mol-1 K-1 R can be determined from standard conditions. PV nT R = ( 1 atm ) ( 22.4 L ) ( 1 mol ) ( 273.15 K) R = = 0.08206 atm L mol-1 K-1

Ideal gas law When you only allow volume and one other factor to vary, you end up with one of the other gas laws. Just remember Boyle Pressure Charles Temperature Avogadro Moles

Ideal gas law P1V1 P2V2 n1T1 n2T2 = R = This one equation says it all. Anything held constant will “cancels out” of the equation

Ideal gas law P1V1 P2V2 n1T1 n2T2 = P1V1 = P2V2 Example - if n and T are held constant P1V1 n1T1 P2V2 n2T2 = This leaves us P1V1 = P2V2 Boyle’s Law

Example If a gas has a volume of 3.0 liters at 250 K, what volume will it have at 450 K ? Cancel P and n They don’t change P1V1 n1T1 P2V2 n2T2 = We end up with Charles’ Law V1 T1 V2 T2 =

Example If a gas has a volume of 3.0 liters at 250 K, what volume will it have at 450 K ? P1V1 n1T1 P2V2 n2T2 V1 T1 = V2 T2 = V2 = (3.0 l) (450 K) (250 K) = 5.4 L

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 in to 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. 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 Now calculate the partial pressures of each. PO2 = = 9.3 atm PO2 = = 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)

Graham’s law 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 =

Diffusion

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

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 = mv2 Because gas molecules hit each other frequently, their speed and direction is 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

Real gases We can plot the compressibility factor (PV/nRT) for gases. If the gas is ideal, it should always give a value of 1. Obviously, none of these gases are ‘ideal.’ H2 N2 Compressibility factor CH4 C2H4 NH3 0 5 10 Pressure, atm

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.

( ) Van der Waals equation This equation is a modification of the ideal gas relationship. It accounts for attractive forces and molecular volume. P + an2 V2 (V - nb) = nRT ( ) Correction for Molecular volume Correction for attractive forces between molecules

Van der Waals constants a b Gas Formula L2 atm mol-2 L mol-1 Ammonia NH3 4.170 0.037 07 Argon Ar 1.345 0.032 19 Chlorine Cl2 6.493 0.056 22 Helium He 0.034 12 0.023 70 Hydrogen H2 0.244 4 0.026 61 Nitrogen N2 1.390 0.039 13 Water H2O 5.464 0.030 49 Xenon Xe 4.194 0.051 05