Chapter 10: Gases Earth is surrounded by a layer of gaseous molecules - the atmosphere - extending out to about 50 km. 10.1 Characteristics of Gases low density; compressible volume and shape of container expand when heated large distance between particles Model of a gas: rapidly moving particles: vol. & shape of container no attraction between particles moving about freely large space between particles States of Matter 10.2 Pressure Pressure = force/area Units: lb/ft2 Pa = N/m2 = kg/m2 torr = mm Hg 1 atm = 760 torr 1 atm = 29.9 in Hg = 14.7 lb/in2 1 atm = 101.3 kPa Measure pressure with barometer or U-tube or manometer Pressure Why does a pin hurt? Why don’t snowshoes sink? Barometer Pressure How does pressure cause this can to collapse? 10.3 The Gas Laws We can describe a gas by the variables: V, P, T, n (or m and MM or d) How do each of the other variables affect the volume of a gas? Ideal Gas: properties are independent of the identity of the gas What is the relationship between the variables for an ideal gas? P-V at constant n,T PV = Constant Boyle’s Law Boyle’s Law Why are potato chip bags puffier at higher altitudes? Why does a water bottle collapse in on itself when you fly? Charles’ Law Investigation of Balloons V-T at constant n,P Charles’ Law Figure 9.8 V/T = constant Combined Gas Law P1V1/T1 = constant P1V1/T1 = P2V2/T2 Avogadro’s Law Gay-Lussac’s Law of combining volumes: at a given temperature and pressure, the volumes of gases which react are ratios of small whole numbers. 2H2O(l) 2H2(g) + O2(g) Avogadro’s Law Explained by Avogadro’s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules. Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas. Mathematically: V = constant n. Combined Gas Law PV=Constant V/T=Constant V/n=Constant Combining these gives: PV/nT = Constant Molar Volume at STP There are 6.02 1023 gas molecules in a volume of 22.414 L of any gas at 0C and 1 atm. 10.4 The Ideal-Gas Equation PV = nRT Ideal Gas Problems PV = nRT Universal Gas Constant: R = 0.08206 L atm/mol K Convert variables to these units to simplify problem solving K = oC + 273.15 1 atm = 760 torr Typical Problems With these relationships, you should be able to solve problems involving the variables that determine the physical properties of gases. Practice Problem The volume of an oxygen cylinder is 1.85 L. What mass of oxygen gas remains in the cylinder when it is “empty” if the pressure is 755 torr and the temperature is 18.1oC? Answer: 2.46 g 10.5 Further Applications of the Ideal-Gas Equation Gas Densities and Molar Mass Density has units of mass over volume. D = mass/V Density is an intrinsic property so we can calculate the density of any amount (such as 1 L, 1 mole, or 1 gram). Practice Problem Bromine gas has the formula Br2. Calculate the density of bromine gas at 50.0oC and 785.0 torr. Answer 6.23 g/L Further Applications of the Ideal-Gas Equation Gas Densities and Molar Mass The molar mass of a gas can be determined using its definition: MM = g/mol Molar mass is also an intrinsic property Practice Problem If 1.48 g of an unknown gas occupies 132 mL at 25.0oC and 722 torr, what is its molar mass? Answer: 289 g/mol Group Work What is the density of neon gas at STP? Further Applications of the Ideal-Gas Equation Volumes of Gases in Chemical Reactions The ideal-gas equation relates P, V, and T to number of moles of gas. The n can then be used in stoichiometric calculations. Practice Problem A tank of hydrogen gas has a volume of 7.49 L and an internal pressure of 22.0 atm at a temperature of 32.0oC. What volume of gaseous water is produced by the following reaction at 100.0oC and 0.975 atm if all the hydrogen gas reacts with iron(III) oxide? Fe2O3(s) + 3H2(g) 2Fe(s) + 3H2O(g) Answer: 207 L 10.6 Gas Mixtures and Partial Pressures Dalton’s Law of Partial Pressures: In a mixture of gases, each exerts a partial pressure the same as it would exert alone. Ptotal = PA + PB + PC + ... The amount of each type of gas in air is proportional to its partial pressure. Gas Mixtures It is common to synthesize gases and collect them by displacing a volume of water. To calculate the amount of gas produced, we need to correct for the partial pressure of the water: Ptotal = Pgas + Pwatervapor 9.7 Kinetic Molecular Theory What causes the observed ideal gas behavior? Kinetic Molecular Theory explains: 1. Small, widely-separated particles low density compressible Example: Xe at STP, only 0.025% of the volume is occupied by the atoms 2. Molecules behave independently no intermolecular forces Dalton’s Law Model of a gas K.M.T. continued 3. Rapid, straight-line motion diffusion of gases expansion of gases no net energy loss from collisions 4. Pressure arises from collisions with the walls of the container Boyle’s Law Pressure proportional to number of moles 5. Average kinetic energy (KE) depends only on the absolute temperature (T) See distribution of KE Distribution of velocities of gaseous particles Depends on temperature: 10.8 Molecular Effusion and Diffusion Average behavior is described by two equations: KEav = 3/2 kT (k = R/N = Boltzmann Constant) KEav = 1/2 mvav2 Pressure is proportional to temperature (more collisions and greater force) Graham’s Law: 3/2 kT = 1/2 m1v12 = 1/2 m2v22 v1/v2 = (m2/m1)1/2 Model of a gas Effusion Figure 10.20 Effusion and Diffusion Effusion - escape of a gas through a pinhole Diffusion - motion of a gas through space Gas motion: rate is inversely proportional to the square root of the mass of the particles Graham’s Law: r1/r2 = (M2/M1)1/2 Effusion and Diffusion Which molecules will escape from a leaky balloon fastest? Group Work How much faster will H2 effuse through a pinhole than H2O? 10.9 Real Gases: Deviations from Ideal Behavior Gases can be liquefied by application of pressure (or cooling) not predicted by gas laws real gases deviate from the gas laws Ideal gas assumptions about gas particles: no volume no attractive forces Near STP, these are good assumptions for most gases. Deviations from Ideality At high pressure, molecules become closer together. How will the actual (measured) volume compare to the ideal (predicted) volume? Measured volume > ideal volume by the volume occupied by gas particles Deviations from Ideality At low temperature, molecules are moving slowly and attractions between particles may become important. How will the actual (measured) pressure compare to the ideal (predicted) pressure? Measured P < ideal P because of fewer collisions with the walls Real Gases The van der Waals Equation We add two terms to the ideal gas equation, one to correct for volume of molecules and the other to correct for intermolecular attractions The correction terms generate the van der Waals equation: (P + n2a/V2)(V-nb) = nRT where a and b are empirical constants. Real Gases