AP CHEMISTRY Gases and Their Properties (Kotz & Treichel, Chapter 12)
12.1 The Properties of Gases • Gas behavior is well-understood – we can usually apply simple mathematical models. • Only 4 quantities are needed to define the state of a gas: • The quantity of the gas, in moles (mol) • The temperature of the gas, in Kelvin (K) • The volume of the gas, in liters (L) • The pressure of the gas, in atmospheres (atm)
12.1 The Properties of Gases • A gas will uniformly fill any container, and will mix completely with any other gas. • Gas particles move rapidly and randomly. • Gas particles move in straight line trajectories, change direction when they collide.
Ideal Gas/Ideal Behavior • Ideal gases fit these assumptions: • Point mass, no volume • Elastic collisions • No forces of attraction or repulsion between particles
12.1 Gas Pressure • A measure of the force that a gas exerts on its container. Caused by collisions. • Force is the physical quantity that interferes with inertia. • Force = mass x acceleration (Newton’s 2nd law) • N = kg x m/s2 • Pressure = force/unit area (N/m2) • SI unit of pressure – Pascal (Pa) • 1 Pa = 1 N/m2
12.1 Pressure • Measured with a barometer or manometer. • Barometers measure atmospheric pressure. • Invented by Evangelista Torricelli in 1643 • Use height of column of mercury to measure gas pressure
12.1 Units of Pressure • Millimeters of mercury (mm Hg) • 1 mm Hg = 1 torr • 760.00 mm Hg = • 760.00 torr = • 1.00 atm = • 101.325 kPa = • standard pressure – the average atmospheric pressure at sea level
12.1 Gas Pressure • Manometers measure the pressure of a gas in a container. • Can be open-ended or closed-ended
Example Problem • If current atmospheric pressure is 752 mmHg, what is the pressure of the gas in the manometer, in mmHg? In atm? In kPa?
12.2 Gas Laws:Compressibility - Boyle’s Law • Gases can be forced to occupy less space if pressure is increased. • Boyle’s Law the volume of a fixed amount of gas at constant temperature is inversely proportional to the pressure it exerts • At constant temperature, if volume , pressure • Pressure graphed against 1/V gives linear plot
Boyle’s Law - Example Problem • Sulfur dioxide (SO2), a gas that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider a 1.53-L sample of gaseous SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 104 Pa at a constant temperature, what will be the new volume of the gas? • 0.57L
12.2 Boyle’s Law • Boyle’s Law only holds true at low pressures.
12.2 Effect of Temperature on Volume – Charles’s Law By the way, this is how the value of absolute zero was determined. Temperature at which gas volume goes to zero. • Charles’s Law the volume of a fixed amount of gas at constant pressure is directly proportional to temperature • At constant pressure, as temperature , volume • YOU MUST USE THE KELVIN TEMPERATURE! • 0°C = -273.15 K
Charles’s Law – Example Problem • A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm? • 2.79 L
12.2 Gay-Lussac and Avogadro • Gay-Lussac’s Law of CombiningVolumes Volumes of gases always combine with each other in the ratio of small whole numbers as long as volumes are measured at the same temperature and pressure • Avogadro’s Hypothesis Equal volumes of gases under the same conditions of temperature and pressure have equal numbers of molecules (equal moles)
12.2 Application to Chemical Reactions Involving Gases • The coefficients of a balanced chemical equation give • Mole ratio • Molecule ratio • Volume ratio (if T and P are constant) • Gay-Lussac’s law tells us that 2 L of hydrogen gas combine with 1 L of oxygen gas in the formation of water 2H2 + O2 2H2O
Avogadro’s Law – Example Problem • What volume of hydrogen gas is required to completely react with 4.3 L of nitrogen to form ammonia at STP? • 13 L • Suppose we have a 12.2-L sample of oxygen gas at 1 atm of pressure and 25°C. If all of this O2 is converted to ozone (O3) at the same temperature and pressure, what volume would the ozone occupy? • 8.13 L
12.2 The Combined Gas Law/General Gas Law • Example: You have a 22.-L cylinder of helium at a pressure of 150 atm and a temperature of 31°C. How many balloons can you fill, each with a volume of 5.0 L, on a day when the atmospheric pressure is 755 mmHg and the temperature is 22°C? • 3200 L, 640 balloons
12.3 The Ideal Gas Law • The four quantities that describe a gas are related to each other… • V nT/P • We can make it an equation if we introduce a proportionality constant, R, the gas constant. • V = R(nT/P) • PV = nRT
12.3 The Value of the Gas Constant • At standard temperature and pressure (STP, 1 atm, 0°C or 273.15K), 1 mol of gas occupies 22.414 L (standard molar volume) • R = PV/nT • R = (1 atm)(22.414L) = 0.08206 L atm (1 mol)(273.15K) mol K
12.3 Ideal Gas Law – Example Problem • A sample of hydrogen gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. How many moles of H2 are present? • 0.57 mol
12.3 Ideal Gas Law – Example Problem • Determine the pressure exerted by a 0.50-mol sample of oxygen gas in a 3.75-L container at 39°C. • 3.4 atm
12.3 Density and Molar Mass from the Ideal Gas Law • Use PV = nRT, n = m/MM, and D = m/V to derive expressions for the density and molar mass of a gas. • For ONE mole of a gas @STP, D = MM/22.4L • Gas densities are reported in g/L, NOT g/mL.
Gas Density/ Molar Mass – Example Problem • The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molar mass of the gas. • 32.0 g/mol
Gas Density/Molar Mass – Example Problem • Calculate the density of dry air at 15.0°C and 1.00 atm if its molar mass (average) is 28.96 g/mol. • 1.22 g/L
Example Problem • An unknown gaseous compound is 80% C and 20% H. • Determine its empirical formula. • Determine its molecular formula if a 7.83-g sample in a 5.10-L container exerts a pressure of 1.25 atm at 25°C. • CH3, C2H6
12.4 Gas Laws and Chemical Reactions – Example Problems • Quicklime, CaO, is produced by the thermal decomposition of calcium carbonate. Calculate the volume of CO2 at STP produced from the decomposition of 152 g of calcium carbonate. • 34.1 L CO2 at STP
12.4 Example Problems • A sample of methane gas with a volume of 2.80 L at 25°C and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31°C and 1.25 atm. The mixture was then ignited. Calculate the volume of carbon dioxide formed at a pressure of 2.50 atm and a temperature of 125°C. • 2.47 L
12.5 Gas Mixtures and Partial Pressures • The pressure of each gas in a mixture is called its partial pressure. • Dalton’s law of partial pressures the pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases • Ptotal = P1 + P2 + P3 + … • In a mixture of ideal gases, each gas behaves independently so we can consider them separately • The identity of the gases is irrelevant • So, in a mixture of gases A, B, and C… • PAV = nART • PBV = nBRT • PCV = nCRT
12.5 Mole Fraction • mole fraction, X, is the number of moles of a substance divided by the total number of moles XA = nA/(nA + nB + nC) = nA/ntotal so… PA = XAPtotal
12.5 Example Problems • Mixtures of helium and oxygen are used in scuba diving tanks to help prevent “the bends.” For a particular dive, 46 L of helium at 25°C and 1.0 atm, and 12 L of oxygen at 25°C and 1.0 atm were pumped into a tank with a volume of 5.0 L at 25°C. Calculate the partial pressures of each gas and the total pressure in the tank. • PHe = 9.3 atm, PO2 = 2.4 atm, Ptot = 11.6 atm
12.5 Example Problems • The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O2. • 0.210
12.5 Example Problems • The mole fraction of nitrogen in the air is 0.7808. Calculate the partial pressure of nitrogen in air when the atmospheric pressure is 760. torr. • 593 torr
12.5 Gas Collection Over Water • Collecting gas by water displacement is a common experimental method to obtain a gas sample. • But any gas sample collected in this way will have some water vapor in it. • This water vapor exerts pressure. • Water vapor pressure depends on temperature. • Appendix G, p. A-24 • Ptotal = Pgas + Pwater
12.5 Example Problem • A sample of solid potassium chlorate was heated in a test tube (as shown on previous slide) and decomposed. The oxygen produced was collected by water displacement at 22°C and a total pressure of 754 torr. The volume of the gas collected was 0.650 L, and the vapor pressure of water at 22°C is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed. • PO2 = 733 torr, 2.11 g KClO3
12.6 The Kinetic Molecular Theory of Gases • A theory that explains the behavior of gases (and liquids and solids) on the molecular level. • Assumptions: • Particles in constant, random motion • Collisions are perfectly elastic • Volume of gas particles negligible • Average kinetic energy of molecules is proportional to the gas sample’s Kelvin temperature • Gas particles neither attract nor repel each other
12.6 Using KMT to Explain Gas Laws • Boyle’s law • Charles’s law • Gay-Lussac’s law • Avogadro’s law
12.6 Distribution of Molecular Speeds • Average kinetic energy, KE, of a collection of molecules depends only on their temperature • KE = ½ mu2 • The relative number of molecules in a sample that have a given speed can be measured experimentally. • Some molecules have high speeds, some have low • Most common speed is the maximum in the distribution curve • Curves are not symmetrical – average speed is a little faster than most common speed Graphs that plot number of molecules versus speed or energy are often called Maxwell-Boltzmann distribution curves.
12.6 Comparing Gases of Different Molecular Masses • Gases at the same temperature have the same average KE • KE = ½ mv2 • For 2 gases, A and B, at the same temperature, KEA = KEB, and mAvA2 = mBvB2 • So, at equal temperatures, heavier molecules move slower and lighter molecules move faster root-mean-square speed (rms speed) – Maxwell’s equation: Must use gas constant expressed in SI units, 8.314510 J/K mol
12.6 Example Problems • Calculate the rms speed of oxygen molecules at 25°C. • 482 m/s (1100 mph)
12.7 Diffusion and Effusion • Diffusion mixing of molecules of two or more gases due to molecular motion • Effusion movement of gas molecules through a tiny opening in a container
12.7 Graham’s Law • Rates of effusion or diffusion of two different gases can be compared quantitatively. • Rates of effusion and diffusion are related to the speeds of the particles. • At equal temperatures, heavier particles move slower and lighter particles move faster. • The definition of kinetic energy can be used to derive Graham’s law
12.7 Example Problems • Calculate the ratio of the effusion rates of hydrogen gas and uranium hexafluoride, a gas used in the enrichment process to produce fuel for nuclear reactors. • 13.2
12.7 Example Problems • A pure sample of methane is found to effuse through a porous barrier in 1.50 minutes. Under the same conditions, an equal number of molecules of an unknown gas effuses through the barrier in 4.73 minutes. What is the molar mass of the unknown gas?
12.7 Example Problems cotton soaked with HCl cotton soaked with NH3 When HCl(g) and NH3(g) meet, a ring of solid NH4Cl forms. Approximately where will it be? If you performed this experiment and the solid did not form where expected, how might you explain it?
12.9 Real Gases and Nonideal Behavior • Behavior of gases at room temperature and standard atmospheric pressure can be modeled quite well with ideal gas law. • What happens at very high pressures or very low temperatures? • Gas particles get closer together and/or slow down, and assumptions of KMT no longer hold true. Van der waals equation of state: term that corrects for intermolecular forces term that corrects for molecular volume a and b are van der Waals constants – depend on the substance
12.9 Real Gases n nitrogen