AP Chemistry Chapter 5 Sections 5. 5.9 Note Organizer Pressure, The Gas Laws of Boyle, Charles, and Avogadro, The Ideal Gas Law, Gas Stoichiometry, Dalton s Law of Partial Pressure, The Kinetic olecular Theory of Gases, Effusion and Diffusion, Real Gases Elements that exist as gases at 25 o C and atmosphere H 2, N 2, O 2, F 2, Cl 2, He, Ne, Ar, Kr, Xe, Rn Physical Characteristics of Gases Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. Pressure Pressure Force/Area Units of pressure pascal (Pa) N/m 2 atm 760 mm Hg 760 torr 0,325 Pa 4.7 psi 29.92 in. Hg A barometer is used to measure atmospheric pressure. Atmospheric pressure varies with altitude. The Gas Laws of Boyle, Charles, Avogadro, Gay-Lussac and The Combined Gas Law Boyle s Law PV k This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. P V P 2 V 2 Charles s Law If n and P are constant, then V α T V and T are directly proportional. V /T V 2 /T 2 If one temperature goes up, the volume goes up! Gay-Lussac s Law If n and V are constant, then P α T P and T are directly proportional. P /T P 2 /T 2 If one temperature goes up, the pressure goes up! Combined Gas Law The good news is that you don t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P V /T P 2 V 2 /T 2
Avogadro s Law For a gas at constant temperature and pressure, the volume is to the number of moles of gas. Obeyed by gases at low pressure. V /n V 2 /n 2 Standard Temperature and Pressure Standard Pressure atm (or an equivalent) Standard Temperature 0 deg C (273 K) STP allows us to compare amounts of gases between different pressures and temperatures Ideal Gas Law Boyle s Law, Charles s Law, and Avogadro s Law can be combined to give the Ideal gas Law equation. PV nrt where R is the gas constant. Remember the conditions 0 0 C and atm are called standard temperature and pressure (STP). R 0.082057 L atm / (mol K) The gas constant, R, has this value when using pressure is in atm and V is in liters. Important!! The ideal gas law is best regarded as a law it expresses behavior that real gases approach at pressures and temperatures. Therefore, an ideal gas is a substance. ost gases obey the ideal gas law closely enough at pressures below atm that only minimal errors result from assuming ideal behavior. olar ass of a Gas The ideal gas law can be used to the of a gas from its measured density. olar ass drt/p d density of gas (in g/l) T temperature in Kelvin P pressure of gas R universal gas constant Gas Stoichiometry Amount of oles of oles of Amount of reactant (grams reactant product product (grams or volume) or volume) What is the volume of CO 2 produced at 37 0 C and.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 2 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l) g C 6 H 2 O 6 mol C 6 H 2 O 6 mol CO 2 V CO 2
Dalton s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. P TOTAL P + P 2 + P 3 +. The symbols P, P 2, P 3, and so on represent the partial pressure. ole Fraction ole fraction: the of the of of a given component in a mixture to the total number of moles in the mixture. n n Χ ntotal n+n2+... Since the mole fraction of each component in a mixture of ideal gases is directly related to its partial pressure: Χ n P ntotal P Total can be rearranged P Χ x P Total Thus, the partial pressure of a particular component of a gaseous mixture is the mole fraction of that component times the total pressure. Collecting a Gas over Water A mixture of gases results whenever a gas is collected by displacement of water. In this situation, the gas in the bottle is a mixture of water vapor and the oxygen being collected. 2KClO 3 (s) 2KCl (s) + 3O 2 (g) P T P(O 2 ) + P(H 2 O) Water vapor is present because molecules of water escape from the surface of the liquid and collect in the space above the liquid. The Kinetic olecular Theory of Gases Simple model that attempts to explain the properties of an ideal gas. The particles are so small compared with distances between them that the volume of the individual particles can be assumed to be negligible (zero). The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. Gas molecules exert neither attractive nor repulsive forces on one another. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. Any two gases at the same temperature will have the same average kinetic energy. Kinetic theory of gases and
Compressibility of Gases (decreasing the volume) Boyle s Law (volume is decreased, pressure is increased) decrease in volume gas particles hit the walls more often increase pressure Charles Law (at constant pressure, volume and temperature are directly proportional) higher temperature speeds of molecules increase and hit walls more often and with more force if pressure is kept constant volume must increase Avogadro s Law (gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas) increase in number of particles volume must increase to keep pressure and temperature constant Dalton s Law of Partial Pressures olecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas Velocity of a Gas Although the molecules in a sample of gas have an kinetic energy (and therefore an average speed) the individual molecules move at speeds, i.e. they exhibit a of speeds; some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same. At the temperature, gases move, on average, than heavier gases. To into account the distribution of speeds we use the to determine the average velocity of gases. R 8.345 J/K mol (molar gas constant) T temperature in Kelvin mass of a mole in kilograms Remember J kg m 2 /s 2 3RT u rms Diffusion and Effusion Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. Effusion term used to describe the passage of a gas through a tiny orifice into an evacuated chamber. Rate of effusion measures the at which the is transferred into the chamber. Rate of of a gas is proportional to the square root of the mass of its particles. Graham s Law of Effusion Rateof effusion for gas Rateof effusion for gas2 2 Where and 2 represent the molar masses of the gases. Real Gases We must for - gas behavior when: of the gas is. is.
Under these conditions: of gas particles is. forces become. Van der Waals equation nonideal gas Correction to ideal gas law to account for real gas behavior. Real gases occupy volume so correction is made to volume. Real gases have attractive forces so pressure must be corrected to account for gas particles hitting walls of container less often.