Chapter 11 Gases Properties of Gases General Information I A 1 2 3 4 B 1 2 3 4 5 1 Matter can exist in one of three states as a solid liquid or as a gas Under appropriate conditions almost all matter can be converted to the gaseous state Elements that occur as gases at room temperature are H2 N2 O2 F2 Cl2 and the noble gases Molecular compounds with low molar mass tend to be gases at room temperature Examples are the hydrogen halides CO CO2 NH3 NO NO2 N2O H2S HCN and SO2 Properties of Gases on the Molecular Level Gases assume the volume and shape of their container Gases are compressible Gases form homogeneous mixtures with one another in all proportions Gases have much lower densities than solids or liquids g L Gases exert pressure on any surface II The Kinetic Molecular Theory of Gases Maxwell and Boltzmann studied the behavior of gases and concluded that the physical properties of gases can be explained in terms of the motion of individual molecules A Basic Assumptions of the Kinetic Molecular Theory Gas molecules are separated from one another by large distances The molecules have mass but their volume is negligible compared to the volume of the container Gases are compressible because the molecules can be moved closer to one another by decreasing the distance between them and this results in an increase in pressure in the container 1 2 Gas molecules are in constant rapid straight line motion colliding with one another and the walls of the container These collisions are elastic that is energy is transferred from one molecule to another but there is no net change in the total energy of the system These collisions are responsible for the pressure of the gas There are no attractive or repulsive forces between gas molecules 3 4 The average kinetic energy Ek of a gas is proportional to the absolute temperature K Ek T Ek mu2 urms 3 RT M where m is the mass of the molecule and u is its velocity The bar above u indicates the average of the square of the speeds of all molecules Mean square speed u2 u1 2 u 2 2 u 3 2 u N 2 N Average of the speeds squared for all the molecules in the sample and N is the number of molecules in the sample Molecular Speed Root mean square speed is the speed of a molecule with the average kinetic energy in a sample of gas 5 B 1 2 Root mean square speed is a b Directly proportional to the square root of the absolute temperature Inversely proportional to the square root of the molar mass 3 Most molecules have speeds higher or lower than the root mean square speed 2 Molecular speed as a function of temperature and molar mass 4 Generally it is more useful to compare the root mean square speed of two different gases at the same temperature The root mean square speed or the molar mass of an unknown gas can be calculated using the equation urms1 urms2 M 2 M 1 5 Determine the molar mass of a gas that moves 4 67 times as fast as CO2 C 1 2 3 4 Diffusion and Effusion Diffusion refers to the mixing of gases as the result of the random motion and frequent collisions of gas molecules Effusion refers to the movement of gas molecules through an orifice or porous barrier by random molecular motion Graham s law rate What is the molar mass of a compound that diffuses 0 411 times as fast as methane CH4 1 M 3 III Gas Pressure General Information A 1 2 B 1 2 C 1 2 Pressure exerted by a gas is due to the collisions of the gas molecules with one another and the sides of the container Atmospheric pressure is the pressure exerted by the Earth s atmosphere Definitions and Units of Pressure Pressure force area The SI unit for pressure is the pascal Pa however other units are more useful and used more frequently 1 Pa 1N m2 3 The most frequently used pressure units are atm mmHg torr bar 1 atm 760mmHg 760 torr 1 01 bar Measurement of Pressure A barometer is used to measure atmospheric pressure Manometers are a devices used to measure the pressures of confined gases Closed tube manometer Open tube manometer 4 Any sample of gas can be described by the following four parameters IV The Gas Laws T Temperature P Pressure Volume V Number of moles n A Boyles s Law The Pressure Volume Relationship The pressure of a fixed amount of gas at a constant temperature is Boyle s Law inversely proportional to the volume of the gas P 1 V A gas occupies a volume of 725 mL at a pressure of 0 970 atm The gas is allowed to expand at constant temperature until its pressure is 0 541 atm What is the volume of the gas B Charles s and Gay Lussac s Law The Temperature Volume Relationship Charles s Law The volume of a fixed amount of gas maintained at constant pressure is directly proportional to the absolute temperature of the gas Absolute temperature C 273 K kelvins P k x 1 V PV k P1V1 P2V2 V T V kT V k T V1T2 V2T1 If the volume and amount of gas are held constant the pressure of a gas is directly proportional to the absolute temperature 5 P kT P T P k T P1 P2 P1T2 P2T1 T1 T2 A gas occupies 50 0L at 75 0 C If the volume changes to 82 3L what is the temperature of the gas in C C Avogadro s Law Amount Volume Relationships Avogadro s Law At constant pressure and temperature the volume of a gas is directly proportional to the number of moles of gas V n V kn V1 V2 n1 n2 V1 n2 V2 n1 Because the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas in a chemical reaction in which the reactants and products are all gases the volume ratios are the same as the molar ratios 6 What volume in liters of CO g and O2 g must react according to the equation to form 3 16 L of CO2 2 CO g O2 g 2 CO2 g D The Gas Laws and the Kinetic Molecular Theory The gas laws describe the behavior of gases on the macroscopic level and each of these laws can be explained on the molecular level in terms of the kinetic molecular theory Boyle s law The pressure of a gas is due to the collision of gas molecules with the walls of the container If the size of the container is decreased there are more collisions because the gas molecules are closer to one another and the pressure in the container increases Charles s law Increasing the temperature increases the average kinetic energy of the molecules which in turn causes more frequent and more forceful collisions thus increases the pressure in the …