All gases share the following characteristics They assume the volume and shape of their containers They are easily compressed They will mix evenly and completely when put into the same container regardless of whether or Chapter 5 Gases 5 1 Substances That Exist as Gases Substances Found as Gases at 1atm and 25 C Elements Compounds Noble GASES H N O O F Cl He Ne Ar Kr Xe Rn HF HCl CO CO CH NH NO NO N O SO H S HCN not a reaction takes place They have much lower densities that liquids and solids 5 2 Pressure of a Gas Constantly in motion so there is always a pressure value SI Units Force mass x acceleration Force Unit is the newton N 1 N 1kg m s Pressure Pressure force area Unit is the pascal Pa 1 Pa 1 N m Atmospheric Pressure Much denser nearer the surface of the Earth Higher density greater pressure Barometer read as the height of the mercury in mm Standard atmospheric pressure 1 atm 1mmHG 1torr 1atm 760mmHg 760torr 1atm 101 325kPa is the tool used to measure this in mmHg pressure impacts a tube of mercury and is 5 3 The Gas Laws Pressure Volume Relationship Boyle s Law Pressure is inversely proportional to volume Temperature remains constant P V P V Temperature Volume Relationship Charles s Law Volume is directly proportional to temperature in K Pressure remains constant V T T V Or if volume is constant P T T P COMBINED GAS LAW HELPFUL P V P V T T 5 4 Ideal Gas Equation PV nRT R is a gas constant 0 08206 L x atm Mol x K Using this we can assume P V P V n T n T Eliminate any constants Density Essentially a rearrangement of the ideal gas law d density g L m v M molar mass g mol d P M RT Molar Mass To find rearrange the above equation Just eliminate the variable that is held constant Volume Amount Relationship Avogadro s Law At constant pressure and temperature volume is directly proportional to the number of moles 5 5 Gas Stoichiometry Amount of reactant grams or volume moles of reactant moles of product amount of product grams or volume 5 6 Dalton s Law of Partial Pressures Partial pressures pressures of individual gas components in a mixture Dalton s Law total pressure of a mixture of gases is just the sum of the pressure of the individual gases alone Rearrangement of PV nRT P nRT V Mole fraction Expresses the ratio of number of moles of one component to the number of total moles X mole fraction n moles initial n moles total X n n If a system contains more than 2 gases P X P Collecting over water P total P gas P water 5 7 Kinetic Molecular Theory Energy force X distance SI unit joule J Kinetic energy energy of motion KE 1 2mu CT Assumptions u average speed of all the speeds of all molecules C proportionality constant 1 Gas is composed of molecules that are separated from each other by large distances 2 Gas molecules are constantly moving in random directions and often collide with one another These are elastic interactions 3 Gas molecules neither attract not repel each other 4 Average kinetic energy is proportional to the temperature Application to gas laws Compressibility due to the large distances assumption 1 gases are easily compressed Boyle s Law pressure exerted results from molecular collisions so decreasing volume increases collision and pressure pressure Charles s Law due to assumption 4 raising the temp increases KE which in turn increases Partial Pressures total pressure is given by sum of individual pressures since gas molecules are unaffected by other molecules assumption 3 Root mean square speed rms U rms 3RT M R is still a constant but in this case is 8 314 J K x mol Take what you know R 0 08206 L x atm mol x K and do a unit conversion with 1 L X atm 101 3 J Gradual mixing of molecules of one gas with those of another in accordance with their kinetic Gas Diffusion properties Gas Effusion Graham s Law rate of diffusion is inversely proportional to molar mass r M entire 2nd half should be under square root symbol r M A gas under pressure escapes from containers using small openings Also uses Graham s Law 5 8 Deviation from Ideal Behavior Can be seen when pressure is high or temperature is low Van der Waals equation P an V nb nRT V Corrected Corrected Pressure Volume
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