Gases Properties (Fall 2023) PDF

Chapter 11: Gases Properties of Gases: gas properties are mainly independent of identity of gas -- different than solids and liquids 1. assume both shape and volume of container -- particles do not have fixed positions with respect to each other 2. compressible -- particles far apart (mainly empty s...

Chapter 11: Gases Properties of Gases: gas properties are mainly independent of identity of gas -- different than solids and liquids 1. assume both shape and volume of container -- particles do not have fixed positions with respect to each other 2. compressible -- particles far apart (mainly empty space) 3. very low densities (highly variable—depend on temp) -- expressed as g L–1 4. form homogenous solutions with each other (any proportion) Which of the following is false concerning gases? 1. Have low densities 2. Are rigid 3. Form solutions gas particles behave like there are no other gas particles present (we will make this assumption for now) several small mass molecular compounds are gases (room temp) HCl NH3 CO2 CH4 few elements are gaseous at room temp: Kinetic Molecular Theory —explains how properties of molecules give rise to macroscopic gas properties -- assembled in 19th century The theory: http://ch301.cm.utexas.edu/gases/index.php#kmt/kinetic-mole-theory.html  Kinetic Molecular Theory —explains how properties of molecules give rise to macroscopic gas properties -- assembled in 19th century The theory: 1. A gas is composed of particles that are separated by relatively large distances. The volume occupied by individual molecules is negligible 2. Gas molecules are constantly in random motion, moving in straight paths, colliding with the walls of their container and with one another in perfectly elastic collisions 3. Gas particles exert no attractive or repulsive forces on one another 4. The average kinetic energy of the particles is proportional to the absolute temperature http://ch301.cm.utexas.edu/gases/index.php#kmt/kinetic-mole-theory.html Which of the following is true concerning gases? 1. Intermolecular forces are strong in gases 2. Kinetic energy and temperature are inversely related 3. Each gas particle is large 4. They have perfectly elastic collisions  Kinetic Energy is proportional to temperature Graph shows the number of molecules – EVERY gas particle does NOT go the same speed! Mass matters: Same temperature; different species Heavier molecules move slower Lighter moves faster Which of the following has the fastest speed at 300 K? 1.He (4.00 amu) 2.Ar (39.94 amu) 3.Xe (131.29 amu) 4.All are the same Which of the following has the greatest kinetic energy at 300 K? 1. He (4.00 amu) 2. Ar (39.94 amu) 3. Xe (131.29 amu) 4. All are the same  3RT = speed of molecule with urms = KEavg Μ urms directly proportional to square root of absolute temp Increase temperature, increase speed u€ rms inversely proportional to square root of M Lower mass, faster speed; greater mass, decrease speed thus, 2 gas samples with same temperature è same average kinetic energy è gas with larger molar mass will have lower urms LITTLE GUYS GO FASTER! (Hobart Schact, 1984) Mass matters!  Some Math… Example: assume five speeds: 2, 4, 4, 6 and 8 m/s 3 common speed statistics: 2+ 4+ 4+6+8 24 (1) mean or average speed uavg = = = 4.8 m/s 5 5 (2) most probable speed ump = 4.0 m/s (3) rms speed 2 2 + 4 2 + 4 2 + 6 2 + 82 136 urms = = = 5.2 m/s 5 5 uave ump urms Place the following gases in order of increasing r.m.s. speed at 300 K, H2, CO2, Ne, NH3, Cl2 Which one has the highest average kinetic energy? Place the following gases in order of increasing r.m.s. speed at 300 K, 2, 44, 20, 17, 71 approximate atomic masses H2, CO2, Ne, NH3, Cl2 ANSWER: Cl2, CO2, Ne, NH3, H2 from lower to highest r.m.s. speed Which one has the highest average kinetic energy? All equal! àAll at same temp àAll have SAME KE What does the graph show? Diffusion vs. Effusion Diffusion = the spread of particles as a result of random thermal motion How fast do gas molecules move? # kg ⋅ m2 & 3%%8.314 (((298 K ) 3RT 2 s mol K ' m uu == 3RT $ = = 515 = 1150 mph MM kg s 28.0 ×10-3 mol If molecules move so fast why do they diffuse so slowly? € How fast do gas molecules move? # kg ⋅ m2 & 3%%8.314 (((298 K ) 3RT 2 s mol K ' m uu == 3RT $ = = 515 = 1150 mph MM kg s 28.0 ×10-3 mol If molecules move so fast why do they diffuse so slowly? àEach molecule collides roughly every 1 ns € àTheir mean free path is ~70 nm or 103 molecular diameters -- mean free path = the average distance a molecule travels between collisions effusion = the escape of molecules through a tiny hole into a vacuum Graham’s Law of Effusion: The effusion rate of a gas is inversely proportional to the square root of its molar mass. Thomas Graham (1846) the effusion rate è r µ urms r1 u1 3RT / M 1 M2 = = = r2 u2 3RT / M 2 M1 r1 M2 = r2 M1 Gas Pressure F P= pressure = force per unit area A Force è 1 Newton (N) = 1 kg m s–2 SI unit for pressure = pascal (Pa) 1 Pa = 1 N m–2 = 1 kg m–1 s–2 magnitude of P depends on how often and how hard the molecules strike the container walls Many Conversions Possible for Pressure conversions:1 atm* è 760 mm Hg* è 760 torr* è 101,325 Pa è 101.3 kPa è 1.01325 bar è 14.7 psi (pounds per sq. in) *exact number (does not limit sig figs)  3RT urms = Μ r1 M2 = € r2 M1 Gas simulation PV=nRT Gas Laws Boyle’s Law: relating pressure to volume Charles and Gay-Lussac’s Law: relating volume to temperature Avogadro’s Law: relating volume to amount of gas https://phet.colorado.edu/sims/html/gas- properties/latest/gas-properties_en.html for gases, we can define relationships for T, P, V and number of moles that hold for all gases (this is not true for solids and liquids!) Boyle’s Law Squeeze a gas and it gets smaller 1 V∝ P 1 V = constant × P PV = constant PV 1 1 = PV 2 2 n & T constant At constant T, as V increases, each particle strikes the walls less frequently and P decreases. At constant T, as V increases, each particle strikes the walls less frequently and P decreases.  Gas Laws Boyle’s Law: P1V1 = P2V2 relating pressure to volume Charles and Gay-Lussac’s Law: relating volume to temperature Avogadro’s Law: relating volume to amount of gas Charles and Gay-Lussac’s Law Temperatures dropped Volume decreased Use pressure gauge http://krexinc.com/2012/03/27/why-tire- pressure-matters/ Charles (and Gay-Lussac’s) Law Heat a gas and it expands V ∝P T V = constant × T V = constant T V1 V2 = n & P constant T1 T2 To maintain constant P, as V increases T must V = const x T increase; fewer collisions require harder collisions. different pressures theoretically, at –273.15 °C, a gas will occupy à all extrapolates to zero zero volume (not observed since gases volume at same T condense or form solid at low temp) regardless of pressure  Where did the Kelvin Scale come from? 1848: Lord Kelvin (Scottish mathematician) -- defined –273.15 °C = absolute zero (lowest attainable temp) -- set up Kelvin temperature scale Δ(1 kelvin (K)) = Δ(1 °C) -- to convert from °C to K è add 273.15 0K = –273.15 °C 273.15 K = 0 °C 373.15 K = 100 °C  Gas Laws http://ch301.cm.utexas.edu/simulations/gas-laws/GasLawSimulator.swf Boyle’s Law: P1V1 = P2V2 relating pressure to volume Charles and Gay-Lussac’s Law: relating volume to temperature Avogadro’s Law: relating volume to amount of gas  Avogadro’s Law: Amadeo Avogadro = At constant pressure and temperature, the volume of a fixed quantity of gas is directly proportional to the number of moles of gas = More gas, larger volume V ∝n V = constant × n V = constant n V1 V2 = P & T constant n1 n2 To maintain constant P and T, as V increases n must increase. equal volumes of gases è equal number of molecules è equal number of moles under standard conditions (1 atm, 273.15 K = STP): volume of 1 mole of gas = 22.4 L = std molar volume  Gas Laws Boyle’s Law: P1V1 = P2V2 relating pressure to volume Charles and Gay-Lussac’s Law: relating volume to temperature Avogadro’s Law: relating volume to amount of gas  The Ideal Gas Equation no gas obeys the gas laws exactly (e.g. no gas goes to zero volume at high pressure) -- come close around STP -- very poor under conditions of high P (> 10 atm) or low T (< 200 K) è on verge of converting to a liquid concept of ideal gas: a gas that DOES obey all gas laws at all temp and all pressures = individual gas particles have no volume = gas particles do not interact with each other, even at high pressures/low temps  Vα1/P VαT nT V ∝ Vαn P Introducing a proportionality constant, R, gives ! nT " V = R⋅ $ % &P' this is the IDEAL GAS EQUATION PV = nRT R = gas constant (many options, many units!) L ⋅ atm J R = the gas constant = 0.08206 = 8.314 mol ⋅ K mol ⋅ K Be ready for math AND concepts https://phet.colorado.edu/en/simulation/gas-properties STP Standard Temperature and Pressure… for GASES 0 °C and 1 atm (NOT the same as in thermo) What is the volume of 1 mole of gas at STP?  3RT urms = Μ r1 M2 = € r2 M1 STP PV=nRT For an ideal gas, calculate the pressure of the gas if 0.215 mol occupies 338 mL at 32.0 ºC. PV = nRT nRT P = n = 0.215 mol V V = 338 mL = 0.338 L T = 32 + 273.15 = 305.15 K P = ? For an ideal gas, calculate the pressure of the gas if 0.215 mol occupies 338 mL at 32.0 ºC. n = 0.215 mol P = nRT V V = 338 mL = 0.338 L T = 32 + 273.15 = 305.15 K P = ? ! L?atm " (0.215 mol )# 0.08206 $ (305.15 K ) % mol?K & P = 0.338 L = 15.928 = 15.9 atm A steel cylinder with a volume of 68.0 L contains O2 at a pressure of 15,900 kPa at 23 °C. What is the volume of this gas at STP? R = 0.08206 L atm mol-1 K-1 1 atm = 101.3 kPa You collect a gas in a 220.0 mL bulb until the pressure = 0.757 atm. The temperature is 25.0 °C and the mass of the gas is determined to be 0.299 grams. What is the molecular mass of the gas?  3RT urms = Μ r1 M2 = € r2 M1 STP PV=nRT STP Standard Temperature and Pressure… for GASES 0 °C and 1 atm (NOT the same as in thermo) What is the volume of 1 mole of gas at STP? under standard conditions (1 atm, 273.15 K = STP): volume of 1 mole of gas = 22.4 L = std molar volume  Partial Pressures in a mixture of nonreacting gases: -- each gas contributes to the total pressure (Ptotal) -- partial pressure = the pressure that one component of a mixture of gases would exert if it were the only gas in the container in a mixture of nonreacting gases: -- each gas contributes to the total pressure (Ptotal) -- partial pressure = the pressure that one component of a mixture of gases would exert if it were the only gas in the container Ptotal = PN2 + PO2 PN2 = partial pressure of N2 PO2 = partial pressure of O2 http://ch301.cm.utexas.edu/gases/index.php# mixtures/partial-pressure.html  Dalton’s Law of Partial Pressures: pressure exerted by a mixture of gases equals the sum of the partial pressures of the gases in the mixture. -- John Dalton (1803) Pt = P1 + P2 + P3 +... Pi = n R T / V P of each gas is proportional to its mole fraction mole fraction = the ratio of the number of moles of one component to the total number of moles in a mixture ni Xi = i = 1, 2, 3,... For component 1 n1 + n2 + n3 +... and n P1 X1 = 1 X1 = ntotal Ptotal http://ch301.cm.utexas.edu/gases/index.php#mixtures/daltons-law.html You want to fill a 4.00 L tank with 50.0 g of O2 (32.00 g mol–1) and 150. g of N2 (28.02 g mol-1). What will be the total pressure at 25.0 °C? LONG one – a bit grindy. Not bad practice but don’t do the whole thing in class. Conceptually? N2 (g) + 3H2 (g) à 2NH3 (g) When 100.0 mL of nitrogen reacts with an excess of hydrogen, how many milliliters of ammonia are produced? Stoichiometry of Reactions Involving Gases Volume of a gas is proportional to the number of moles (at constant temp and pressure) For the given reaction: CaCO3(s) ® CO2(g) + CaO(s) 1.25 g CaCO3 is placed into a flask and the reaction is run, at a pressure of 740. torr and a temperature of 25.0 °C. How big does the flask need to be to catch the products? mol CaCO3 (g) = 1.25 x 10–2 mol = 1.25 x 10–2 mol CO2 V= (1.25 x 10–2 mol) (0.0821 L atm mol–1 K–1) (25.0 + 273.15 K) (740. torr) (1 atm / 760 torr) = 0.314 L One way to purify (scrub) air involves LiOH, which reacts with CO2 (g): 2 LiOH(aq) + CO2(g) ® Li2CO3(s) + H2O(l) Consider the air supply in a submarine with a total volume of 2.50 x 105 L. The pressure is 0.9970 atm and the temp is 25.0 °C. If the pressure drops by 0.0100 atm as a result of CO2 reacting with LiOH, how many moles of CO2 were consumed?  Deviation from Ideal Behavior: Recall: real gases deviate from ideal gas behavior at high pressure and low temperature conditions 1. real molecules have volume -- cannot compress gas to zero volume 2. real molecules interact (attracted to each other) --causes lower P (vs. ideal gas), especially at lower temperatures