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Slide 1 ___________________________________ 12 The Gaseous State of Matter ___________________________________ ___________________________________ Air in a hot air balloon expands upon heating. Some air escapes from the top, lowering the air density, making the balloon buoyant. ___________________________________ ___________________________________ ___________________________________ Foundations of College Chemistry, 14th Ed. Morris Hein and Susan Arena Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Chapter Outline 2 ___________________________________ 12.1 Properties of Gases A. Measuring the Pressure of a Gas B. Pressure Dependence: Number of Molecules and Temperature 12.2 Boyle’s Law 12.3 Charles’ Law 12.4 Avogadro’s Law A. Mole-Mass-Volume Calculations 12.5 Combined Gas Laws 12.6 Ideal Gas Law A. Kinetic-Molecular Theory B. Real Gases 12.7 Dalton’s Law of Partial Pressures 12.8 Density of Gases 12.9 Gas Stoichiometry ___________________________________ ___________________________________ ___________________________________ ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Properties of Gases 3 ___________________________________ Gases: i) Have indefinite volume Expand to fill a container ___________________________________ ii) Have indefinite shape Assume the shape of a container iii) Have low densities Example dair = 1.2 g/L at 25 °C dwater = 1.0 g/mL at 25 °C ___________________________________ ___________________________________ Volume occupied by 1 mol of H2O: as a liquid (18 mL) as a gas (22.4 L) ___________________________________ ___________________________________ iv) Have high velocities and kinetic energies © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 4 ___________________________________ Measuring Pressure Pressure: Force per unit area ___________________________________ force Pressure = area ___________________________________ Pressure depends on: 1) The number of gas molecules 2) Gas temperature 3) Volume occupied by the gas ___________________________________ Pressure results from gas molecule collisions with the container walls. ___________________________________ SI unit of pressure is the pascal (Pa) = 1 newton/meter2 ___________________________________ Unit Conversions: 1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 1.013 bar = 14.69 psi © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 5 ___________________________________ ___________________________________ Practicing Pressure Conversions ___________________________________ Convert 740. mm Hg to a) atm and b) kPa. ___________________________________ a) Use the conversion factor: 1 atm = 760 mm Hg 740. mm Hg × ___________________________________ 1 atm = 0.974 atm 760 mm Hg ___________________________________ b) Use the conversion factor: 101.3 kPa = 760 mm Hg 740. mm Hg × ___________________________________ 101.3 kPa = 98.63 kPa 760 mm Hg ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 6 ___________________________________ Atmospheric Pressure ___________________________________ Definition: total pressure exerted by gases in the atmosphere ___________________________________ Due to the mass of the atmospheric gases pressing downward on the Earth’s surface. ___________________________________ Major Components of Dry Air ___________________________________ ___________________________________ ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Measuring Pressure 7 ___________________________________ Measuring Pressure ___________________________________ Use a Barometer 1) Invert a long tube of Hg over an open dish of Hg. ___________________________________ 2) Hg will be supported (pushed up) by the pressure of the atmosphere. ___________________________________ ___________________________________ 3) Height of Hg column can be used to measure pressure. © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Pressure Dependence 8 ___________________________________ 1) On the Number of Molecules Pressure (P ) is directly proportional to the number of gas molecules present (n ) at constant temperature (T ) and volume (V ). ___________________________________ ___________________________________ Increasing n creates more frequent collisions with the container walls, increasing the pressure ___________________________________ V = 22.4 L T = 25.0 °C 0.5 mol H2 P = 0.5 atm 1 mol H2 P = 1 atm ___________________________________ 2 mol H2 P = 2 atm © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 9 ___________________________________ ___________________________________ Pressure Dependence ___________________________________ 2) On Temperature Pressure is directly proportional to temperature when moles (n ) and volume (V ) are held constant. T = 0 °C T = 100 °C 2.24 atm 3.06 atm ___________________________________ ___________________________________ Increasing T causes: a) more frequent and b) higher energy collisions ___________________________________ ___________________________________ 0.1 mol of gas in a 1L container ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Boyle’s Law 10 The volume of a fixed quantity of gas is inversely proportional to the pressure exerted by the gas at constant mass and temperature. ___________________________________ PV = constant (k ) or P 1 V ___________________________________ P=k ×1 V ___________________________________ Most common form: ___________________________________ P1V1 = P2V2 ___________________________________ Graph showing inverse PV relationship © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Boyle’s Law Problems 11 ___________________________________ What volume will 3.5 L of a gas occupy if the pressure is changed from 730. mm Hg to 600. mm Hg? ___________________________________ P1V1 = P2V2 Knowns ___________________________________ V1 = 3.5 L P1 = 730. mm Hg P2 = 600. mm Hg ___________________________________ P1V1 V2 = P2 Solve For V2 Calculate V2 = 3.5 L × ___________________________________ 730. mm Hg = 4.3 L 600. mm Hg © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Boyle’s Law Problems 12 ___________________________________ A sample of Ne gas occupies 250. mL at 880. torr. Calculate the PNe if the volume is increased to 1.0 L, assuming constant temperature. (Note: Convert mL to L.) ___________________________________ P1V1 = P2V2 Knowns ___________________________________ V1 = 0.250 L V2 = 1.0 L P1 = 880. mm Hg Solving For P2 P2 = ___________________________________ P1V1 V2 ___________________________________ 0.250 L = 220 mm Hg Calculate P2 = 880. torr × 1.0 L © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide 13 ___________________________________ Boyle’s Law Problems A sample of gaseous nitrogen in a 65.0 L automobile air bag has a pressure of 745 mm Hg. If the sample is transferred to a 25.0 L bag at the same temperature, what is the pressure in the bag? ___________________________________ a) 2.18 mm Hg ___________________________________ ___________________________________ b) 1940 mm Hg ___________________________________ c) 287 mm Hg d) 0.458 mm Hg ___________________________________ P1V1 65.0 L P2 = = 745 torr × = 1940 mm Hg 25.0 L V2 ___________________________________ Sense check: As volume decreases, pressure should increase! © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 14 ___________________________________ Temperature in Gas Law Problems Kelvin Temperature Scale ___________________________________ Derived from the relationship between temperature and volume of a gas. ___________________________________ As a gas is cooled by 1 ºC increments, the gas volume decreases in increments of 1/273. ___________________________________ All gases are expected to have zero volume if cooled to −273 ºC. ___________________________________ V ‐T relationship of methane (CH4) with extrapolation (‐‐‐‐‐) to absolute zero. ___________________________________ ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 15 ___________________________________ Temperature in Gas Law Problems ___________________________________ This temperature (−273 ºC) is referred to as absolute zero. Absolute zero is the temperature (0 K) when the volume of an ideal gas becomes zero. ___________________________________ All gas law problems use the Kelvin temperature scale! ___________________________________ Celsius temperature ___________________________________ TK = T°C + 273 ___________________________________ ___________________________________ Kelvin temperature © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Charles’ Law 16 ___________________________________ The volume of a fixed quantity of gas is directly proportional to the absolute temperature of the gas at constant pressure. ___________________________________ V = k T or V T ___________________________________ V =k T ___________________________________ Most common form: ___________________________________ V1 V2 = T1 T2 © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Charles’ Law Problems 17 ___________________________________ 3.0 L of H2 gas at −15 ºC is allowed to warm to 27 ºC at constant pressure. What is the gas volume at 27 ºC? ___________________________________ V1 V2 = T1 T2 V1 = 3.0 L T1 = −15 ºC = 258 K V1T2 Solving For V2 V2 = T1 ___________________________________ Knowns Calculate V2 = ___________________________________ V1T2 300. K = 3.5 L = 3.0 L × 258 K T1 © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ T2 = 27 ºC = 300. K ___________________________________ ___________________________________ Charles’ Law Problems 18 ___________________________________ A gas has a volume of 3.00 L at 10.0 ºC. What is the temperature of the gas if it expands to 6.00 L, assuming constant pressure? ___________________________________ V1 V2 = T1 T2 ___________________________________ V1 = 3.00 L V2 = 6.00 L T1 = 10.0 ºC = 283 K T1V2 Solving For T2 T2 = V1 T1V2 6.00 L = 566 K Calculate T2 = = 283 K × 3.00 L V1 Knowns © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ ___________________________________ ___________________________________ Slide ___________________________________ Charles’ Law Problems 19 ___________________________________ At 321 K, a gas occupies 635 mL of volume. If the temperature is decreased to 216 K, what is the new gas volume? ___________________________________ ___________________________________ a) 916 mL b) 109 mL V2 = c) 943 mL V1T2 216 K = 427 mL = 635 mL × 321 K T1 ___________________________________ d) 427 mL ___________________________________ Sense Check: As temperature decreases, volume decreases! ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Avogadro’s Law 20 ___________________________________ Equal volumes of different gases at constant T and P contain the same number of molecules. ___________________________________ ___________________________________ ___________________________________ ___________________________________ 1 volume unit 4 molecules 1 volume unit 4 molecules 2 volume units 8 molecules © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Avogadro’s Law 21 ___________________________________ Given the following gas phase reaction: N2 + 3 H 2 2 NH3 ___________________________________ If 12.0 L of H2 gas are present, what volume of N2 gas is required for complete reaction? T and P are held constant. ___________________________________ By Avogadro’s Law, we can use the reaction stoichiometry to predict the N2 gas needed. Knowns ___________________________________ VH2 = 12.0 L ___________________________________ Solving For VN2 Calculate 12.0 L H2 × 1 L N2 = 4.00 L N2 required 3 L H2 © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide ___________________________________ Avogadro’s Law 22 ___________________________________ Given the following gas phase reaction: 2 H2 + O 2 2 H2 O ___________________________________ At constant T and P, how many liters of O2 are required to make 45.6 L of H2O? ___________________________________ a) 11.4 L b) 45.6 L c) 22.8 L ___________________________________ 45.6 L H2O × d) 91.2 L 1 L O2 = 22.8 L O2 required 2 L H 2O ___________________________________ ___________________________________ Sense Check: Less moles of O2 equal less L of O2! © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 23 ___________________________________ Mole/Mass/Volume Relationships ___________________________________ Molar Volume: volume 1 mol of gas occupies at STP molar volume = 22.4 L/mol at STP ___________________________________ Molar volume can be used as a conversion factor if the mass and volume occupied by a gas are known. ___________________________________ Example: ___________________________________ 1.0 L of O2 at STP has a mass of 1.429 g. Show that the molar mass of O2 is 32.0 g/mol. ___________________________________ 22.4 L O2 = 32.0 g/mol O2 1.429 g O2 × 1.0 L O2 1 mol O2 © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 24 ___________________________________ ___________________________________ Mole/Mass/Volume Relationships ___________________________________ If 3.00 L of a gas measured at STP has a mass of 5.35 g, calculate the molar mass. ___________________________________ a) 39.9 g/mol b) 79.6 g/mol c) 12.6 g/mol ___________________________________ 22.4 L O2 = 39.9 g/mol 5.35 g gas × 1 mol gas 3.00 L gas ___________________________________ d) 25.0 g/mol ___________________________________ Unit Check: Molar mass has units of g/mol, so use dimensional analysis when setting up the problem! © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide ___________________________________ Combined Gas Laws 25 A combination of Boyle’s and Charles’ Laws. ___________________________________ Used in problems involving changes in P, T, and V with a constant amount of gas. ___________________________________ P1V1 P V = 2 2 T1 T2 ___________________________________ The volume of a fixed quantity of gas depends on the temperature and pressure. It is not possible to state the volume of gas without stating the temperature and pressure. ___________________________________ ___________________________________ Standard Temperature and Pressure (STP): ___________________________________ 0.00 °C (273.15 K) and 1 atm (760 torr) © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 26 ___________________________________ Combined Gas Law Problems A sample of gas occupies 125 mL at STP. What is the volume of the gas at 65 ºC and 320. torr? ___________________________________ P1V1 P V = 2 2 T1 T2 ___________________________________ Knowns V1 = 0.125 L P1 = 760 torr P2 = 320 torr Solving For V2 ___________________________________ T1 = 273 K T2 = 65 ºC = 338 K ___________________________________ P1V1T2 V2 = T1P2 ___________________________________ Calculate V2 = V1 × P1 ×T2 = 0.125 L × 760. torr × 338 K = 0.368 L 320. torr 273 K P2 T 1 © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 27 ___________________________________ ___________________________________ Combined Gas Law Problems What is the volume at STP for a gas that occupies 1.62 L at 616 torr and 42 °C? ___________________________________ P1V1 P V = 2 2 T1 T2 ___________________________________ Knowns V1 = 1.62 L Solving For V2 ___________________________________ P1 = 616 torr T1 = 42 °C = 315 K P2 = 760. torr T2 = 273 K ___________________________________ P1V1T2 V2 = T1P2 ___________________________________ Calculate V2 = V1 ×P1 × T2= 1.62 L × 616 torr × 273 K = 1.14 L 760. torr 315 K P2 T 1 © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide 28 ___________________________________ Combined Gas Law Problems ___________________________________ A balloon is filled with 266 L of He gas, measured at 38 °C and 0.995 atm. What will its volume be when the temperature is lowered to −76 ° C and the pressure is 0.561 atm? ___________________________________ ___________________________________ a) 299 L b) 95.0 L ___________________________________ c) 745 L d) 237 L ___________________________________ V2 = V1 × P1 × = 266 L × 0.995 atm × 197 K = 299 L T2 P2 T1 0.561 atm 311 K © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Ideal Gas Law 29 ___________________________________ A single equation relating all properties of a gas. PV = nRT ___________________________________ where R is the universal gas constant ___________________________________ ___________________________________ Constant n and T Constant n and P V 1/P Boyle’s Law V T Charles’ Law V n Avogadro’s Law © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Constant P and T ___________________________________ ___________________________________ Ideal Gas Constant 30 ___________________________________ R is derived from conditions at STP. Calculate R. PV = nRT ___________________________________ Knowns P = 1.00 atm V = 22.4 L T = 273 K n = 1.00 mol Solving For R R = ___________________________________ PV nT ___________________________________ Calculate ___________________________________ R = P × V = 1.00 atm × 22.4 L = 0.0821 L . atm mol . K 1.00 mol × 273 K n× T ___________________________________ Units are critical in ideal gas problems! © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Ideal Gas Law Practice 31 ___________________________________ How many moles of He are contained in a 0.900 L container at 30. ºC and 0.800 atm? ___________________________________ PV = nRT Knowns P = 0.800 atm V = 0.900 L T = 30. ºC = 303 K Solving For n ___________________________________ PV RT n = ___________________________________ Calculate n = P × V= R× T © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ = 0.0289 mol 0.800 atm × 0.900 L 0.0821 L . atm × 303 K mol . K ___________________________________ ___________________________________ Ideal Gas Law Practice 32 ___________________________________ What volume will be occupied by 0.393 mol of N2 at 0.971 atm and 24 °C? ___________________________________ PV = nRT Knowns P = 0.971 atm n = 0.393 mol T = 24 ºC = 297 K Solving For V V = ___________________________________ nRT P ___________________________________ Calculate ___________________________________ V = nRT = 0.393 mol × 0.0821 L . atm × 297 K = 9.87 L P mol . K ___________________________________ 0.971 atm © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 33 ___________________________________ Ideal Gas Law Practice ___________________________________ The ideal gas law can also be written in terms of molar mass of a gas. ___________________________________ PV = nRT n = ___________________________________ mass in grams (g) ___________________________________ molar mass ( ) ___________________________________ PV = gRT © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide ___________________________________ Ideal Gas Law Practice 34 ___________________________________ A 0.210 g gas sample has a pressure of 432 torr in a 333 mL container at 23 ºC. What is the molar mass of the gas? ___________________________________ PV = gRT Knowns ___________________________________ P = 432 torr = 0.568 atm V = 0.333 L T =296 K mass = 0.210 g ___________________________________ Solving For ___________________________________ Calculate = gRT = 0.210 g × 0.0821 L atm/mol K × 296 K= 27.0 g/mol PV Slide 35 0.568 atm × 0.333 L © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ ___________________________________ Ideal Gas Law Practice ___________________________________ Calculate the molar mass () of an unknown gas if 0.768 g occupies a volume of 754 mL at 30. ºC and 342 torr. ___________________________________ a) 35.4 g/mol ___________________________________ b) 21.9 g/mol ___________________________________ c) 87.3 g/mol d) 55.0 g/mol ___________________________________ = gRT = 0.768 g × 0.0821 L atm/mol K × 303 K= 56.3 g/mol PV 0.450 atm × 0.754 L © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 36 ___________________________________ ___________________________________ Kinetic Molecular Theory ___________________________________ A general theory developed to explain the behavior and theory of gases, based on the motion of particles. ___________________________________ Assumptions of Kinetic Molecular Theory (KMT): 1) Gases consist of tiny particles. ___________________________________ 2) The distance between particles is large when compared to particle size. The volume occupied by a gas is mostly empty space. 3) Gas particles have no attraction for one another. ___________________________________ ___________________________________ 4) Gas particles move linearly in all directions, frequently colliding with the container walls or other particles. © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide 37 ___________________________________ Kinetic Molecular Theory ___________________________________ Assumptions of KMT (continued): 5) Collisions are perfectly elastic. No energy is lost during collisions. ___________________________________ 6) The average kinetic energy for particles is the same for all gases (regardless of molar mass) at the same temperature. KE = 1/2mv 2 ___________________________________ ___________________________________ where m is the mass and v is the velocity of the particle The average kinetic energy is directly proportional to temperature (in K). ___________________________________ Gases which behave under these assumptions are know as ideal gases. © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Real Gases 38 ___________________________________ Real gases typically behave like ideal gases over a fairly wide range of temperatures and pressures. ___________________________________ Conditions where real gases deviate from ideal gases: ___________________________________ 1) At high pressure (small volumes) ___________________________________ Distance between particles is small and the particles do not behave independently. ___________________________________ 2) At low temperature Particles experience intermolecular interactions. © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 39 ___________________________________ ___________________________________ Dalton’s Law of Partial Pressures The total pressure of a mixture is the sum of the partial pressures of the different gases in the mixture. ___________________________________ Ptotal = P1 + P2 + P3… ___________________________________ Each gas behaves independently in the mixture. ___________________________________ Application of Dalton’s Law Gases collected over H2O contain both the gas and H2O vapor. ___________________________________ Vapor pressure of H2O is constant at a given T. ___________________________________ Pbottle is equalized so that Pbottle = Patm thus Collecting a gas over water ___________________________________ Patm = Pgas + PH2O © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Partial Pressures Problems 40 ___________________________________ A sample of O2 gas is collected over water at 22 ºC and 662 torr. What is the partial pressure of O2 gas? The vapor pressure of water is 19.8 torr at 22 ºC. ___________________________________ ___________________________________ Knowns Patm = 662 torr Solving For PO2 Calculate PH2O = 19.8 torr ___________________________________ PO2 = Patm – PH2O ___________________________________ PO2 = 662 torr – 19.8 torr = 642 torr ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Partial Pressures Problems 41 ___________________________________ A 250. mL sample of O2 was collected over water at 23 ºC and 760 torr. What volume will the O2 occupy at 23 ºC when PO2 is 760. torr? The vapor pressure of water at 23 ºC is 21.2 torr. Knowns VO2 + H2O = 250 mL PH2O= 21.2 torr Solving For VO2 ___________________________________ ___________________________________ Patm = PO2 + PH2O = 760. torr ___________________________________ 1) Solve for PO2 using Dalton’s Law 2) Solve for VO2 using Boyle’s Law ___________________________________ Calculate ___________________________________ PO2 = Ptotal – PH2O= 760 torr – 21.2 torr = 739 torr © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ Partial Pressures Problems 42 ___________________________________ (continued) A 250. mL sample of O2 was collected over water at 23 ºC and 760 torr. What volume will the O2 occupy at 23 ºC when PO2 is 760 torr? The vapor pressure of water at 23 ºC is 21.2 torr. ___________________________________ ___________________________________ Calculate Solve for VO2 with Boyle’s Law P1V1 = P2V2 V2 = ___________________________________ P1V1 V2 = P2 ___________________________________ P1V1 739 mm Hg = 0.250 L × = 0.243 L O2 760 mm Hg P2 © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide ___________________________________ Gas Density 43 ___________________________________ Density of a liquid or solid is expressed in g/mL, but gas density is very low, so the standard units are g/L. density (d ) = ___________________________________ g mass = L volume ___________________________________ The density of a gas at STP can also be related to the compound’s molar mass. g 1 mol dstp = molar mass × 22.4 L mol ( ) )( ___________________________________ g = L ___________________________________ Note: gas densities must be cited at a specific temperature as volume changes as a function of temperature (Charles’ Law). © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Gas Density Practice 44 ___________________________________ Calculate the density of Cl2 at STP. ( d = molar mass ___________________________________ g g 1 mol × = 22.4 L L mol )( ) ___________________________________ molar mass Cl2 = 70.9 g/mol d = 70.9 g Cl2 1 mol Cl2 ___________________________________ × 1 mol Cl2 = 3.17 g/L 22.4 L Cl2 ___________________________________ Sense Check: Gas densities are expected to be low. © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 45 ___________________________________ ___________________________________ Gas Stoichiometry ___________________________________ ___________________________________ ___________________________________ ___________________________________ At STP: the molar volume can be used as a conversion factor to convert between moles and volume. ___________________________________ Non STP Conditions: use the ideal gas law to convert between moles and volume. © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide 46 ___________________________________ Gas Stoichiometry Practice at STP ___________________________________ For the following reaction: Calculate the number of moles of phosphorus needed to react with 4.0 L of H2 gas at 273 K and 1.0 atm. P4 (s) + 6 H2 (g) ___________________________________ 4 PH3 (g) ___________________________________ Knowns V =4.0 L T = 273 K P = 1.0 atm Solution Map L H2 mol H2 ___________________________________ mol P4 ___________________________________ Calculate 1 mol H2 × 1 mol P4 mol P4 = 4.0 L H2 × 22.4 L H2 6 mol H2 = 0.0030 mol P4 © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 47 ___________________________________ ___________________________________ Gas Stoichiometry Volume Practice ___________________________________ Calculate the volume of N2 necessary to react with 9.0 L of H2 gas at 450 K and 5.00 atm. N2 (g) + 3 H2 (g) ___________________________________ 2 NH3 (g) ___________________________________ a) 9.0 L b) 3.0 L c) 27.0 L 9.0 L H2 × 1 L N2 3 L H2 ___________________________________ = 3.0 L N2 d) 1.0 L ___________________________________ At constant T and P, the volume ratio can be used in place of the mole ratio! © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ ___________________________________ Gas Stoichiometry Practice With the Ideal Gas Law 48 ___________________________________ Given the following reaction: 2 NaN3 (s) 2 Na (s) + 3 N2 (g) ___________________________________ If an air bag should be filled with a pressure of 1.09 atm at 22 ºC, what amount of solid NaN3 is needed to fill a bag with a volume of 45.5 L? ___________________________________ Knowns P = 1.09 atm V = 45. 5L T = 295K ___________________________________ Solving for n of N2 then find the mass of NaN3 needed. ___________________________________ Calculate = 2.05 mol N2 n = PV = 1.09 atm × 45.5 L RT 0.0821 L atm/mol K × 295 K © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide ___________________________________ Gas Stoichiometry Practice With the Ideal Gas Law 49 ___________________________________ (continued) Given the following reaction: 2 NaN3 (s) ___________________________________ 2 Na (s) + 3 N2 (g) ___________________________________ If an air bag should be filled with a pressure of 1.09 atm at 22.0 ºC, what amount of solid NaN3 is needed to fill a bag with a volume of 45.5 L? Calculate ___________________________________ Use the reaction stoichiometry! 2.05 mol N2 × 2 mol 3 mol NaN 3 N2 ___________________________________ × 64.99 g NaN3 = 88.8 g NaN3 1 mol NaN3 © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 50 ___________________________________ ___________________________________ Gas Stoichiometry Practice What volume of O2 at 760. torr and 25 ºC is needed to react fully with 3.2 g of C2H6 (propane)? 2 C2H6 (g) + 7 O2 (g) ___________________________________ 4 CO2 (g) + 6 H2O (l) ___________________________________ m = 3.2 g T = 298 K P = 1.00 atm Knowns Solution Map m C2H6 Calculate ___________________________________ mol C2H6 mol O2 volume O2 ___________________________________ 1 mol C2H6 7 mol O2 = 0.37 mol O2 × 3.2 g C2H6 × 30.08 g C2H6 2 mol C2H6 V = nRT P = 1.00 atm ___________________________________ = 9.1 L © 2014 John Wiley & Sons, Inc. All rights reserved. Slide ___________________________________ 0.37 mol × 0.0821 L . atm × 298 K mol . K ___________________________________ Gas Stoichiometry Practice 51 ___________________________________ What volume of H2 at 739 torr and 21 ºC is liberated by 42.7 g of Zn when it reacts with HCl? Zn (s) + 2 HCl (g) a) 7.6 L b) 16.2 L c) 3.2 L d) 1.8 L m Zn ___________________________________ ZnCl2 (s) + H2 (g) mol Zn mol H2 ___________________________________ volume H2 42.7 g Zn × 1 mol Zn × 1 mol H2 = 0.653 mol H2 65.38 g Zn 1 mol Zn ___________________________________ ___________________________________ V = nRT = 0.653 mol × 0.0821 L atm/mol K × 294 K= 16.2 L H 2 P 0.972 atm © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide 52 ___________________________________ Chemistry in Action ___________________________________ What the Nose Knows Dogs use smell to detect many drugs, explosives, etc. based on trace amounts of chemical compounds in the air. ___________________________________ Sensing low concentrations of chemicals is useful! ___________________________________ Better Coffee Better Science Artificial noses could sniff out cancer or explosives! ___________________________________ For more information, see: http://www.scs.illinois.edu/suslick/smell_seeing.html ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 53 ___________________________________ ___________________________________ Learning Objectives ___________________________________ 12.1 Properties of Gases 1) Explain atmospheric pressure and how it is measured. 2) Be able to convert between the various units of pressure. ___________________________________ 12.2 Boyle’s Law ___________________________________ 3) Use Boyle’s Law to calculate changes in pressure or volume of a gas at constant temperature. ___________________________________ 12.3 Charles’ Law ___________________________________ 4) Use Charles’ Law to calculate changes in temperature or volume of a gas at constant pressure. ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved. Slide 54 ___________________________________ Learning Objectives ___________________________________ 12.4 Avogadro’s Law 5) Solve problems using the relationships between moles, mass, and volume of gases. ___________________________________ ___________________________________ 12.5 Combined Gas Law 6) Use the combined gas law to calculate changes in pressure, volume, or temperature of a gas sample. ___________________________________ 12.6 Ideal Gas Law ___________________________________ 7) Use the ideal gas law to solve problems involving pressure, volume, temperature, and moles of a gas. © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________ Slide 55 ___________________________________ Learning Objectives ___________________________________ 12.7 Dalton’s Law of Partial Pressures ___________________________________ 8) Use Dalton’s Law of Partial Pressures to calculate the total pressure for a mixture of gases or the pressure of a single gas in a mixture of gases. ___________________________________ 12.8 Density of Gases 9) Calculate the density of a gas. (Pay attention to units!) ___________________________________ 12.9 Gas Stoichiometry ___________________________________ 10) Solve stoichiometry problems involving gases. (Pay attention to the states of matter and use gas laws only for gases!) © 2014 John Wiley & Sons, Inc. All rights reserved. ___________________________________