Chapter 11 - Gases Properties of Gases Gas Pressure Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 2 of 81 Kinetic Theory of Gases Gases consist of _____ particles that Move rapidly in ___________ lines. Have essentially no attractive (or repulsive) ___________. Are very ______ ____________. Have very small volumes compared to the volume of the ____________ they occupy. Have kinetic energies that increase with an __________ in temperature. Chapter 11 Slide 3 of 81 Properties of Gases Gases are described in terms of four properties: pressure (P), volume (V), temperature (T), and amount (n, number of moles). Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Table 11.1 Chapter 11 Slide 4 of 81 Units of Pressure Gas pressure Is described as a force acting on a specific area. Pressure (P) = Force Area Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Table 11.1 Chapter 11 Slide 5 of 81 Atmospheric Pressure The atmospheric pressure Is the pressure exerted by a column of air from the top of the atmosphere to the surface of the Earth. Is about 1 atmosphere or a little less at sea level. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 6 of 81 Altitude and Atmospheric Pressure Atmospheric pressure Depends on the altitude and the weather. Is lower at high altitudes where the density of air is less. Is higher on a rainy day than on a sunny day. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 7 of 81 What is 475 mm Hg expressed in atm? 475 mm Hg x 1 atm = atm 760 mm Hg The pressure of a tire is measured as 2.00 atm. What is this pressure in mm Hg? 2.00 atm x 760 mm Hg = 1520 mm Hg 1 atm Learning Check Chapter 11 Slide 8 of 81 Barometer A barometer Measures the pressure exerted by the gases in the atmosphere. Indicates atmospheric pressure as the height in mm of the mercury column. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 9 of 81 Chapter 11Gases Pressure and Volume Boyles Law Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 10 of 81 Boyles Law Boyles Law states that The pressure of a gas is ___________ related to its volume when T and n are constant. If volume decreases, the pressure ______________. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 11 of 81 In Boyles Law The product P x V is constant as long as T and n do not change. P 1 V 1 = 8.0 atm x 2.0 L = 16 atm L P 2 V 2 = 4.0 atm x 4.0 L = 16 atm L P 3 V 3 = 2.0 atm x 8.0 L = 16 atm L Boyles Law can be stated as P 1 V 1 = P 2 V 2 (T, n constant) PV Constant in Boyles Law Chapter 11 Slide 12 of 81 Solving for a Gas Law Factor The equation for Boyles Law can be rearranged to solve for any factor. P 1 V 1 = P 2 V 2 Boyles Law To obtain V 2, divide both sides by P 2. P 1 V 1 = P 2 V 2 P 2 P 2 P 1 V 1 = V 2 P 2 Chapter 11 Slide 13 of 81 PV in Breathing In inhalation, The lungs expand. The pressure in the lungs decreases. Air flows towards the lower pressure in the lungs. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 14 of 81 PV in Breathing In exhalation Lung volume decreases. Pressure within the lungs increases. Air flows from the higher pressure in the lungs to the outside. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 15 of 81 Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 16 of 81 Freon-12, CCl 2 F 2, is used in refrigeration systems. What is the new volume (L) of a 8.0 L sample of Freon gas initially at 550 mm Hg after its pressure is changed to 2200 mm Hg at constant T? 1. Set up a data table Conditions 1Conditions 2 P 1 = 550 mm HgP 2 = 2200 mm Hg V 1 = 8.0 LV 2 = (predict smaller V 2 ) Calculation with Boyles Law ? Chapter 11 Slide 17 of Because pressure increases, we predict that the volume will decrease. Solve Boyles Law for V 2 : P 1 V 1 = P 2 V 2 V 2 = V 1 P 1 P 2 V 2 = 8.0 L x 550 mm Hg = 2.0 L 2200 mm Hg pressure ratio decreases volume Calculation with Boyles Law (Continued) Chapter 11 Slide 18 of 81 Learning Check For a cylinder containing helium indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant): 1) Pressure decreases 2) Pressure increases Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 19 of 81 Learning Check If the helium in a cylinder has a volume of 120 mL and a pressure of 850 mm Hg, what is the new volume if the pressure is changed to 425 mm Hg inside the cylinder? A) 60 mL B) 120 mLC) 240 mL P 1 = 850 mm Hg P 2 = 425 mm Hg V 1 = 120 mL V 2 = ?? V 2 = P 1 V 1 = 120 mL x 850 mm Hg = 240 mL P mm Hg Chapter 11 Slide 20 of 81 Learning Check A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T constant), is the new volume represented by A, B, or C? Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 21 of 81 If the sample of helium gas has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)? A) 3.2 LB) 6.4 LC) 12.8 L V 2 = V 1 P 1 P 2 V 2 = 6.4 L x 0.70 atm = 3.2 L 1.40 atm Volume decreases when there is an increase in the pressure (Temperature is constant.) Learning Check Chapter 11 Slide 22 of 81 A sample of oxygen gas has a volume of 12.0 L at 600. mm Hg. What is the new pressure when the volume changes to 36.0 L? (T and n constant). 1) 200. mm Hg 2) 400. mm Hg 3) 1200 mm Hg Learning Check Practice At Home Chapter 11 Slide 23 of 81 Chapter 11Gases Temperature and Volume (Charles Law) Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 24 of 81 Charles Law In Charles Law The Kelvin temperature of a gas is directly related to the volume. P and n are constant. When the temperature of a gas increases, its volume increases. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 25 of 81 For two conditions, Charles Law is written V 1 = V 2 (P and n constant) T 1 T 2 Rearranging Charles Law to solve for V 2 T 2 xV 1 = V 2 x T 2 T 1 T 2 V 2 = V 1 T 2 T 1 Charles Law: V and T Chapter 11 Slide 26 of 81 Learning Check Solve Charles Law expression for T 2. V 1 = V 2 T 1 T 2 Cross multiply to give V 1 T 2 =V 2 T 1 Isolate T2 by dividing through by V1 V 1 T 2 =V 2 T 1 V 1 T 2 =V 2 T 1 V 1 T2T2 Chapter 11 Slide 27 of 81 A balloon has a volume of 785 mL at 21C. If the temperature drops to 0C, what is the new volume of the balloon (P constant)? 1.Set up data table: Conditions 1Conditions 2 V 1 = 785 mLV 2 = ? (decrease) T 1 = 21C = 294 KT 2 = 0C = 273 K Be sure to use the Kelvin (K) temperature in gas calculations. Calculations Using Charles Law Chapter 11 Slide 28 of 81 Calculations Using Charles Law (continued) 2. Solve Charles law for V 2 V 1 = V 2 T 1 T 2 V 2 = V 1 T 2 T 1 V 2 = 785 mL x 273 K = 729 mL 294 K When temperature decreased, the volume decreased as predicted. Chapter 11 Slide 29 of 81 A sample of oxygen gas has a volume of 420 mL at a temperature of 18C. At what temperature (in C) will the volume of the oxygen be 640 mL (P and n constant)? A) 443C B) 170C C) - 82C T 2 = T 1 V 2 V 1 T 2 = 291 K x 640 mL = 443 K 420 mL = 443 K K = 170C Learning Check 18 o C = 291 K Chapter 11 Slide 30 of 81 Chapter 11Gases Temperature and Pressure (Gay-Lussacs Law) Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 31 of 81 Gay-Lussacs Law: P and T In Gay-Lussacs Law The pressure exerted by a gas is directly related to the Kelvin temperature. V and n are constant. P 1 = P 2 T 1 T 2 Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 32 of 81 A gas has a pressure at 2.0 atm at 18C. What is the new pressure when the temperature is 62C? (V and n constant) 1. Set up a data table. Conditions 1Conditions 2 P 1 = 2.0 atmP 2 = (increase) T 1 = 18C T 2 = 62C = 291 K = 335 K Calculation with Gay- Lussacs Law ? Chapter 11 Slide 33 of 81 Calculation with Gay- Lussacs Law (continued) 2. Solve Gay-Lussacs Law for P 2 P 1 = P 2 T 1 T 2 P 2 = P 1 T 2 T 1 P 2 = 2.0 atm x 335 K = 2.3 atm 291 K Chapter 11 Slide 34 of 81 Blank Chapter 11 Slide 35 of 81 Chapter 11 Gases The Combined Gas Law Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 36 of 81 The combined gas law uses Boyles Law, Charles Law, and Gay-Lussacs Law (n is constant). P 1 V 1 =P 2 V 2 T 1 T 2 Combined Gas Law Chapter 11 Slide 37 of 81 A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29C. At what temperature (C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n constant)? 1. Set up Data Table Conditions 1Conditions 2 P 1 = atm P 2 = 3.20 atm V 1 = L (180 mL) V 2 = 90.0 mL T 1 = 29C = 302 KT 2 = ?? Combined Gas Law Calculation Chapter 11 Slide 38 of Solve for T 2 P 1 V 1 =P 2 V 2 T 1 T 2 T 2 = T 1 P 2 V 2 P 1 V 1 T 2 = 302 K x 3.20 atm x 90.0 mL = 604 K atm mL T 2 = 604 K = 331 C Combined Gas Law Calculation (continued) Chapter 11 Slide 39 of 81 A gas has a volume of 675 mL at 35C and atm pressure. What is the volume(mL) of the gas at -95C and a pressure of 802 mm Hg (n constant)? Learning Check Chapter 11 Slide 40 of Data Table Conditions 1Conditions 2 T 1 = 308 KT 2 = -95C = 178K V 1 = 675 mL V 2 = ??? P 1 = 646 mm Hg P 2 = 802 mm Hg 2. Solve for V 2 V 2 =V 1 P 1 T 2 P 2 T 1 V 2 = 675 mL x 646 mm Hg x 178K = 314 mL 802 mm Hg x 308K A gas has a volume of 675 mL at 35C and atm pressure. What is the volume (mL) of the gas at -95C and a pressure of 802 mm Hg (n constant)? P 1 V 1 = P 2 V 2 T 1 T 2 Chapter 11 Slide 41 of 81 Chapter 11 Gases Volume and Moles (Avogadros Law) Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 42 of 81 Avogadro's Law: Volume and Moles In Avogadros Law The volume of a gas is directly related to the number of _____ of gas. T and P are constant. V 1 = V 2 n 1 n 2 Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 43 of 81 Learning Check If 0.75 mol of helium gas occupies a volume of 1.5 L, what volume will 1.2 mol of helium occupy at the same temperature and pressure? 1) 0.94 L 2)1.8 L 3) 2.4 L Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 44 of 81 If 0.75 mol of helium gas occupies a volume of 1.5 L, what volume will 1.2 mol of helium occupy at the same temperature and pressure? 1) 0.94 L 2) 1.8 L 3) 2.4 L Conditions 1Conditions 2 V 1 = 1.5 LV 2 = ??? n 1 = 0.75 mol Hen 2 = 1.2 mol He V 2 = V 1 n 2 n 1 V 2 = 1.5 L x 1.2 mol He = 2.4 L 0.75 mol He V 1 = V 2 n 1 n 2 Chapter 11 Slide 45 of 81 The volumes of gases can be compared when they have the same conditions of temperature and pressure (STP, Standard Temperature and Pressure). Standard temperature (T) 0C or 273 K Standard pressure (P) 1 atm (760 mm Hg) STP Chapter 11 Slide 46 of 81 Molar Volume At standard temperature and pressure (STP). 1 mol of a gas occupies a volume of 22.4 L, which is called its molar volume. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 47 of 81 The molar volume At STP Can be used to form conversion factors L and 1 mol 1 mol 22.4 L Molar Volume as a Conversion Factor Chapter 11 Slide 48 of 81 Guide to Using Molar Volume Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 49 of What is the volume at STP of 4.00 g CH 4 ? A) 5.59 LB) 11.2 LC) 44.8 L 4.00 g CH 4 x 1 mol CH 4 x 22.4 L (STP) = g CH 4 1 mol CH 4 Learning Check 5.59 L Chapter 11 Slide 50 of How many grams of He are present in 8.00 L at STP? A) 25.6 gB) gC) 1.43 g 8.00 L x 1 mol He x g He = 22.4 L 1 mol He Learning Check 1.43 g He Chapter 11 Slide 51 of 81 AT STP, the density of gas can be calculated using the mass of the gas and its volume. Density = Molar mass Molar volume Density of a Gas at STP Chapter 11 Slide 52 of 81 Density of a Gas Calculate the density in g/L of O 2 gas at STP. At STP, we know that 1 mol O 2 (32.00 g) occupies a volume of 22.4 L. Density O 2 at STP = g O 2 = 1.43 g/L 22.4 L (STP) Chapter 11 Slide 53 of 81 Chapter 11 Gases The Ideal Gas Law Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 54 of 81 The ideal gas law Provides a relationship between the four properties (P, V, n, and T) of gases that can be written equal to a constant R. PV = R nT Rearranges these properties to give the ideal gas law expression. PV = nRT Ideal Gas Law Chapter 11 Slide 55 of 81 The universal gas constant, R Can be calculated using the molar volume of a gas at STP. Calculated at STP uses 273 K,1.00 atm, 1 mol of a gas, and a molar volume of 22.4 L. P V R = PV = (1.00 atm)(22.4 L) nT (1 mol) (273K) n T = L atm mol K Universal Gas Constant, R Chapter 11 Slide 56 of 81 Another value for the universal gas constant is obtained using mm Hg for the STP pressure. The units of R are dependent on the units of the parameters that are used to calculate R. What is the value of R when a pressure of 760 mm Hg is placed in the R value expression? Learning Check Chapter 11 Slide 57 of 81 What is the value of R when a pressure of 760 mm Hg is placed in the R value expression? R = PV = (760 mm Hg) (22.4 L) nT (1 mol) (273 K) = 62.4 L mm Hg mol K Solution Chapter 11 Slide 58 of 81 Dinitrogen oxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If a 20.0 L tank of laughing gas contains 2.86 mol N 2 O at 23C, what is the pressure (mm Hg) in the tank? Learning Check Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 59 of Adjust the units of the given properties to match the units of R. V = 20.0 L20.0 L T = 23C K n = 2.86 mol2.86 mol P = ? ? Solution Chapter 11 Slide 60 of Rearrange the ideal gas law for P. P = nRT V 3. Substitute quantities and solve. P = (2.86 mol)(62.4 L mm Hg)(296 K) (20.0 L) (mol K) = 2.64 x 10 3 mm Hg Solution Chapter 11 Slide 61 of 81 Learning Check A cylinder contains 5.0 L O 2 at 20.0C and 0.85 atm. How many grams of oxygen are in the cylinder? Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 62 of Determine the given properties. P = 0.85 atm, V = 5.0 L, T = 293 K, n ( or g =?) 2. Rearrange the ideal gas law for n (moles). n = PV RT = (0.85 atm)(5.0 L)(mol K) = 0.18 mol O 2 (0.0821atm L)(293 K) 3. Convert moles to grams using molar mass. = mol O 2 x 32.0 g O 2 = 5.8 g O 2 1 mol O 2 Solution Chapter 11 Slide 63 of 81 What is the molar mass of a gas if g of the gas occupy 215 mL at atm and 30.0C? 1. Solve for the moles (n) of gas. n = PV = (0.813 atm) (0.215 L) molK = mol RT ( L atm)(303K) 2. Set up the molar mass relationship. Molar mass = g = g mol mol = 35.6 g/mol Molar Mass of a Gas Chapter 11 Slide 64 of 81 Chapter 11 Gases Gas Laws and Chemical Reactions Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 65 of 81 Gases in Equations The volume or amount of a gas in a chemical reaction can be calculated from STP conditions or the ideal gas law. Mole factors from the balanced equation. Chapter 11 Slide 66 of 81 STP and Gas Equations What volume (L) of O 2 gas is needed to completely react with 15.0 g of aluminum at STP? 4Al(s) + 3O 2 (g) 2Al 2 O 3 (s) Plan: g Al mol Al mol O 2 L O 2 (STP) 15.0 g Al x 1 mol Al x 3 mol O 2 x 22.4 L (STP) g Al 4 mol Al 1 mol O 2 = 9.34 L O 2 at STP Chapter 11 Slide 67 of 81 Ideal Gas Equation and Reactions What volume (L) of Cl 2 gas at 1.2 atm and 27C is needed to completely react with 1.5 g aluminum? 2Al(s) + 3Cl 2 (g) 2AlCl 3 (s) Plan? g Al moles Al moles Cl 2 L Cl 2 Chapter 11 Slide 68 of 81 Ideal Gas Equation and Reactions 2Al(s) + 3Cl 2 (g) 2AlCl 3 (s) 1.5 g ? L 1.2 atm, 300K 1. Calculate the moles of Cl 2 needed. 1.5 g Al x 1 mol Al x 3 mol Cl 2 = mol Cl g Al 2 mol Al 2. Place the moles Cl 2 in the ideal gas equation. V = nRT =(0.083 mol Cl 2 )( L atm/mol K)(300 K) P 1.2 atm = 1.7 L Cl 2 Chapter 11 Slide 69 of 81 What volume (L) of O 2 at 24C and atm is needed to react with 28.0 g NH 3 ? 4NH 3 (g) + 5O 2 (g) 4NO(g) + 6H 2 O(g) Learning Check Chapter 11 Slide 70 of 81 4NH 3 (g) + 5O 2 (g) 4NO(g) + 6H 2 O(g) 1. Calculate the moles of O 2 needed g NH 3 x 1 mol NH 3 x 5 mol O g NH 3 4 mol NH 3 = 2.06 mol O 2 2. Place the moles of O 2 in the ideal gas equation. V = nRT =(2.06 mol)( L atm/mol K)(297 K) P atm = 52.9 L O 2 Solution Chapter 11 Slide 71 of 81 Chapter 11 Gases Partial Pressure (Daltons Law) Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 72 of 81 The partial pressure of a gas Is the pressure of each gas in a mixture. Is the pressure that gas would exert if it were by itself in the container. Partial Pressure Chapter 11 Slide 73 of 81 Daltons Law of Partial Pressures states that the total pressure Depends on the total number of gas particles, not on the types of particles. Exerted by a gas mixture is the sum of the partial pressures of those gases. P T = P 1 + P Daltons Law of Partial Pressures Chapter 11 Slide 74 of 81 Illustrating Partial Pressures Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 75 of 81 At STP, One mole of a pure gas in a volume of 22.4 L will exert the same pressure as one mole of a gas mixture in 22.4 L. V STP = 22.4 L Gas mixtures Total Pressure 0.5 mol O mol He 0.2 mol Ar 1.0 mol 1.0 mol N mol O mol He 1.0 mol 1.0 atm Chapter 11 Slide 76 of 81 Scuba Diving When a scuba diver makes a deep dive, the increased pressure causes N 2 (g) to dissolve in the blood. If the rise is too fast, the dissolved N 2 forms bubbles in the blood, a dangerous condition called "the bends". Helium is mixed with O 2 to prepare breathing mixtures for deep descents. Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 77 of 81 Learning Check A scuba tank contains O 2 with a pressure of atm and He at 855 mm Hg. What is the total pressure in mm Hg in the tank? Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings Chapter 11 Slide 78 of Convert the pressure in atm to mm Hg atm x 760 mm Hg = 342 mm Hg = P O 2 1 atm 2. Calculate the sum of the partial pressures. P total = PO 2 + P He P total = 342 mm Hg mm Hg = 1197 mm Hg Solution Chapter 11 Slide 79 of 81 For a deep dive, some scuba divers are using a mixture of helium and oxygen gases with a pressure of 8.00 atm. If the oxygen has a partial pressure of 1280 mm Hg, what is the partial pressure of the helium? 1) 520 mm Hg 2) 2040 mm Hg 3) 4800 mm Hg Learning Check Chapter 11 Slide 80 of 81 A) 520 mm Hg B) 2040 mm Hg C) 4800 mm Hg P Total = 8.00 atm x 760 mm Hg = 6080 mm Hg 1 atm P Total = P O + P He 2 P He = P Total - P O 2 P He = 6080 mm Hg mm Hg = 4800 mm Hg Solution Chapter 11 Slide 81 of 81 Gases We Breathe The air we breathe Is a gas mixture. Contains mostly N 2 and O 2 and small amounts of other gases. Table 11.7 Copyright 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings