Avogadro’s Law: Volume and Moles General, Organic, and Biological Chemistry Fourth Edition Karen Timberlake Avogadro’s law states that The Other Gas Law the volume of a gas is directly related to the number of moles (n) of gas. Volume and Moles Relationship (Avogadro’s Law) T and P are constant. © 2013 Pearson Education, Inc. © 2013 Pearson Education, Inc. Chapter 7, Section 7 2 Chapter 7, Section 7 © 2013 Pearson Education, Inc. Learning Check Solution If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume will 1.2 moles of helium occupy at the same temperature and pressure? A. 0.94 L B. 1.8 L C. 2.4 L If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume will 1.2 moles of helium occupy at the same temperature and pressure? Step 1 Organize the data in a table of initial and final conditions. Analyze the Problem. Conditions 1 Conditions 2 V1 = 1.5 L Chapter 7, Section 7 3 © 2013 Pearson Education, Inc. Predict V increases n1 = 0.75 mole n2 = 1.2 moles © 2013 Pearson Education, Inc. Know V2 = ? n increases Chapter 7, Section 7 Solution STP If 0.75 mole of helium gas occupies a volume of 1.5 L, what volume will 1.2 moles of helium occupy at the same temperature and pressure? To make comparisons between different gases, we use arbitrary conditions called standard temperature (273 K) and standard pressure (1 atm). Standard temperature and pressure is abbreviated as STP. Step 2 Rearrange the gas law equation to solve for the unknown quantity. 4 Standard temperature (T) = 0 °C or 273 K Step 3 Substitute values into the gas law equation and calculate. Standard pressure (P) = 1 atm (760 mmHg) Answer is C. © 2013 Pearson Education, Inc. Chapter 7, Section 7 5 © 2013 Pearson Education, Inc. Chapter 7, Section 7 6 1 Molar Volume as a Conversion Factor Molar Volume The molar volume of a gas measured at STP (standard temperature and pressure) is 22.4 L for 1 mole of any gas. The molar volume at STP has about the same volume as 3 basketballs. can be used to form 2 conversion factors. and Avogadro’s law indicates that 1 mole of any gas at STP has a volume of 22.4 L. © 2013 Pearson Education, Inc. Chapter 7, Section 7 7 Guide to Using Molar Volume Chapter 7, Section 7 © 2013 Pearson Education, Inc. 8 Using Molar Volume What is the volume occupied by 2.75 moles of N2 gas at STP? Step 1 State the given and needed quantities. Analyze the Problem. Given Need 2.75 moles of N2 at STP Liters of N2 Step 2 Write a plan to calculate the needed quantity. moles N2 © 2013 Pearson Education, Inc. Chapter 7, Section 7 9 © 2013 Pearson Education, Inc. molar volume liters N2 Chapter 7, Section 7 Using Molar Volume Gases in Chemical Reactions What is the volume occupied by 2.75 moles of N2 gas at STP? Step 3 Write the equalities and conversion factors including 22.4 L/mole at STP. The volume or amount of a gas at STP in a chemical reaction can be calculated from 10 STP conditions. mole−mole factors from the balanced equation. Step 4 Set up the problem with factors to cancel units. © 2013 Pearson Education, Inc. Chapter 7, Section 7 11 © 2013 Pearson Education, Inc. Chapter 7, Section 7 12 2 Gases in Equations at STP Guide to Reactions Involving Gases What volume (L) of O2 gas is needed to completely react with 15.0 g of aluminum at STP? Step 1 State the given and needed quantities. Analyze the Problem. © 2013 Pearson Education, Inc. Chapter 7, Section 7 13 © 2013 Pearson Education, Inc. Chapter 7, Section 7 14 Gases in Equations at STP Gases in Equations at STP What volume (L) of O2 gas is needed to completely react with 15.0 g of aluminum at STP? What volume (L) of O2 gas is needed to completely react with 15.0 g of aluminum at STP? Step 2 Write a plan to calculate the needed quantity. Step 3 Write the equalities and conversion factors including the molar volume. mole-mole grams molar molar moles mole−mole moles molar molar liters volume mass of Al factor factor of O2 volume of O2 of Al mass © 2013 Pearson Education, Inc. Chapter 7, Section 7 15 © 2013 Pearson Education, Inc. Chapter 7, Section 7 16 General, Organic, and Biological Chemistry Gases in Equations at STP Fourth Edition Karen Timberlake What volume (L) of O2 gas is needed to completely react with 15.0 g of aluminum at STP? Chapter 7 The Ideal Gas Law Step 4 Set up the problem and calculate © 2013 Pearson Education, Inc. © 2013 Pearson Education, Inc. Chapter 7, Section 7 © 2013 Pearson Education, Inc. Chapter 7, Section 8 3 Ideal Gas Law R, Ideal Gas Constant The four properties used in the measurement of a gas, pressure (P), volume (V), temperature (T), and amount (n), can be combined to give a single expression called the ideal gas law. PV = nRT Rearranging the ideal gas law equation shows that the four gas properties equal a constant, R. © 2013 Pearson Education, Inc. Chapter 7, Section 8 To calculate the value of R, we substitute the STP conditions for molar volume into the expression: 19 © 2013 Pearson Education, Inc. Chapter 7, Section 8 Learning Check Solution Another value for the universal gas constant, R, is obtained using mmHg for the STP pressure. What is the value of R when a pressure of 760 mmHg rather than 1.00 atm is used? Another value for the universal gas constant, R, is obtained using mmHg for the STP pressure. What is the value of R when a pressure of 760 mmHg rather than 1.00 atm is used? © 2013 Pearson Education, Inc. Chapter 7, Section 8 21 Unit Summary for R, the Ideal Gas Constant © 2013 Pearson Education, Inc. Chapter 7, Section 8 © 2013 Pearson Education, Inc. Chapter 7, Section 8 20 22 Guide to Using the Ideal Gas Law 23 © 2013 Pearson Education, Inc. Chapter 7, Section 8 24 4 Learning Check Solution Dinitrogen oxide (N2O), laughing gas, is used by dentists as an anesthetic. If a 20.0 L tank of laughing gas contains 2.86 moles of N2O at 23 °C, what is the pressure (mmHg) in the tank? If a 20.0 L tank of laughing gas contains 2.86 moles of N2O at 23 ˚C, what is the pressure (mmHg) in the tank? Step 1 State the given and needed quantities. Analyze the Problem. © 2013 Pearson Education, Inc. Chapter 7, Section 8 25 © 2013 Pearson Education, Inc. Chapter 7, Section 8 26 Solution Solution If a 20.0 L tank of laughing gas contains 2.86 moles of N2O at 23 ˚C, what is the pressure (mmHg) in the tank? If a 20.0 L tank of laughing gas contains 2.86 moles of N2O at 23 ˚C, what is the pressure (mmHg) in the tank? Step 2 Rearrange the ideal gas law equation to solve for the needed quantity. Step 3 Substitute the gas data into the equation and calculate the needed quantity. © 2013 Pearson Education, Inc. Chapter 7, Section 8 27 Ideal Gas Law and Molar Mass © 2013 Pearson Education, Inc. Chapter 7, Section 8 28 Learning Check A cylinder contains 5.0 L of an unknown gas at 20.0 ˚C and 0.85 atm. If the mass of the gas in the cylinder is 5.8 g, what is the molar mass of the gas? © 2013 Pearson Education, Inc. Chapter 7, Section 8 29 © 2013 Pearson Education, Inc. Chapter 7, Section 8 30 5 Solution Solution A cylinder contains 5.0 L of an unknown gas at 20.0 ˚C and 0.85 atm. If the mass of the gas in the cylinder is 5.8 g, what is the molar mass of the gas? Step 2 Rearrange the ideal gas law equation to solve for the number of moles. A cylinder contains 5.0 L of an unknown gas at 20.0 ˚C and 0.85 atm. If the mass of the gas in the cylinder is 5.8 g, what is the molar mass of the gas? Step 1 State the given and needed quantities. Analyze the Problem Step 3 Obtain the molar mass by dividing the given number of grams by the number of moles. © 2013 Pearson Education, Inc. Chapter 7, Section 8 31 Chemical Reactions and the Ideal Gas Law Chapter 7, Section 8 © 2013 Pearson Education, Inc. 32 Learning Check Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? © 2013 Pearson Education, Inc. Chapter 7, Section 8 33 Chapter 7, Section 8 © 2013 Pearson Education, Inc. 34 Solution Solution How many liters of NH3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? How many liters of NH3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 1 State the given and needed quantities. Analyze the Problem. Step 2 Write a plan to convert the given quantity to the needed moles. grams of N2 © 2013 Pearson Education, Inc. Chapter 7, Section 8 35 © 2013 Pearson Education, Inc. molar mass moles mole−mole moles of N2 factor of NH3 Chapter 7, Section 8 36 6 Solution Solution How many liters of NH3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? How many liters of NH3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Step 3 Write the equalities for molar mass and mole– mole factors. Step 4 Set up the problem to calculate moles of needed quantity. © 2013 Pearson Education, Inc. Chapter 7, Section 8 37 © 2013 Pearson Education, Inc. Chapter 7, Section 8 38 General, Organic, and Biological Chemistry Solution Fourth Edition Karen Timberlake How many liters of NH3 can be produced at 0.93 atm and 24 ˚C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? Dalton’s Law of Partial Pressures Step 5 Convert the moles of needed to volume using the ideal gas law equation. © 2013 Pearson Education, Inc. © 2013 Pearson Education, Inc. Chapter 7, Section 8 39 © 2013 Pearson Education, Inc. Chapter 7, Section 9 Partial Pressure, Dalton’s Law Dalton’s Law of Partial Pressures In a gas mixture, each gas exerts its partial pressure, which is the pressure it would exert if it were the only gas in the container. Dalton’s Law of Partial Pressures indicates that pressure depends on the total number of gas particles. Dalton’s law states that the total pressure of a gas mixture is the sum of the partial pressures of the gases in the mixture. © 2013 Pearson Education, Inc. Chapter 7, Section 9 41 © 2013 Pearson Education, Inc. Chapter 7, Section 9 42 7 Total Pressure Composition of Air For example, at STP, one mole of a pure gas will exert the same pressure as one mole of a gas mixture in a 22.4 L container. V = 22.4 L Gas mixtures Air is a mixture of gases, including nitrogen, oxygen, carbon dioxide, argon, and water gases. 1.0 mole N2 0.4 mole O2 0.6 mole He 1.0 mole 1.0 atm 1.0 atm © 2013 Pearson Education, Inc. 0.5 mole O2 0.3 mole He 0.2 mole Ar 1.0 mole 1.0 atm Chapter 7, Section 9 43 Guide to Solving for Partial Pressure © 2013 Pearson Education, Inc. Chapter 7, Section 9 44 Learning Check A scuba tank contains a mixture of He and O2 gases at 7.00 atm. If the pressure of O2 gas is 1140 mmHg, what is the partial pressure of He gas in the tank? © 2013 Pearson Education, Inc. Chapter 7, Section 9 45 © 2013 Pearson Education, Inc. Chapter 7, Section 9 46 Solution Solution A scuba tank contains a mixture of He and O2 gases at 7.00 atm. If the pressure of O2 gas is 1140 mmHg, what is the partial pressure of He gas in the tank? Step 1 Write the equation for partial pressures. A scuba tank contains a mixture of He and O2 gases at 7.00 atm. If the pressure of O2 gas is 1140 mmHg, what is the partial pressure of He gas in the tank? Step 3 Substitute known pressures into the equation and calculate the unknown partial pressure. Step 2 Rearrange the equation to solve for the unknown pressure. © 2013 Pearson Education, Inc. Chapter 7, Section 9 47 © 2013 Pearson Education, Inc. Chapter 7, Section 9 48 8 Blood Gases Blood Gases In the lungs, O2 enters the blood, at the same time that CO2 is released. In the tissues, O2 enters the cells, which release CO2 into the blood. In the body, O2 flows into the tissues because the partial pressure of O2 is higher in blood and lower in the tissues. CO2 flows out of the tissues because the partial pressure of CO2 is higher in the tissues and lower in the blood. Partial Pressures (mmHg) in Blood and Tissue Oxygenated Deoxygenated Tissues Blood Blood O2 100 mmHg 40 mmHg 30 mmHg or less CO2 40 mmHg 46 mmHg 50 mmHg or greater Gas © 2013 Pearson Education, Inc. Chapter 7, Section 9 49 © 2013 Pearson Education, Inc. Chapter 7, Section 9 50 Changes in Partial Pressures of Blood Gases During Breathing © 2013 Pearson Education, Inc. Chapter 7, Section 9 51 9

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