# The Gaseous State of Matter

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The Gaseous State of Matter
Chapter 12 The Gaseous State of Matter The air in a hot air balloon expands When it is heated. Some of the air escapes from the top of the balloon, lowering the air density inside the balloon, making the balloon buoyant. Introduction to General, Organic, and Biochemistry 10e John Wiley & Sons, Inc Morris Hein, Scott Pattison, and Susan Arena

Copyright 2012 John Wiley & Sons, Inc
Chapter Outline 12.1 General Properties 12.2 The Kinetic-Molecular Theory 12.3 Measurement of Pressure 12.4 Dependence of Pressure on Number of Molecules and Temperature 12.5 Boyle’s Law 12.6 Charles’ Law 12.7 Gay-Lussac’s Law 12.8 Combined Gas Laws 12.9 Dalton’s Law of Partial Pressures 12.10 Avogadro’s Law 12.11 Mole-Mass-Volume Relationships of Gases 12.12 Density of Gases 12.13 Ideal Gas Law 12.14 Gas Stoichiometry 12.15 Real Gases Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
General Properties Gases Have an indefinite volume Expand to fill a container Have an indefinite shape Take the shape of a container Have low densities Have high kinetic energies A mole of water occupies 18 mL as a liquid but would fill this box (22.4 L) as a gas at the same temperature. Copyright 2012 John Wiley & Sons, Inc

Kinetic Molecular Theory (KMT)
Assumptions of the KMT and ideal gases include: Gases consist of tiny particles The distance between particles is large compared with the size of the particles. Gas particles have no attraction for each other Gas particles move in straight lines in all directions, colliding frequently with each other and with the walls of the container. Copyright 2012 John Wiley & Sons, Inc

Kinetic Molecular Theory
Assumptions of the KMT (continued): Collisions are perfectly elastic (no energy is lost in the collision). The average kinetic energy for particles is the same for all gases at the same temperature. The average kinetic energy is directly proportional to the Kelvin temperature. Copyright 2012 John Wiley & Sons, Inc

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Diffusion Copyright 2012 John Wiley & Sons, Inc

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Effusion Gas molecules pass through a very small opening from a container at higher pressure of one at lower pressure. Graham’s law of effusion: Copyright 2012 John Wiley & Sons, Inc

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Your Turn! Which gas will diffuse most rapidly? He Ne Ar Kr Copyright 2012 John Wiley & Sons, Inc

Measurement of Pressure
Pressure depends on the Number of gas molecules Temperature of the gas Volume the gas occupies Copyright 2012 John Wiley & Sons, Inc

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Atmospheric Pressure Atmospheric pressure is due to the mass of the atmospheric gases pressing down on the earth’s surface. Copyright 2012 John Wiley & Sons, Inc

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Barometer Figure Preparation of a mercury barometer. The full tube of mercury at the left is inverted and placed in a dish of mercury. Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Pressure Conversions Convert 675 mm Hg to atm. Note: 760 mm Hg = 1 atm Convert 675 mm Hg to torr. Note: 760 mm Hg = 760 torr. Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! A pressure of 3.00 atm is equal to 819 torr 3000 torr 2280 torr 253 torr Copyright 2012 John Wiley & Sons, Inc

Dependence of Pressure on Number of Molecules
P is proportional to n (number of molecules) at Tc (constant T) and Vc (constant V). The increased pressure is due to more frequent collisions with walls of the container as well increased force of each collision. Figure The pressure exerted by a gas is directly proportional to the number of molecules present. In each case shown, the volume is 22.4 L and the temperature is 0°C. Copyright 2012 John Wiley & Sons, Inc

Dependence of Pressure on Temperature
P is proportional to T at nc (constant number of moles) and Vc. The increased pressure is due to more frequent collisions higher energy collisions Figure 12.5 The pressure of a gas in a fixed volume increases with increasing temperature. The increased pressure is due to more frequent and more energetic collisions of the gas molecules with the walls of the container at the higher temperature. Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! If you change the temperature of a sample of gas from 80°C to 25°C at constant volume, the pressure of the gas will increase. will decrease. will not change Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Boyle’s Law What happens to V if you double P? V decreases by half! What happens to P if you double V? P decreases by half! Figure Graph of pressure versus volume showing the inverse PV relationship of an ideal gas. Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Boyle’s Law A sample of argon gas occupies mL at 920. torr. Calculate the pressure of the gas if the volume is increased to 937 mL at constant temperature. Knowns V1 = 500 mL P1 = 920. torr V2 = 937 mL Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Boyle’s Law Another approach to the same problem: Since volume increased from 500. mL to 937 ml, the pressure of 920. torr must decrease. Multiply the pressure by a volume ratio that decreases the pressure: Copyright 2012 John Wiley & Sons, Inc

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Your Turn! A 6.00 L sample of a gas at a pressure of 8.00 atm is compressed to 4.00 L at a constant temperature. What is the pressure of the gas? 4.00 atm 12.0 atm 24.0 atm 48.0 atm Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! A 400. mL sample of a gas is at a pressure of 760. torr. If the temperature remains constant, what will be its volume at 190. torr? A mL B mL C mL D. 1.60x102 mL Copyright 2012 John Wiley & Sons, Inc

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Charles’ Law The volume of an ideal gas at absolute zero (-273°C) is zero. Real gases condense at their boiling point so it is not possible to have a gas with zero volume. The gas laws are based on Kelvin temperature. All gas law problems must be worked in Kelvin! Figure Volume-temperature relationship of methane (CH4). Extrapolated portion of the graph is shown by the broken line. Copyright 2012 John Wiley & Sons, Inc

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Charles’ Law A 2.0 L He balloon at 25°C is taken outside on a cold winter day at -15°C. What is the volume of the balloon if the pressure remains constant? Knowns V1 = 2.0 L T1 = 25°C= 298 K T2 = -15°C = 258 K Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Charles’ Law Another approach to the same problem: Since T decreased from 25°C to -15°C, the volume of the 2.0L balloon must decrease. Multiply the volume by a Kelvin temperature ratio that decreases the volume: Copyright 2012 John Wiley & Sons, Inc

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Your Turn The volume of a gas always increases when Temperature increases and pressure decreases Temperature increases and pressure increases Temperature decreases and pressure increases Temperature decreases and pressure decreases Copyright 2012 John Wiley & Sons, Inc

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Your Turn! A sample of CO2 has a volume of 200. mL at 20.0 ° C. What will be its volume at 40.0 °C, assuming that the pressure remains constant? 18.8 mL 100. mL 213 mL 400. mL Copyright 2012 John Wiley & Sons, Inc

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Your Turn! A sample of gas has a volume of 3.00 L at 10.0 °C. What will be its temperature in °C if the gas expands to 6.00 L at constant pressure? 20.0°C 293°C 566°C 142°C Copyright 2012 John Wiley & Sons, Inc

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Gay-Lussac’s Law Copyright 2012 John Wiley & Sons, Inc

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Combined Gas Laws Used for calculating the results of changes in gas conditions. Boyle’s Law where Tc Charles’ Law where Pc Gay Lussacs’ Law where Vc P1 and P2 , V1 and V2 can be any units as long as they are the same. T1 and T2 must be in Kelvin. Copyright 2012 John Wiley & Sons, Inc

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Combined Gas Law If a sample of air occupies 500. mL at STP, what is the volume at 85°C and 560 torr? STP: Standard Temperature 273K or 0°C Standard Pressure 1 atm or 760 torr Knowns V1 = 500. mL T1 =273K P1= 760 torr T2 = 85°C = 358K P2= 560 torr Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

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Combined Gas Law A sample of oxygen gas occupies mL at 722 torr and –25°C. Calculate the temperature in °C if the gas has a volume of 2.53 L at 491 mmHg. Knowns V1 = mL T1 = -25°C = 248K P1= 722 torr V2 = 2.53 L = 2530 mL P2= 560 torr Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! A sample of gas has a volume of 8.00 L at 20.0 ° C and 700. torr. What will be its volume at STP? 1.20 L 9.32 L 53.2 L 6.87 L Copyright 2012 John Wiley & Sons, Inc

Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases is the sum of the partial pressures exerted by each of the gases in the mixture. PTotal = PA + PB + PC + …. Atmospheric pressure is the result of the combined pressure of the nitrogen and oxygen and other trace gases in air. Copyright 2012 John Wiley & Sons, Inc

Collecting Gas Over Water
Gases collected over water contain both the gas and water vapor. The vapor pressure of water is constant at a given temperature Pressure in the bottle is equalized so that the Pinside = Patm Figure Oxygen collected over water. Copyright 2012 John Wiley & Sons, Inc

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Your Turn! A sample of oxygen is collected over water at 22 ° C and 762 torr. What is the partial pressure of the dry oxygen? The vapor pressure of water at 22°C is 19.8 torr. 742 torr 782 torr 784 torr 750. torr Copyright 2012 John Wiley & Sons, Inc

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Avogadro’s Law Equal volumes of different gases at the same T and P contain the same number of molecules. Figure Avogadro’s Law proved the concept of diatomic molecules for hydrogen and chlorine The ratio is the same: 1 volume 1 molecule 1 mol 1 volume 1 molecule 1 mol 2 volumes 2 molecules 2 mol Copyright 2012 John Wiley & Sons, Inc

Mole-Mass-Volume Relationships
Molar Volume: One mole of any gas occupies 22.4 L at STP. Determine the molar mass of a gas, if 3.94 g of the gas occupied a volume of 3.52 L at STP. Knowns m = 3.94 g V = 3.52 L T = 273 K P = 1 atm Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! What is the molar mass of a gas if 240. mL of the gas at STP has a mass of grams? 8.57 g 22.4 g 16.8 g 29.9 g Copyright 2012 John Wiley & Sons, Inc

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Density of Gases Calculate the density of nitrogen gas at STP. Note that densities are always cited for a particular temperature, since gas densities decrease as temperature increases. Copyright 2012 John Wiley & Sons, Inc

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Your Turn! Which of the following gases is the most dense? H2 N2 CO2 O2 Carbon dioxide fire extinguishers can be used to put out fires because CO2 is more dense than air and can be used to push oxygen away from the fuel source. Copyright 2012 John Wiley & Sons, Inc

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Ideal Gas Law Calculate the volume of 1 mole of any gas at STP. Knowns n = 1 mole T = 273K P = 1 atm Set-Up Molar volume! Calculate Copyright 2012 John Wiley & Sons, Inc

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Ideal Gas Law How many moles of Ar are contained in 1.3L at 24°C and 745 mm Hg? Knowns V = 1.3 L T = 24°C = 297 K P = 745 mm Hg = atm Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

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Ideal Gas Law Calculate the molar mass (M) of an unknown gas, if 4.12 g occupy a volume of 943mL at 23°C and 751 torr. Knowns m =4.12 g V = 943 mL = L T = 23°C = 296 K P = 751 torr = atm Set-Up Calculate Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! What is the molar mass of a gas if 40.0 L of the gas has a mass of 36.0 g at 740. torr and 30.0 ° C? 33.1 g 23.0 g 56.0 g 333 g Copyright 2012 John Wiley & Sons, Inc

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Gas Stoichiometry Convert between moles and volume using the Molar Volume if the conditions are at STP : 1 mol = 22.4 L. Use the Ideal Gas Law if the conditions are not at STP. Figure Summary of the primary conversions involved in stoichiometry. The conversion for volumes of gases is included. Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Gas Stoichiometry Calculate the number of moles of phosphorus needed to react with 4.0L of hydrogen gas at 273 K and 1 atm. P4(s) + 6H2(g)  4PH3(g) Knowns V = 4.0 L T = 273 K P = 1 atm Solution Map L H2  mol H2  mol P4 Calculate Copyright 2012 John Wiley & Sons, Inc

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Gas Stoichiometry What volume of oxygen at 760 torr and 25°C are needed to react completely with 3.2 g C2H6? 2 C2H6(g) + 7 O2(g)  4 CO2(g) + 6 H2O(l) Knowns m = 3.2 g C2H T = 25°C = 298K P = 1 atm Solution Map m C2H6  mol C2H6  mol O2  volume O2 Calculate Copyright 2012 John Wiley & Sons, Inc

Your Turn! How many moles of oxygen gas are used up during the reaction with 18.0 L of CH4 gas measured at STP? CH4(g) + 2 O2(g)  CO2(g) + 2 H2O(l) 1.61 moles 2.49 moles 18.0 moles 36.0 moles Copyright 2012 John Wiley & Sons, Inc

Volume-Volume Calculations
Calculate the volume of nitrogen needed to react with 9.0L of hydrogen gas at 450K and 5.00 atm. N2(g) + 3H2(g)  2NH3(g) Knowns V = 9.0 L T = 450K P = 5.00 atm Assume T and P for both gases are the same. Use volume ratio instead of mole ratio! L H2  L N2 Solution Map Calculate Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Your Turn! What volume of sulfur dioxide gas will react when 12.0 L of oxygen is consumed at constant temperature and pressure?   SO2 + O2  2 SO3 6.00 L 12.0 L 24.0 L 60.0 L Copyright 2012 John Wiley & Sons, Inc

Copyright 2012 John Wiley & Sons, Inc
Real Gases Most real gases behave like ideal gases under ordinary temperature and pressure conditions. Conditions where real gases don’t behave ideally: At high P because the distance between particles is too small and the molecules are too crowded together. At low T because gas molecules begin to attract each other. High P and low T are used to condense gases. Copyright 2012 John Wiley & Sons, Inc

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