Chapter 10 Key Terms Diffusion Permeability Compressibility Pressure Barometer Ideal Gas Law Molar Volume STP Vapor Pressure Avogadro’s Law Boyle’s Law Charles’s Law Pascal PSI

Chapter 10 Gases

Gases Comes from the Greek word khaos which means “formless matter” Meaning the move about freely Kinetic Theory: Particles move at random, with high velocities, in all directions, and at many different speeds Particles are tiny compared to the great distances between them Particles do not interact except during momentary collisions

Gases Collisions between gas particles are elastic They conserve energy Sum of the particles energies before = sum of the energy after Ex. Newton’s cradle Ex. If particle A, with an energy of 560 J, bumps into particle B, which has an energy of 240 J. Both particles leave the collision with an energy of 400 J. If particle A leaves the collision with an energy of 500 J, what energy does particle B have? The average kinetic energy of the gas particles is directly proportional to the temperature of the gas in Kelvin

Physical Properties of Gases Low Density Amount of matter within a certain volume Density = mass/volume Diffusibility Expands to fill its container with an even concentration Diffusion: when a substance goes from an area of high concentration to an area of low concentration

Physical Properties of Gases Permeability Ability of a gas to mingle with another porous substance Gas particles move into the spaces between other molecules Compressibility A gas can be “compressed” into a smaller container Expansibility Gases can expand without limit This happens because molecules are constantly in motion

Gases cause pressure Pressure: the average force exerted per unit area when molecules collide with a boundary Measured in force per unit area Pounds per square inch (PSI) Millimeters of mercury (mm Hg) Torr Atmosphere (atm) Pascal (Pa, kPa)

Pressure Measured with a barometer Mercury barometers measure pressure in millimeters mercury (mm Hg) Another name for mm Hg is a torr Pascal is the SI unit for pressure Standard pressure is the normal atmospheric pressure at sea level at 45o latitude 1 atmosphere = 760 mm Hg = 760 torr = 14.7 psi = 101,325 Pa = 101.325 kPa

Pressure Conversions 1atm = 760 mm Hg = 760 torr = 14.7 psi = 101,325 Pa = 101.325 kPa 12 atm = ________ kPa 526 mm Hg = ________ Pa 1000. torr = ________ atm 0.91 kPa = ________ psi 892 mm Hg = ________ torr

Pressure, Temperature, & Volume Case Pressure (P) Temperature (T) Volume (V) 1 Increase/Decrease Constant Decrease/Increase 2 3 Case 1: Inverse Relationship Case 2: Direct Relationship Case 3: Direct Relationship

Standard Conditions Standard Temperature and Pressure (STP) Standard temp: 0oC or 273 K Standard Pressure: 760 torr, 1 atm…

Boyle’s Law Named for Robert Boyle (1627-1691) Found that increased pressure decreased the volume of gas Boyle’s Law: The volume of a dry gas is inversely related to the pressure if the temperature is held constant P1V1 = P2V2 Twice the pressure = half the volume Units: Volume: mL, L, ft3, cm3, m3 Pressure: torr, atm, mm Hg…

Boyle’s Law A gas at 35oC occupies 85 mL at standard pressure. What will the volume be if the pressure increases to 2.67 atm? At standard pressure, the Helium in a balloon occupies 8.340 mL. What is the new volume of Helium when the pressure increases to 120,014 Pa?

Charles’ Law Named for Jacques Charles (1747-1823) Charles’s Law: When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume are directly related Temperature doubles: volume doubles V 1 T 1 = V 2 T 2

Gay-Lussac’s Law Pressure is directly proportional to Kelvin temperature for a fixed mass of gas held in a constant volume Ex. Car tire pressure increasing during trip, basketball loses bounce when cold P 1 T 1 = P 2 T 2 At the beginning of her trip, Glenda measured the pressure in her tires to be 38 psi at a temperature of 14oC. When she stopped for gas 3 hours later, she measured the pressure to now be 41 psi. What was the new temp of the air in her tires?

Review Boyle’s Law Charles’ Law Gay-Lussac’s Law P1V1 = P2V2 𝑽 𝟏 𝑻 𝟏 = 𝑽 𝟐 𝑻 𝟐 Gay-Lussac’s Law 𝑷 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑻 𝟐

Combined Gas Law 𝑷 𝟏 𝑽 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟐 𝑷 𝟏 𝑽 𝟏 𝑻 𝟏 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟐 When all 3 values change, we can use the combined gas law When 1 value is constant, we use one of the laws A gas has a volume of 3.6 L when it is at STP. What will its new volume be at a pressure of 1.104 atm and -15oC?

Dalton’s Law Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures 1 L of oxygen at STP is added to 1 L of nitrogen at the same pressure. The pressure inside the container of nitrogen and oxygen is now 1520 torr. What are the partial pressures of nitrogen and oxygen? 1520 torr x 50% Partial pressure of O = 760 torr Partial pressure of N = 760 torr

Dalton’s Law A sample of dry air contains 78% N, 21% O, and 1% Ar. At 760 torr, what are the partial pressures of those gases? N = 592.8 torr O = 159.6 torr Ar = 7.6 torr

Vapor Pressure When gases are collected “over water” some of the water evaporates and mixes with the gas The water molecules exert a pressure called “vapor pressure” If no pressure is given, we can assume the pressure is the same as the atmospheric pressure at STP To find the pressure of the gas being measured, we subtract the vapor pressure from the total pressure

Vapor Pressure A sample of He is collected over water at a temperature of 95oC with a total pressure of 801 torr. What is the actual pressure of Helium? 801 torr – 633.9 torr = 167.1 torr A sample of gas collected over water has a pressure of 1052 torr at 15.0oC. The gas is a mixture of 38.21% oxygen and 61.79% nitrogen (without factoring in the water vapor). What are the partial pressures of oxygen and nitrogen?

Sample Problem 𝐏 𝟏 𝐕 𝟏 𝐓 𝟏 = 𝐏 𝟐 𝐕 𝟐 𝐓 𝟐 46 mL of O2 gas is collected over water at 25oC when the atmospheric pressure is 102 kPa. What volume of pure oxygen would this be at STP? 102kPa – 3.167kPa = 98.833 kPa = 99 kPa Now we can use the Combined Gas Law 𝐏 𝟏 𝐕 𝟏 𝐓 𝟏 = 𝐏 𝟐 𝐕 𝟐 𝐓 𝟐 41.174 mL or with sig figs, 41 mL

Law of Combining Volumes Formulated by Joseph-Louis Gay-Lussac in 1808 Under equivalent conditions, the volumes of reacting gases and their gaseous products are expressed in ratios of small whole numbers (mole ratios) H2 + Cl2  2 HCl 2 H2 + O2  2 H2O N2 + 3 H2  2 NH3

Avogadro’s Law The volume of a gas, maintained at a constant temperature and pressure, is directly proportional to the number of moles of the gas H2 + Cl2  2 HCl 2 H2 + O2  2 H2O At STP, a volume of 22.4 L contains 1 mole of a gas 22.4 L is considered the molar volume of a gas Does not matter what type of gas is being considered

Avogadro’s Law What volume would 4.00 mol of ammonia occupy at STP? How many moles of a gas is contained in 420 L at STP? What volume will 2.50 mol of hydrogen gas occupy at 300. K and at a pressure of 400. torr? A sample of oxygen gas occupies 1.00 L when its temperature is 190. K and its pressure is 129 kPa. How many moles of oxygen are present?

Densities of Gases Density is defined as mass per unit of volume Just because a volume contains the same number of particles/molecules does not mean they have the same density Density is what causes certain objects to float and to sink Same idea with gases – Helium balloons Explained by the molar volume concept 1 mole of gas occupies 22.4 L at STP 1 mole of a compound has a certain mass Density at STP = 𝐌𝐨𝐥𝐚𝐫 𝐦𝐚𝐬𝐬 𝐌𝐨𝐥𝐚𝐫 𝐕𝐨𝐥𝐮𝐦𝐞 = g L

Densities Use 3 significant figures What is the density of Hydrogen gas? An unknown gas has a density of 2.144 g/L at STP. What is its Molar Mass? What is the density of carbon dioxide?

Mass (grams) Mass (grams) Mole Mole Particles Particles Molar mass (periodic table) Molar mass (periodic table) Mass (grams) mole ratio Mole Mole Particles (atoms, molecules, formula units) Particles (atoms, molecules, formula units) 6.02 x 1023 6.02 x 1023

Stoichiometry Using the following equation, what mass of aluminum acetate is made if 125 grams of acetic acid reacts with excess aluminum hydroxide? 3 C2H3O2H + Al(OH)3  Al(C2H3O2)3 + 3 H2O 125 g C2H3O2H x 𝟏 𝐦𝐨𝐥 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 𝐇 𝟔𝟎.𝟎𝟓𝟐𝟓𝟔 𝐠 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 𝐇 x 𝟏 𝐦𝐨𝐥 𝐀𝐥( 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 ) 𝟑 𝟑 𝐦𝐨𝐥 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 𝐇 x 𝟐𝟎𝟒.𝟏𝟏𝟓𝟑𝟗𝟖 𝐠 𝐀𝐥( 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 ) 𝟑 𝟏 𝐦𝐨𝐥 𝐀𝐥( 𝐂 𝟐 𝐇 𝟑 𝐎 𝟐 ) 𝟑 141.6227 = 142 g Al(C2H3O2)3

Volume of Gas at nonstandard conditions Mass Volume of Gas at nonstandard conditions Volume of Gas at STP Number of Particles Moles Combined Gas Law Coefficient from balanced equation Molar Volume Molar Mass Mole Ratio Avogadro’s Number

Stoichiometry When 2.00 mol of Ca reacts with excess water, what volume of hydrogen gas will be produced at STP? Ca + 2 H2O  Ca(OH)2 + H2 How many grams of water will be produced if 0.500 L of oxygen gas at STP is burned with hydrogen? 2 H2 + O2  2 H2O

Stoichiometry If 15.0 L of oxygen were used in the following reaction, determine the mass AND volume of carbon dioxide produced in the following reaction. Assume STP for both gases. 2 C4H10 + 13 O2  8 CO2 + 10 H2O In the reaction above, if 20.00 g of C4H10 were used in the reaction, what volume of CO2 will be produced at 755 torr and 20oC?

Ideal Gases A gas that behaves just as kinetic theory says it should Not yet been found on Earth Kinetic Theory assumes: Gas molecules are very small Molecules are far apart from each other Forces act on the particles only during collisions

Ideal Gas Law PV = nRT Relates pressure, volume, temperature and number of moles The value and units depend on the units used for P, V, n and T R = 0.0821 L•atm mol•k R = 62.36 L•torr mol•k How many moles of H2 is in a 3.1 L sample measured at 300. atm and 20.oC?

Ideal Gas Law How many moles of CO2 is in a 5.6 L sample measured at STP? Calculate the volume of 4.50 mol of SO2 measured at STP. What volume would the previous gas occupy at 25oC and 150 atm? Make sure all units in your equations are the same Don’t combine atm with torr, or L with mL