2 Review of KMT of Gases Assumptions Gases consist of tiny particles far apart from one anotherCollision between gas particles are elastic, with no loss of KEGas particles are in constant, rapid motion.No forces of attraction or repulsion exist between gas particlesAverage KE of particles depends on absolute temperature of the gas
3 Review of Pressure Pressure is force per unit area SI unit of force is the Newton (N)SI unit of pressure is the pascal1Pa = 1N/m2
4 14.1 Properties of Gases Compressibility Factors affecting Gas PressureAmount of gas (n)number of particles, i.e. moles of gasVolume (V)space occupied by the gasTemperature (T, absolute temperature)Recall TK = TC + 273
5 14.2 The Gas LawsThe gas laws describe the relationship of the 4 important variables that describe gas behaviorPressure (P)Moles (n)Volume (V)Temperature (T in Kelvins)
6 Boyle’s Law: Pressure & Volume Volume is inversely related to PressureWhen Pressure increases, Volume decreasesIf temperature and moles are constant
7 Practice Problems page 419 Given a volume of 2.50 L, if the pressure of N2O (an anesthetic) decreases from 105 kPa to 40.5 kPa, what is its new volume? (assume n & T are constant)If 4.00 L of NH3 at 205 kPa is allowed to expand to 12.0L, what is the new pressure if T and n remain constant?
8 Charles’ Law: Volume and Temperature Volume is directly proportional to absolute temperatureWhen temperature of an enclosed gas increases, its volume increasesIf pressure is constant
9 Sample Problems page 421If a sample of CO2 occupies a volume of 6.80 L at 325ºC, what will its volume be at 25ºC if the pressure does not change?Exactly 5.00 L of air at -50.0ºC is warmed to 100.0ºC. What is the new volume if pressure remains constant?
10 Gay-Lussac Law: Pressure and Temperature Pressure is directly proportional to absolute temperatureAs the temperature of an enclosed gas increases, its pressure increases if volume is constant
14 Sample Problems page 423A sample of N2 gas has a pressure of 6.58 kPa at 539K. If the volume does not change, what will the pressure be at 211K?The pressure in a car tire is 198 kPa at 27ºC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire?
15 The Combined Gas Law: Pressure, Volume and Temperature Combines Boyle’s, Charles’, and Gay-Lussac’s LawsRelates pressure, volume and temperature
16 Sample Problems page 424A gas at 155 kPa and 25ºC has an initial volume of 1.00L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125ºC. What is the new volume?A 5.00 L sample of air has a pressure of 107 kPa at 50.0ºC. If the temperature is raised to 102ºC and the volume expands to 7.00 L, what will the new pressure be?
17 14.3 Ideal GasesGases at ordinary temperatures and pressures comply with the assumptions of the KMT of gasesThese are called ideal gasesGases at extremely low temperatures and/or extremely high pressures do notThese are called real gases
18 Avagadro’s Law: Moles & Volume The volume of a confined gas is directly proportional to moles of a gasIf the moles of gas increases, the volume of the gas increasesIf temperature and pressure are constantn = kV n/V = kn1/V1 = n2/V2
19 Practice ProblemA cylinder of gas with a moveable piston contains mol N2 with a volume of 11.0 L. What is the new volume if 1.50 mol of CO2 is injected into the cylinder? Assume that pressure and temperature are unchanged and that the N2 and CO2 do not react with one another.19.3 L
20 Molar Volume of Gases: Remember This! At STP, the standard molar volume of any gas is 22.4LOne mole of a gas has a volume of 22.4L at STPUse this as a conversion factor when solving stoichiometry problems involving gases
21 Practice ProblemsA chemical reaction produces mol of oxygen gas. What is the volume of the gas at STP?A reaction produced 98.0 mL of SO2 gas at STP.a. How many moles of SO2 were produced?b. What was the mass in grams of the gas?c. What is the density of the gas?
22 14.3 Ideal Gas Law: Pressure, Volume, Moles, Temperature A single law that relates pressure, volume, moles, and temperature of a gasPV=nRTn is number of moles of gasR is the ideal gas constantValue of R varies depending on units used for pressure and volume
24 Sample ProblemsA rigid hollow sphere containing 685 L He has a temperature of 621K and a pressure of 1.89 x 103 kPa. How many moles of He are in the sphere? (251 mol)What volume will 12.0 g of methane gas (CH4) occupy at a temperature of 25ºC and pressure of 0.52 atm?A gaseous product of a reaction is collected in a 30.0 L container at 25ºC. The measured pressure of the gas was kPa. The mass of gas produced was about 116 g. What is the molar mass of the gas?
25 Ideal Gases and Real Gases Ideal gases are real gases which comply with the ideal gas equationReal gases deviate from the ideal gas equation at low temperatures and high pressuresThis is because the assumptions of KMT are no longer valid at low T and high P
27 14.4 Gas Mixtures and Movements Very often gases are mixturesPure substancesHomogeneous mixturesSolutionsThe total pressure of a mixture of gases is the sum of the pressures of each individual gas (component gas) in the mixture
29 Dalton’s Law of Partial Pressures The total pressure of a mixture of gases is the sum of the partial pressure of each component of the mixturePartial pressure is the pressure of each gas within a mixture of gases
30 Example of Dalton’s Law If you mix 2 moles O2 at 0.12 atm with 2 moles of N2 at 0.12 atm, the total pressure is the sum of the partial pressures.Do Problem 32, p. 434
31 Mole Fraction can be used to calculate partial pressures The mole fraction of a gas is the moles of a gas divided by the total moles of gas in a mixtureX = moles x/ total molesIn a mixture of 200 moles of O2 and 500 moles N2, what is the mole fraction of O2?XO2 = 200 mol O2/700 mol = 0.29Suppose this mixture had a total pressure of 600 kPa. What is the PO2?PO2 = XO2 · Ptotal = 0.29 x 600 kPa = 174 kPa
32 Graham’s Law of Effusion DiffusionMovement of molecules from an area of higher concentration to lower concentration
33 Effusion Effusion Rate of effusion Movement of gas molecules through a pinholeRate of effusionHow much gas effuses per secondSometimes velocity is used
34 Graham’s Law of Effusion At a given temperature, lower mass molecules diffuse and effuse faster than greater mass moleculesThis is because they have the same KEKE = ½ mv2