Presentation on theme: "How do gases behave under different conditions?"— Presentation transcript:
1How do gases behave under different conditions? Unit 9 – The Gas LawsHow do gases behave under different conditions?
2Essential QuestionWhat are the properties and behavior of gases under different conditions such as pressure, volume and temperature?
3States of MatterGas ParticlesLiquid ParticlesSolid Particles
4Properties of Gases An important property of gases is Compressibility Measure of how much the volume of matter decreases under pressureWhy are gases so compressible?Large spaces between particles
5Kinetic Molecular Theory Explains why ideal gases behave the way they doAssumptions that simplify the theory, but don’t work in real gases:The particles are so small we can ignore their volumeThe particles are in constant motion and their collisions cause pressure.
6Kinetic Molecular Theory The particles do not affect each other, neither attracting or repelling.The average kinetic energy is proportional to the Kelvin temperature.The molecules move in a straight pathAll collisions are elasticWe need the formula KE = 1/2 mv2
7Pressure Force per unit area Factors Affecting Pressure Amount of gas More particles – more pressureVolumeMore volume – less pressureTemperatureHigher temperature – more pressure
8What causes pressure? Gas molecules fill container Molecules move around and hit sidesCollisions are the forceContainer is the area
9Barometer Vacuum 760 mm Hg 1 atm Pressure Measures air pressure The pressure of the atmosphere at sea level will hold a column of mercury 760 mm Hg.1 atm = 760 mm Hg760 mm Hg1 atm Pressure
10Manometer h Gas Column of mercury to measure pressure of a gas One end has gas, the other is openh is how much lower the pressure of the gas is than atmospherehGas
11Manometerh is how much higher the gas pressure is than the atmosphere.hGas
13Units of pressure 1 atmosphere = 760 mm Hg 1 mm Hg = 1 torr 1 atm = 101,325 Pascals = kPaOccasionally, we must convert between theseExamples:What is 724 mmHg in torr?in atm?in kPa?724 torr0.953 atm96.5 kPa
14Summary of Units of Pressure AbbreviationUnit Equivalent to 1 atmAtmosphereAtm1 atmMillimeters of Hgmm Hg760 mm HgTorr760 torrPascalPa101,325 PaKilopascalkPa101.3 kPa
15The Gas LawsThere are several laws we use to quantify the behavior of gasesThe laws describe some combination of changes in pressure (P), volume (V), moles/amount of gas (n),or temperature (T)Standard Temperature and Pressure (STP)0ºC and 1 atm1 mole of gas occupies 22.4 LBE CAREFUL!!Units are vital to solving these problemsTemperature must ALWAYS be in KELVIN
16Boyle’s LawPressure and volume are inversely related at constant temperaturePV= k, where k is a constantAs one goes up, the other goes downP1V1 = P2 V2
21Boyle’s Law ExamplesGiven the volume of gas as 200.mL at 1.05atm pressure, calculate the volume of the same gas at 1.01atm.208mL30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa?4.0kPa20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume?2.0L
22Charles’ LawVolume of a gas varies directly with the absolute temperature at constant pressure.V = kT (if T is in Kelvin)One goes up, the other goes upV1 = V2T T2
24Charles’ Law ExamplesWhat would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is held constant?311mLAt what temperature would 40.5 L of gas at 23.4ºC have a volume of L at constant pressure?593K or 320ºC
25Gay-Lussac’s LawAt constant volume, pressure and absolute temperature are directly related.P = k TOne goes up, the other goes upP1 = P2T T2
28Gay–Lussac’s Law Examples A steel tank contains a gas at 27.0°C and a pressure of 12.0atm. Determine the gas pressure when the tank is heated to 100.°C.14.9 atmAt 120°C, the pressure of a sample of nitrogen is 1.07atm. What will the pressure be at 205°C, assuming constant volume?1.30 atm
29Avogadro's LawAt constant temperature and pressure, the volume of gas is directly related to the number of moles.V = k n (n is the number of moles)V1 = V2n n2
30Combined Gas Law P1 V1 = P2 V2 . T1 T2 Combines Boyles’, Charles’ and Gay-Lussac’s lawsDescribes the relationship between pressure, temperature, and volumeIf the moles of gas remains constant, use this formula and cancel out the other things that don’t changeP1 V1 = P2 V T T2
31ExamplesA sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr?3.99L5.00L of air at a temperature of -50ºC has a pressure of 107kPa. What is its pressure if the temperature is raised to 102ºC and its volume to 7.00L129kPaThe volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa pressure.What would the volume be at standard temperature and pressure (STP)?39.5 L
32Ideal Gas Law PV = nRT An Equation of state An Empirical Equation Independent of how you end up where you are atDoes not depend on the pathAn Empirical EquationBased on experimental evidenceTells you about current state of gasThe other laws tell you about a gas when it changesGiven 3 factors you can determine the fourth
33Ideal Gas Law PV = nRT R is the ideal gas constant V = L at P = 1 atm, T = 0ºC, n = 1 moleWhat is R?R = (L·atm)/(mol·K)With different units: R = 8.31 (L·kPa)/(mol·K)
34Ideal Gas Law Ideal gases are hypothetical substances Think of it as a limitGases only approach ideal behavior at low pressure (< 1 atm) and high temperatureUse the laws anyway, unless told to do otherwiseThey give good estimates
37ExamplesA 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature?658KKr gas in a 18.5 L cylinder exerts a pressure of atm at 24.8ºC What is the mass of Kr?546g Kr
38Real GasesReal gas particles have volume and there are attractions between the particles (especially polar molecules)A real gas behaves ideally at low pressure and high temperature.Under conditions of high pressures and low temperatures, deviations from the expected results of the ideal gas law will occur.Need to add correction factors to the ideal gas law to account for these.
40Gas Density and Molar Mass D = m/VLet M stand for molar massM = m/nn= PV/RTM = m PV/RTM = mRT = mRT = DRT PV VP P
41Gas Density ExampleWhat is the density of ammonia at 23ºC and 735 torr?M = DRTPD = MP / RTD = (17.04g/mol)(735torr/760 torr/atm)( (L·atm)/(mol·K)(296K)D = 0.678g/L
42Gases and Stoichiometry Reactions happen in molesAt Standard Temperature and Pressure (STP),0ºC and 1 atm1 mole of gas occupies 22.4 LIf not at STP, use the ideal gas law to calculate moles of reactant or volume of product.
434NH3(g) + 5O2(g) ® 4NO(g) +6H2O(g) ExamplesConsider the following reaction:4NH3(g) + 5O2(g) ® 4NO(g) +6H2O(g)What volume of NO at STP will be produced from 23.7L of NH3?23.7LWhat volume of O2 measured at STP will be consumed when 10.0L NH3 is reacted?12.5L
44Examples Mercury can be produced by the following reaction: 2HgO ® 2Hg +O2What volume of oxygen gas can be produced from 4.10 g of mercury (II) oxide at STP?0.229LAt 400.ºC and 740 torr?0.580L
45NaHCO3(s)+ HCl(aq)® NaCl(aq) +CO2(g)+H2O(l) ExamplesUsing the following reaction:NaHCO3(s)+ HCl(aq)® NaCl(aq) +CO2(g)+H2O(l)Calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm19.7g NaHCO3
46Dalton’s LawThe total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container.The total pressure is the sum of the partial pressures.PTotal = P1 + P2 + P3 + P4 + P5 ...For each P = nRT/V
47Dalton's Law PTotal = n1RT + n2RT + n3RT +... V V V In the same container R, T and V are the same.PTotal = (n1+ n2 + n3+...)RT VPTotal = (nTotal)RT V
49Dalton’s Law ExamplesAir contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen at kPa of total pressure if the partial pressures of nitrogen, carbon dioxide,and other gases are kPa, kPa, and kPa, respectively?21.22kPa
50The mole fraction Ratio of moles of the substance to the total moles. Symbol is Greek letter chi cc1 = n1 = P nTotal PTotal
51ExamplesThe partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen?0.787What is the partial pressure of nitrogen if the container holding the air is compressed to atm?4.13 atm
52Examples 4.00 L CH4 1.50 L N2 3.50 L O2 0.752 atm 2.70 atm 4.58 atm When these valves are opened, what is each partial pressure and the total pressure?
53Vapor Pressure Water evaporates! When that water evaporates, the vapor has a pressure.Gases are often collected over water so the vapor. pressure of water must be subtracted from the total pressure.It must be given.
54Example N2O can be produced by the following reaction what volume of N2O collected over water at a total pressure of 94 kPa and 22ºC can be produced from 2.6 g of NH4NO3? ( the vapor pressure of water at 22ºC is 21 torr)
55Effusion Passage of gas through a small hole, into a vacuum. The effusion rate measures how fast this happens.Graham’s Law the rate of effusion is inversely proportional to the square root of the mass of its particles.
56Diffusion The spreading of a gas through a room. Slow considering molecules move at 100’s of meters per second.Collisions with other molecules slow down diffusions.Best estimate is Graham’s Law.