2 PressureIs caused by the collisions of molecules with the walls of a containeris equal to force/unit areaSI units = Newton/meter2 = 1 Pascal (Pa)1 atmosphere = 101,325 Pa1 atmosphere = 1 atm = 760 mm Hg = 760 torr
3 Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelliduring the 17th century.The device was called a “barometer” Baro = weight Meter = measure
4 An Early BarometerThe normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.
5 Standard Temperature and Pressure “STP” P = 1 atmosphere, 760 torrT = 0°C, 273 KelvinsThe molar volume of an ideal gas is liters at STP
6 Converting Celsius to Kelvin Gas law problems involving temperature requirethat the temperature be in KELVINS!Kelvins = C + 273°C = Kelvins - 273
7 Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant.
8 P1V1 = P2V2 P1 = P2V2/V1 P1 = 3.00 cm Hg x 0.240 cm3/200 cm3 A sample of helium gas at 25°C is compressed from 200 cm3 to cm3. Its pressure is now 3.00 cm Hg. What was the original pressure of the helium?P1 = ?V1 = 200 cm3P2 = 3.00 cmV2 = cm3 HgP1V1 = P2V2P1 = P2V2/V1P1 = 3.00 cm Hg x cm3/200 cm3P1 = 3.60 x 10-3 cm Hg
9 Charles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.(P = constant)
10 Gay Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volumeremains constant.
11 A sample of oxygen gas has a volume of 2. 73 dm3 at 21. 0 oC A sample of oxygen gas has a volume of 2.73 dm3 at 21.0 oC. At what temperature would the gas have a volume of 4.00 dm3?V1 = V2T T2T1 = 294 K V1 = 2.73 dm3 T2 = ? V2 = 4.00 dm32.73 dm3 = dm3294 K T2T2 = 294 K x 4.00 dm3 2.73 dm3T2 = K
12 The Combined Gas LawThe combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.
13 A 350 cm3 sample of helium gas is collected at 22. 0 oC and 99. 3 kPa A 350 cm3 sample of helium gas is collected at 22.0 oC and 99.3 kPa. What volume would this gas occupy at STP ?V1 = 350 cm3 P1 = 99.3 kPa T1 = 295 K V2 = ? P2 = kPa (standard press) T2 = 273 K (standard temp))P1 V1 = P2 V2T T2(99.3 kPa )(350 cm3 ) = (101.3 kPa) V2___________________( 295 K) (273 K)V2 = 320 cm3
14 ------------------------------------ Avogadro’s LawFor a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas.V = ana = proportionality constantV = volume of the gasn = number of moles of gas31. D32. D33. D34. C35. C36. B37. B
15 Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic moleculartheory.Gases consist of tiny particles that are far apartrelative to their size.Collisions between gas particles and betweenparticles and the walls of the container areelastic collisionsNo kinetic energy is lost in elastic collisions
16 Ideal Gases (continued) Gas particles are in constant, rapid motion. Theytherefore possess kinetic energy, the energy ofmotionThere are no forces of attraction between gasparticlesThe average kinetic energy of gas particlesdepends on temperature, not on the identityof the particle.
17 The Nature of Gases Gases expand to fill their containers Gases are fluid – they flowGases have low density1/1000 the density of the equivalent liquid or solidGases are compressibleGases effuse and diffuseEffusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.Effusion is gas escaping through a hole,Example: air escaping through a hole in your tireDiffusion, again because the molecules are moving at a high rate of speed, they will spread outExample: perfume diffusing through airExample: Liquids also diffuse: food coloring in water
18 PV = nRT Ideal Gas Law P = pressure in atm V = volume in liters n = molesR = proportionality constant= L atm/ mol·KT = temperature in KelvinsHolds closely at P < 1 atm
19 What volume is occupied by 5. 03 g of O2 at 28°C and a pressure of 0 What volume is occupied by 5.03 g of O2 at 28°C and a pressure of atm?P = atmV= ?Mass = 5.03 g O2 / 1 mol O2 / =/ 32 g O2 /n= molesR = L atmmol KT = 28°C = 301 KPV = nRT(0.998 atm) V = (0.157 mol) ( L atm ) ( 301 K)mol K=3.89 L
20 Standard Molar VolumeEqual volumes of all gases at the same temperature and pressure contain the same number of molecules.- Amedeo Avogadro
21 Density and the Ideal Gas Law Combining the formula for density with the IdealGas law, substituting and rearranging algebraically:M = Molar MassP = PressureR = Gas ConstantT = Temperature in KelvinsdRT = molarP mass
22 Gas Stoichiometry #1If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.3 H2(g) N2(g) NH3(g)3 moles H mole N moles NH33 liters H liter N liters NH3
23 Gas Stoichiometry #2How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?3 H2(g) N2(g) NH3(g)12 L H22L NH3= L NH38.03L H2
24 Gas Stoichiometry #3How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?2 KClO3(s) 2 KCl(s) + 3 O2(g)50.0 g KClO31 mol KClO33 mol O222.4 L O2g KClO32 mol KClO31 mol O2= L O213.7
25 Gas Stoichiometry #4How many liters of oxygen gas, at 37.0C and atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?2 KClO3(s) 2 KCl(s) + 3 O2(g)50.0 g KClO31 mol KClO33 mol O2= “n” mol O2g KClO32 mol KClO30.612mol O2= 16.7 L
26 Dalton’s Law of Partial Pressures For a mixture of gases in a container,PTotal = P1 + P2 + PThis is particularly useful in calculating the pressure of gases collected over water.nTotal = n1 + n2 + n
27 Dalton’s law of partial pressures collecting gases over water Mixture of gas and water vapor.PT = pgas + pvap(H2O)
28 Ptotal = Pgas + P water vapor Hydrogen gas is collected over water ata total pressure of 95.0 kPa and a temperature of 25 C. What is the partial pressure of hydrogen gas?According to a water vapor pressure table, the vapor pressure of water at 25C is 3.17 kPa.Ptotal = Pgas + P water vapor95.0 kPa = X kPaX = 91.8 kPa
29 e. g. , If 6. 00 g of O2 and 9. 00 g of CH4 are placed in a 15 e.g., If 6.00 g of O2 and 9.00 g of CH4 are placed in a 15.0-L containerat 0ºC, what is the partial pressure of each gas and the total pressure inthe container.
30 Kinetic Energy of Gas Particles At the same conditions of temperature, all gaseshave the same average kinetic energy.
31 The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)
32 Kinetic Molecular Theory Particles of matter are ALWAYS in motionVolume of individual particles is zero.Collisions of particles with container walls cause pressure exerted by gas.Particles exert no forces on each other.Average kinetic energy µ Kelvin temperature of a gas.
33 DiffusionDiffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.
34 EffusionEffusion: describes the passage of gas into an evacuated chamber.
35 Kinetic Molecular Theory Gases have certain properties that can be explained by the KMT.Low Density, because the molecules are moving at a high rate of speed and are not held back by electrostatic attractions, they, spread out. And because gases have small volume as well as being spread out, they have low densityCompressibility, because the molecules have space between them, they can be forced to compress unlike liquids and solids where there is little space between the moleculesExpansion, because the molecules are moving at a high rate of speed, they will spread out if given the opportunityDiffusion, again because the molecules are moving at a high rate of speed, they will spread outExample: perfume diffusing through airExample: Liquids also diffuse: food coloring in waterEffusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.Effusion is gas escaping through a hole,Example: air escaping through a hole in your tire
37 Real Gases corrected pressure corrected volume Videal Pideal Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).corrected pressurecorrected volumeVidealPideal