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GASES Chapter 5

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A Gas -Uniformly fills any container. -Mixes completely with any other gas -Exerts pressure on its surroundings.

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Simple barometer invented by Evangelista Torricelli

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Pressure -is equal to force/unit area -SI units = Newton/meter 2 = 1 Pascal (Pa) -1 standard atmosphere = 101,325 Pa -1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

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Pressure Unit Conversions The pressure of a tire is measured to be 28 psi. What would the pressure in atmospheres, torr, and pascals. (28 psi)(1.000 atm/14.69 psi) = 1.9 atm (28 psi)(1.000 atm/14.69 psi)(760.0 torr/1.000atm) = 1.4 x 10 3 torr (28 psi)(1.000 atm/14.69 psi)(101,325 Pa/1.000 atm) = 1.9 x 10 5 Pa

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Simple Manometer

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Volume of a gas decreases as pressure increases at constant temperature

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BOYLES LAW DATA P vs VV vs 1/P

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Boyles Law * (Pressure)( Volume) = Constant (T = constant) P 1 V 1 = P 2 V 2 (T = constant) V 1/P (T = constant) ( * Holds precisely only at very low pressures.)

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Boyles Law Calculations A 1.5-L sample of gaseous CCl 2 F 2 has a pressure of 56 torr. If the pressure is changed to 150 torr, will the volume of the gas increase or decrease? What will the new volume be? Decrease P 1 = 56 torr P 2 = 150 torr V 1 = 1.5 L V 2 = ? V 1 P 1 = V 2 P 2 V 2 = V 1 P 1 /P 2 V 2 = (1.5 L)(56 torr)/(150 torr) V 2 = 0.56 L

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Boyles Law Calculations In an automobile engine the initial cylinder volume is L. After the piston moves up, the volume is L. The mixture is 1.00 atm, what is the final pressure? P 1 = 1.00 atm P 2 = ? V 1 = L V 2 = L V 1 P 1 = V 2 P 2 P 2 = V 1 P 1 /V 2 P 2 = (0.725 L)(1.00 atm)/(0.075 L) P 2 = 9.7 atm Is this answer reasonable?

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A gas that strictly obeys Boyles Law is called an ideal gas.

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Plot of PV vs. P for several gases at pressures below 1 atm.

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Plot of V vs. T( o C) for several gases

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Volume of a gas increases as heat is added when pressure is held constant.

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Charless Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. V = bT (P = constant) b = a proportionality constant

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Charless Law

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Charless Law Calculations Consider a gas with a a volume of L at 35 o C and 1 atm pressure. What is the temperature (in C o ) of the gas when its volume is L at 1 atm pressure? V 1 = L V 2 = L T 1 = 35 o C = 308 K T 2 = ? V 1 /V 2 = T 1 /T 2 T 2 = T 1 V 2 /V 1 T 2 = (308 K)(0.535 L)/(0.675 L) T 2 = 244 K -273 T 2 = - 29 o C

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At constant temperature and pressure, increasing the moles of a gas increases its volume.

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Avogadros Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas

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AVOGADROS LAW V 1 /V 2 = n 1 /n 2

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AVOGADROS LAW A 12.2 L sample containing 0.50 mol of oxygen gas, O 2, at a pressure of 1.00 atm and a temperature of 25 o C is converted to ozone, O 3, at the same temperature and pressure, what will be the volume of the ozone? 3 O 2(g) ---> 2 O 3(g) (0.50 mol O 2 )(2 mol O 3 /3 mol O 2 ) = 0.33 mol O 3 V 1 = 12.2 L V 2 = ? n 1 = 0.50 mol n 2 = 0.33 mol V 1 /V 2 = n 1 /n 2 V 2 = V 1 n 2 /n 1 V 2 = (12.2 L)(0.33 mol)/(0.50 mol) V 2 = 8.1 L

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COMBINED GAS LAW V 1 / V 2 = P 2 T 1 / P 1 T 2

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COMBINED GAS LAW V 1 / V 2 = P 2 T 1 / P 1 T 2 V 2 = V 1 P 1 T 2 /P 2 T 1 V 2 = (309 K)(0.454 atm)(3.48 L) (258 K)(0.616 atm) V 2 = 3.07 L What will be the new volume of a gas under the following conditions? V 1 = 3.48 L V 2 = ? P 1 = atm P 2 = atm T 1 = - 15 o C = 258 K T 2 = 36 o C T 2 = 309 K

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Pressure exerted by a gas increases as temperature increases provided volume remains constant.

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If the volume of a gas is held constant, then V 1 / V 2 = 1. Therefore: P 1 / P 2 = T 1 / T 2

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Ideal Gas Law -An equation of state for a gas. -state is the condition of the gas at a given time. PV = nRT

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IDEAL GAS 1. Molecules are infinitely far apart. 2. Zero attractive forces exist between the molecules. 3. Molecules are infinitely small--zero molecular volume. What is an example of an ideal gas?

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REAL GAS 1. Molecules are relatively far apart compared to their size. 2. Very small attractive forces exist between molecules. 3. The volume of the molecule is small compared to the distance between molecules. What is an example of a real gas?

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Ideal Gas Law PV = nRT R = proportionality constant = L atm mol P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins Holds closely at P < 1 atm

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Ideal Gas Law Calculations A 1.5 mol sample of radon gas has a volume of 21.0 L at 33 o C. What is the pressure of the gas? p = ? V = 21.0 L n = 1.5 mol T = 33 o C T = 306 K R = Latm/molK pV = nRT p = nRT/V p = (1.5mol)( Latm/molK)(306K) (21.0L) p = 1.8 atm

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Ideal Gas Law Calculations A sample of hydrogen gas, H 2, has a volume of 8.56 L at a temperature of O o C and a pressure of 1.5 atm. Calculate the number of moles of hydrogen present. p = 1.5 atm V = 8.56 L R = Latm/molK n = ? T = O o C T = 273K pV = nRT n = pV/RT n = (1.5 atm)(8.56L) ( Latm/molK)(273K) n = 0.57 mol

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Standard Temperature and Pressure STP P = 1 atmosphere T = C The molar volume of an ideal gas is liters at STP

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GAS STOICHIOMETRY 1. Mass-Volume 2. Volume-Volume

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Molar Volume pV = nRT V = nRT/p V = (1.00 mol)( Latm/molK)(273K) (1.00 atm) V = 22.4 L

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Gas Stoichiometry Not at STP (Continued) p = 1.00 atm V = ? n = 1.28 x mol R = Latm/molK T = 25 o C = 298 K pV = nRT V = nRT/p V = (1.28 x mol)( Latm/molK)(298K) (1.00 atm) V = 3.13 L O 2

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Gases at STP A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N 2 are present? (1.75L N 2 )(1.000 mol/22.4 L) = 7.81 x mol N 2

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Gas Stoichiometry at STP Quicklime, CaO, is produced by heating calcium carbonate, CaCO 3. Calculate the volume of CO 2 produced at STP from the decomposition of 152 g of CaCO 3. CaCO 3(s) ---> CaO (s) + CO 2(g) (152g CaCO 3 )(1 mol/100.1g)(1mol CO 2 /1mol CaCO 3 ) (22.4L/1mol) = 34.1L CO 2 Note: This method only works when the gas is at STP!!!!!

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Volume-Volume If 25.0 L of hydrogen reacts with an excess of nitrogen gas, how much ammonia gas will be produced? All gases are measured at the same temperature and pressure. 2N 2(g) + 3H 2(g) ----> 2NH 3(g) (25.0 L H 2 )(2 mol NH 3 /3 mol H 2 ) = 16.7 L NH 3

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MOLAR MASS OF A GAS n = m/M n = number of moles m = mass M = molar mass

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MOLAR MASS OF A GAS P = mRT/VM or P = DRT/M therefore: M = DRT/P

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Molar Mass Calculations M = ? d = 1.95 g/L T = 27 o C p = 1.50 atm T = 300. K R = Latm/mol K M = dRT/p M = (1.95g/L)( Latm/molK)(300.K) (1.5atm) M = 32.0 g/mol

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Daltons Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P

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Daltons Law of Partial Pressures Calculations A mixture of nitrogen gas at a pressure of 1.25 atm, oxygen at 2.55 atm, and carbon dioxide at.33 atm would have what total pressure? P Total = P 1 + P 2 + P 3 P Total = 1.25 atm atm +.33 atm P total = 4.13 atm

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Water Vapor Pressure 2KClO 3(s) ----> 2KCl (s) + 3O 2(g) When a sample of potassium chlorate is decomposed and the oxygen produced collected by water displacement, the oxygen has a volume of L at a temperature of 22 o C. The combined pressure of the oxygen and water vapor is 754 torr (water vapor pressure at 22 o C is 21 torr). How many moles of oxygen are produced? P ox = P total - P HOH P ox = 754 torr - 21 torr p ox = 733 torr

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MOLE FRACTION -- the ratio of the number of moles of a given component in a mixture to the total number of moles of the mixture. 1 = n 1 / n total 1 = V 1 / V total 1 = P 1 / P total (volume & temperature constant)

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Kinetic Molecular Theory 1.Volume of individual particles is zero. 2.Collisions of particles with container walls cause pressure exerted by gas. 3.Particles exert no forces on each other. 4.Average kinetic energy Kelvin temperature of a gas.

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Plot of relative number of oxygen molecules with a given velocity at STP (Boltzmann Distribution).

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Plot of relative number of nitrogen molecules with a given velocity at three different temperatures.

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The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

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Effusion: describes the passage of gas into an evacuated chamber. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

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Effusion of a gas into an evacuated chamber

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Effusion: Diffusion:

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Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).

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Plots of PV/nRT vs. P for several gases at 200 K. Note the significant deviation from ideal behavior.

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Real Gases corrected pressure corrected volume P ideal V ideal

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Concentration for some smog components vs. time of day

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NO 2(g) NO (g) + O (g) O (g) + O 2(g) O 3(g) NO (g) + 1/2 O 2(g) NO 2(g) __________________________ 3/2 O 2(g) O 3(g) What substances represent intermediates? Which substance represents the catalyst?

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Chemistry is a gas!!

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