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Gas Laws and KMT Chapter 5

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Pressure Barometer – first pressure measuring device –Torricelli, 1643 –A glass tube filled with mercury, inverted into a dish of mercury. –At sea level, height of mercury in the tube is 760 mm Why does the Hg stay in the tube, defying gravity?

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Air Pressure Why does a barometer measure lower air pressure when a storm is approaching? –Lower air pressure means the weight of air being pulled toward the earth is lower Air is being pulled UP, so air is rushing into a low (wind) Air pressure is also lower at higher elevation –At 9600 ft, air pressure is only 560 mm –Less air pushing down on earth’s surface

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Manometer The principle of a manometer measurement depends on the fact that given the same fluid, pressure is the same at equal heights. P gas = P atm – h OR P gas = P atm + h Manometer is a substitute for a Barometer and both measure mm Hg Mm Hg =Torr

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Pressure Standard Atmosphere = 760 torr = 760 mm Hg Pressure = Force/area SI units of measure –Force = Newtons –Area = m 2 –SI unit of measure for pressure is Pascal (Pa) 1 Standard atmosphere – 101,325 Pa

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Gas Laws Boyles Law Charles Law Guy-Lussac’s Law (Not used much) Avogadro’s Law Ideal Gas Law All Lead To: –Gas Stoichiometry

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Boyles Law Boyle studied pressure and volume PV = k –Temperature constant –Amount of gas constant Variation: –V=k/P –P=k/V Boyles Law is also frequently written and used as: –P 1 V 1 = P 2 V 2

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Charles Law Studied relationship between pressure and temperature Determined that plots of volume vs. temperature are linear V = bT –Constant pressure –Constant amount of gas –NOTE: gas cannot have a negative volume, so temperature cannot be negative. Thus we MUST use Kelvin scale for temperature at all times. –More on this later Variations: –V/T=b

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Charles Law Charles Law is also frequently written and used as: –V 1 /T 1 = V 2 /T 2

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Avogadro’s Law Postulated that equal volumes of gases at the same temperature and pressure contain the same number of ‘particles’. Avogadro’s Law –V = an a = proportionality constant N = number of moles of gas Variations: –V/n = a (constant)

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Combined Gas Law Assumes constant amount of gas –PV/T = k –Or –P 1 V 1 /T 1 = P 2 V 2 /T 2

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Ideal Gas Law Boyles Law: V = k/P (constant T & n) Charles Law: V = bT (constant P & n) Avogadro’s Law: V=an (constant P & T) Combined: V = R(Tn/P) –Or PV=nRT –R is universal gas constant ( L*Atm/mole*K) –MAKE SURE ALL TEMPS ARE IN KELVIN This is the IDEAL GAS LAW –Real gasses behave somewhat differently

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Gas Stoichiometry Molar volume of a gas = L at standard temperature and pressure STP (standard temperature and pressure) –0ºC (273K) –1 atm (760 torr or 760 mm Hg Using gas density: –Density = mass/volume –PV=nRT P = nRT/V

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Gas Stoichiometry Using Density Density = mass/volume –PV=nRT P = nRT/V –n = mass/molar mass =m/molar mass –P = (m/molar mass)RT/V –P = mRT/V(molar mass) –m/V = density (d) –P = dRT/molar mass –Molar mass = dRT/P

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Dalton’s Law of Partial Pressures Applies to Gasses For a mixture of gasses in a container, the total pressure is the sum of the pressures that each gas will exert if it were alone –P TOTAL = P 1 + P 2 + P 3 +….. –P TOTAL = n 1 RT/V + n 2 RT/V + n 3 RT/V…. –Equals (n 1 + n 2 + n 3 + …)RT/V –Equals N total RT/V

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Collecting Gas Over Water Whenever you collect gas over water, water vapor is present: –Water molecules escape from surface of water –Pressure due to water, depends on temperature, and is the vapor pressure of water. –Total pressure of gas collected is Pressure of gas + pressure of water vapor

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Kinetic Molecular Theory A theory summarizes observed behavior A model allows you to use theories to predict behavior –Also can be viewed as a way of understanding, a way of thinking, a mental construct KMT is a model based on gas laws

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Kinetic Molecular Theory Particles are so small compared to distances between the particles that the volume of the particles can be assumed to be negligible (zero). The particles are in constant motion. Collisions of the particles with the walls of the container are the cause of pressure exerted by the gas. The particles are assumed to exert no forces on each other; they are assumed to neither attract nor repel each other. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

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Boyles Law If volume decreases, pressure increases. KMT says a decrease in volume means the particles will hit the wall more often

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Pressure and Temperature Ideal Gas Law: Pressure is directly proportional to temperature KMT: as temperature increases; –Speeds of particles increases –Particles hit wall with greater force –Particles hit walls with greater frequency –Result: increased pressure

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Charles Law Ideal Gas Law: at constant pressure, volume of gas is directly proportional to temperature Kelvin KMT: When heated; –Speed of molecules increases –Hit walls with greater force –Hit walls with greater frequency –Only way to keep pressure constant is to increase volume

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Avogadro’s Law Ideal Gas Law: Volume is directly proportional to number of particles present –Constant temperature & pressure KMT: If you add more particles to a container; –Pressure would increase –Only way to maintain pressure is to increase volume

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Dalton’s Law Dalton: Total pressure is the sum of the partial pressures KMT: Assumes; –all gas particles are independent of each other –Volumes of individual particles are unimportant –Identities of particles do not matter

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Deriving Ideal Gas Law Apply particle physics to assumptions of KMT: –Use definitions of velocity, momentum, force, pressure –See Appendix 2 for details –KE = 1/2 mv 2 where v is root mean squared speed. –Total kinetic energy is KE = N A (1/2 mv 2 ) where N is Avogadro's number –Final derivation is: P = 2/3 (n N A (1/2 mv 2 ) / V)

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What is Temperature? KMT bases temperature on Kelvin –Because it is based on average kinetic energy of the particles –Requires an absolute energy scale –Hence: Kelvin

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Problem: Calculate the average kinetic energy of the CH 4 particles in a sample of CH 4 gas at 273K and at 546K

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Thursday Effusion and Graham’s Law Diffusion Real Gases and van der Waal’s equation.

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Effusion & Diffusion Diffusion – the mixing of gases without agitation Effusion – passage of a gas through a tiny orifice (hole)

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Effusion Graham’s Law of Effusion Rate of Effusion for gas 1 Rate of Effusion for gas 2 = √M 2 √M 1 M 1 and M 2 are molar masses for the gases.

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Diffusion Diffusion takes a long time –Even though molecules are travleing 450 and 660 m/s –Why? –Tube is filled with air –Lots of collisions with air that don’t lead to a reaction –Difficult to describe theoretically

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Next Real Gases –Corrections for pressure –Corrections for volume

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Real Gases Ideal gas behavior is best thought of as the behavior approached by real gases under certain conditions. Ideal gas behavior fails at: –Low temperatures –High pressures Real gases behave most like ideal gases at: –High temperature –Low pressure

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Real Gases Ideal gas assumption of volume is incorrect: –Molecules always take up some space. –Correct for volume by subtracting volume for the molecules –V REAL = V IDEAL -nb n is number of moles b is an empirical correction constant So: –P ’ = nRT/(V-nb)

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Real Gases But we still have to correct for the fact that real gases DO have attraction forces. –Effect is to make observed pressure P OBS smaller than it normally would if there were no attractions: –P OBS = (P ’ – correction factor)(nRT/(V-nb) – correction factor –Size of correction factor depends on concentration of the gas molecules in particles per liter (n/V) Higher concentration, more likely particles are close enough to attract. Depends on square of number of particles because 2 particles have to get close enough.

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Real Gases So: –P OBS = P ’ – s(n/V) 2 Inserting correction factors for both volume and attractions gives the equation: –P OBS = (nRT/(V-nb)) – a(v/V) 2 Volume of container Volume correction factor Pressure correction factor

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Van Der Waals Equation P OBS + a(n/V) 2 x (V-nB) = nRT

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