Difficult to place a barometer inside a gas to be measured. Manometers compare gas pressure and barometric pressure.
The kinetic theory of gases 1
GASES• Gases are one of the most pervasiveaspects of our environment on theEarth. We continually exist withconstant exposure to gases of allforms.• The steam formed in the air during ahot shower is a gas.• The Helium used to fill a birthdayballoon is a gas.• The oxygen in the air is an essentialgas for life.
GASESA windy day or a still day is a result of the difference in pressure of gasesin two different locations. A fresh breeze on a mountain peak is a study inbasic gas laws.
Important Characteristics of Gases1) Gases are highly compressibleAn external force compresses the gas sample and decreases itsvolume, removing the external force allows the gas volume toincrease.2) Gases are thermally expandableWhen a gas sample is heated, its volume increases, and when it iscooled its volume decreases.3) Gases have high viscosityGases flow much easier than liquids or solids.4) Most Gases have low densitiesGas densities are on the order of grams per liter whereas liquidsand solids are grams per cubic cm, 1000 times greater.5) Gases are infinitely miscibleGases mix in any proportion such as in air, a mixture of many gases.
• Helium He 4.0• Neon Ne 20.2• Argon Ar 39.9• Hydrogen H2 2.0• Nitrogen N2 28.0• Nitrogen Monoxide NO 30.0• Oxygen O2 32.0• Hydrogen Chloride HCl 36.5• Ozone O3 48.0• Ammonia NH3 17.0Substances That Are Gases underNormal ConditionsSubstance Formula MM(g/mol)
Kinetic Molecular Theory• To fully understand the world around usrequires that we have a good understandingof the behavior of gases. The description ofgases and their behavior can be approachedfrom several perspectives.• The Gas Laws are a mathematicalinterpretation of the behavior of gases.• However, before understanding themathematics of gases, a chemist must havean understanding of the conceptualdescription of gases. That is the purpose ofthe Kinetic Molecular Theory.
Kinetic Molecular Theory• The Kinetic Molecular Theory is a single set ofdescriptive characteristics of a substance known asthe Ideal Gas.• All real gases require their own unique sets ofdescriptive characteristics. Considering the largenumber of known gases in the World, the task oftrying to describe each one of them individuallywould be an awesome task.• In order to simplify this task, the scientificcommunity has decided to create an imaginary gasthat approximates the behavior of all real gases. Inother words, the Ideal Gas is a substance that doesnot exist.• The Kinetic Molecular Theory describes that gas.While the use of the Ideal Gas in describing all realgases means that the descriptions of all real gaseswill be wrong, the reality is that the descriptions ofreal gases will be close enough to correct that anyerrors can be overlooked.
The Nature of GasesThree basic assumptions of the kinetictheory as it applies to gases:1. Gas is composed of particles- usuallymolecules or atoms–Small, hard spheres–Insignificant volume; relatively farapart from each other–No attraction or repulsion betweenparticles
The Nature of Gases2. Particles in a gas move rapidly inconstant random motion–Move in straight paths, changingdirection only when colliding with oneanother or other objects–Average speed of O2 in air at 20 oC isan amazing 1660 km/h!(1.6km=1mile)
The Nature of Gases3. Collisions are perfectly elastic-meaning kinetic energy is transferredwithout loss from one particle toanother- the total kinetic energy remainsconstantNewtonian Cradle-Where the collisions between the balls elastic?Yes, because kinetic energy was transferredwith each collision
• Why did the balls eventually stopswinging? The collisions were notperfectly elastic, some kinetic energywas lost as heat during each collision.• At constant temperatures and low tomoderate pressures, collisions betweengas particles are perfectly elastic
THE KINETIC THEORY OF GASES• Gas consists of large number of particles(atoms or molecules)• Particles make elastic collisions with eachother and with walls of container• There exist no external forces (densityconstant)• Particles, on average, separated by distanceslarge compared to their diameters• No forces between particles except whenthey collideRemember the assumptions
What happens to a ball when itdrops?The potential energyof the ballWhich is converted tokinetic energy in theballWhich is convertedto potential energyin the ballIs converted to kineticenergy in the ballWhich is converted intothe potential energy ofthe ball…………..…..but in reality the ballloses height andeventually stops bouncingWhy does thishappen?
How does the bouncing ball loseenergy?• Through friction with the air (airresistance)• Through sound when it hits the floor• Through deformation of the ball• Through heat energy in the bounce
IDEAL GAS MODEL• The gas consists of objects with a defined mass and ze• The gas particles travel randomly in straight-line motion• All collisions involving gas particles are elastic; the kin• The gas particles do not interact with each other or the• The gas phase system will have an average kinetic ener
Boltzman Distribution. The behaviour ofthe gas molecules under the action ofgravity.
Maxwell Distribution. Experiment withGalton board demonstrates thestatistical sense of Maxwell distribution.
Ideal Gas Model Kinetic Molecular Theory (KMT) for an idealgas states that all gas particles:• are in random, constant, straight-line motion.• are separated by great distances relative totheir size; the volume of the gas particles isconsidered negligible.• have no attractive forces between them.• have collisions that may result in the transferof energy between gas particles, but the totalenergy of the system remains constant.
Brownian motion. Chaotic motion ofminute particle suspended in a gas orliquid
This animation illustrates the concept offree path length of molecules in a gas.
Ideal vs. Non-Ideal Gases• Kinetic Theory Assumptions– Point Mass– No Forces Between Molecules– Molecules Exert Pressure Via Elastic Collisions With Wallsxx(courtesy F. Remer)
Ideal vs. Non-Ideal Gases• Non-Ideal Gas– Violates Assumptions• Volume of molecules• Attractive forces of molecules(courtesy F. Remer)
Deviations from ideal behaviour• A real gas is most like an ideal gas when thereal gas is at low pressure and hightemperature.• At high pressures gas particles are close therefore the volume of the gas particles is considered.• At low temperatures gas particles have low kinetic energy therefore particles have some attractive force• Example• Dry ice, liquid oxygen and nitrogen
Ideal GasesBehave as described by the ideal gasequation; no real gas is actually idealWithin a few %, ideal gas equation describesmost real gases at room temperature andpressures of 1 atm or lessIn real gases, particles attract each otherreducing the pressureReal gases behave more like ideal gases aspressure approaches zero.
Atmospheric Pressure• Weight of column of air above your head.• We can measure the density of the atmosphere by measuring the pressure it exerts.
Effect of Atmospheric Pressure onObjects at the Earth’s Surface
Atmospheric PressurePressure = Force per Unit AreaAtmospheric Pressure is the weight ofthe column of air above a unit area. Forexample, the atmospheric pressure feltby a man is the weight of the column ofair above his body divided by the areathe air is resting onP = (Weight of column)/(Area of base)Standard Atmospheric Pressure:1 atmosphere (atm)14.7 lbs/in2(psi)760 Torr (mm Hg)1013.25 KiloPascals or Millibars (kPa =N/m2)
Pressure MeasurementTorricellis Barometer• Torricelli determined from this experiment that the pressure of the atmosphere is approximately 30 inches or 76 centimeters (one centimeter of mercury is equal to 13.3 millibars. He also noticed that height of the mercury varied with changes in outside weather conditions. For climatological and meteorological purposes, standard sea-level pressureis said to be 76.0 cm or 29.92 inches or 1013 millibars
The Nature of Gases Atmospheric pressure results from the collisions of air molecules with objects–Decreases as you climb a mountain because the air layer thins out as elevation increases Barometer is the measuring instrument for atmospheric pressure; dependent upon weather
Common Units of PressureUnit Atmospheric Pressure Scientific Fieldpascal (Pa); 1.01325 x 105Pa SI unit; physics,kilopascal(kPa) 101.325 kPa chemistryatmosphere (atm) 1 atm* Chemistrymillimeters of mercury 760 mmHg* Chemistry, medicine,( mm Hg ) biologytorr 760 torr* Chemistrypounds per square inch 14.7 lb/in2Engineering( psi or lb/in2)bar 1.01325 bar Meteorology,chemistry, physics
Converting Units of PressureProblem: A chemist collects a sample of carbon dioxide from thedecomposition of limestone (CaCO3) in a closed end manometer, theheight of the mercury is 341.6 mm Hg. Calculate the CO2 pressure intorr, atmospheres, and kilopascals.Plan: The pressure is in mmHg, so we use the conversion factors fromTable 5.2(p.178) to find the pressure in the other units.Solution:PCO2 (torr) = 341.6 mm Hg x = 341.6 torr1 torr1 mm Hgconverting from mmHg to torr:converting from torr to atm:PCO2( atm) = 341.6 torr x = 0.4495 atm1 atm760 torrconverting from atm to kPa:PCO2(kPa) = 0.4495 atm x = 45.54 kPa101.325 kPa1 atm
Change in PressureChange in averageatmospheric pressure withaltitude.
The Nature of Gases Gas Pressure – defined as the force exerted by a gas per unit surface area of an object–Due to: a) force of collisions, and b) number of collisions–No particles present? Then there cannot be any collisions, and thus no pressure – called a vacuum
ManometersRules of thumb: When evaluating, start from the knownpressure end and work towards theunknown end At equal elevations, pressure isconstant in the SAME fluid When moving down a manometer,pressure increases When moving up a manometer,pressure decreases Only include atmospheric pressure onopen endsManometers measure a pressure difference by balancing theweight of a fluid column between the two pressures of interest
ManometersFind the pressure atpoint A in this open u-tube manometer with anatmospheric pressure PoPD = γH2O x hE-D + PoPc = PDPB = PC - γHg x hC-BPA = PBExample 2P = γ x h + PO
The Gas Laws• What would PollyParcel look like if shehad no gas moleculesinside?zero molecules = zero pressure insidezero pressure inside = zero force on theinside
Gas Law Variables• In order to describe gases, mathematically, itis essential to be familiar with the variablesthat are used. There are four commonlyaccepted gas law variables• Temperature• Pressure• Volume• Moles
Temperature• The temperature variable is always symbolized as T.• It is critical to remember that all temperature valuesused for describing gases must be in terms ofabsolute kinetic energy content for the system.• Consequently, T values must be converted to theKelvin Scale. To do so when having temperaturesgiven in the Celsius Scale remember the conversionfactor• Kelvin = Celsius + 273• According to the Kinetic Molecular Theory, everyparticle in a gas phase system can have its ownkinetic energy. Therefore, when measuring thetemperature of the system, the average kineticenergy of all the particles in the system is used.• The temperature variable is representing theposition of the average kinetic energy as expressedon the Boltzmann Distribution.
Pressure• The pressure variable is represented by thesymbol P.• The pressure variable refers to the pressurethat the gas phase system produces on thewalls of the container that it occupies.• If the gas is not in a container, then thepressure variable refers to the pressure itcould produce on the walls of a container if itwere in one.• The phenomenon of pressure is really a forceapplied over a surface area. It can best beexpressed by the equation
Pressure• Consider the Pressure equation and the impact ofvariables on it.• The force that is exerted is dependent upon thekinetic energy of the particles in the system. If thekinetic energy of the particles increases, forexample, then the force of the collisions with a givensurface area will increase. This would cause thepressure to increase. Since the kinetic energy of theparticles is increased by raising the temperature,then an increase in temperature will cause anincrease in pressure.• If the walls of the container were reduced in totalsurface area, there would be a change in thepressure of the system. By allowing a given quantityof gas to occupy a container with a smaller surfacearea, the pressure of the system would increase.
Pressure• As this container of gasis heated, thetemperature increases.As a result, the averagekinetic energy of theparticles in the systemincreases.• With the increase inkinetic energy, the forceon the available amountof surface area increases.As a result, the pressureof the system increases.• Eventually,..........................Ka-Boom
Volume• The Volume variable is represented by the symbol V.It seems like this variable should either be very easyto work with or nonexistent.• Remember, according to the Kinetic MolecularTheory, the volume of the gas particles is set at zero.Therefore, the volume term V seems like it should bezero.• In this case, that is not true. The volume beingreferred to here is the volume of the container, notthe volume of the gas particles.• The actual variable used to describe a gas should bethe amount of volume available for the particles tomove around in. In other words
Volume• Since the Kinetic Molecular Theorystates that the volume of the gasparticles is zero, then the equationsimplifies.• As a result, the amount of availablespace for the gas particles to movearound in is approximately equal to thesize of the container.• Thus, as stated before, the variable V isthe volume of the container.
Moles• The final gas law variable is the quantity of gas. This is alwaysexpressed in terms of moles. The symbol that represents themoles of gas is n. Notice that, unlike the other variables, it is inlower case.• Under most circumstances in chemistry, the quantity of asubstance is usually expressed in grams or some other unit ofmass. The mass units will not work in gas law mathematics.Experience has shown that the number of objects in a systemis more descriptive than the mass of the objects.• Since each different gas will have its own unique mass for thegas particles, this would create major difficulties when workingwith gas law mathematics.• The whole concept of the Ideal Gas says that all gases can beapproximated has being the same. Considering the largedifference in mass of the many different gases available, usingmass as a measurement of quantity would cause major errorsin the Kinetic Molecular Theory.• Therefore, the mole will standardize the mathematics for allgases and minimize the chances for errors.
ConclusionsThere are four variables used mathematically for describing agas phase system. While the units used for the variables maydiffer from problem to problem, the conceptual aspects of thevariables remain unchanged.1. T, or Temperature, is a measure of the average kinetic energy ofthe particles in the system and MUST be expressed in theKelvin Scale.2. P, or Pressure, is the measure of the amount of force per unitof surface area. If the gas is not in a container, then Prepresents the pressure it could exert if it were in a container.3. V, or Volume, is a measure of the volume of the container thatthe gas could occupy. It represents the amount of spaceavailable for the gas particles to move around in.4. n, or Moles, is the measure of the quantity of gas. Thisexpresses the number of objects in the system and does notdirectly indicate their masses.
Gas Laws• (1) When temperature is held constant, the density of agas is proportional to pressure, and volume is inverselyproportional to pressure. Accordingly, an increase inpressure will cause an increase in density of the gas anda decrease in its volume. – Boyles’s Law• (2) If volume is kept constant, the pressure of a unitmass of gas is proportional to temperature. Iftemperature increase so will pressure, assuming nochange in the volume of the gas.• (3) Holding pressure constant, causes the temperature ofa gas to be proportional to volume, and inverselyproportional to density. Thus, increasing temperature ofa unit mass of gas causes its volume to expand and itsdensity to decrease as long as there is no change inpressure. - Charles’s Law
Boyle’s Law• Hyperbolic Relation Between Pressure andVolumepVp – V Diagramp – V DiagramisothermsT1 T2 T3 T3 >T2>T1(courtesy F. Remer)
Charles’ Law• Linear Relation Between Temperature andPressurePT (K)0 100 200 300P – T DiagramP – T DiagramisochorsisochorsV1V2V3V1 <V2 <V3(courtesy F. Remer)
Charles’ LawReal data must beobtained aboveliquefactiontemperature.Experimental curves fordifferent gasses,different masses,different pressures allextrapolate to acommon zero.
Compression and expansion ofadiabatically isolated gas isaccompanied by its heating and cooling.
The Gas Laws• What would PollyParcel look like if shehad a temperature ofabsolute zero inside?absolute zero = no molecular motionno molecular motion = zero force onthe inside
Ideal Gas LawThe equality for the four variables involvedin Boyle’s Law, Charles’ Law, Gay-Lussac’sLaw and Avogadro’s law can be writtenPV = nRTR = ideal gas constant
PV = nRTR is known as the universal gas constantUsing STP conditionsP VR = PV = (1.00 atm)(22.4 L)nT (1mol) (273K)n T= 0.0821 L-atmmol-K
Partial PressurePartial PressurePressure each gas in a mixture would exertif it were the only gas in the containerDaltons Law of Partial PressuresThe total pressure exerted by a gas mixtureis the sum of the partial pressures of thegases in that mixture.PT = P1 + P2 + P3 + .....
Partial PressuresThe total pressure of a gas mixture dependson the total number of gas particles, not onthe types of particles.STPP = 1.00 atm P = 1.00 atm1.0 mol He0.50 mol O2+ 0.20 mol He+ 0.30 mol N2