Presentation on theme: "Kinetic Molecular Theory of Gases"— Presentation transcript:
1 Kinetic Molecular Theory of Gases A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic.Gas molecules exert neither attractive nor repulsive forces on one another.The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energyKE = ½ mu2
2 Kinetic theory of gases and … Compressibility of GasesBoyle’s LawP a collision rate with wallCollision rate a number densityNumber density a 1/VP a 1/VGay-Lussac’s LawCollision rate a average kinetic energy of gas moleculesAverage kinetic energy a TP a T
3 Kinetic theory of gases and … Compressibility of GasesCharles’s LawT a average kinetic energy of moleculesCollision rate a average kinetic energy of gas moleculesP a collision rate with wall…. But! In Charles’s law, pressure stays constant…To decrease the collision rate, the volume needs to be increasedV a T
7 Kinetic theory of gases and … Avogadro’s LawP a collision rate with wallCollision rate a number densityNumber density a nP a nDalton’s Law of Partial PressuresMolecules do not attract or repel one anotherP exerted by one type of molecule is unaffected by the presence of another gasPtotal = SPi
9 KMT – What happens in “real” gases A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic.Gas molecules exert neither attractive nor repulsive forces on one another.Under what conditions will gases mostlikely exhibit nonideal behavior??
10 Deviations from Ideal Behavior 1 mole of ideal gasRepulsive ForcesPV = nRTn =PVRT= 1.0Attractive Forces
11 Effect of intermolecular forces on the pressure exerted by a gas.
12 Which element/molecule has the weakest attraction to each other?? Van der Waals equationnonideal gasP (V – nb) = nRTan2V2()}correctedpressurevolumePressure Correction: Takes into account the probability that a molecule will end up close enough to another molecule causing an intermolecular attractionVolume Correction: Takes into account that molecules, while extremely small, do take up some amount of volumeWhich element/molecule has the weakest attraction to each other??
13 Given that 3. 50 moles of NH3 occupy 5 Given that 3.50 moles of NH3 occupy 5.20 L at 47˚C, calculate the pressure of the gas (in atm) using the ideal gas law, and then the van der Waals equation.Ideal gas lawVan der Waals EquationV=5.20 LT=( ) = 3.20x102 Kn=3.50 molR= L·atm/K·molV=5.20 LT=( ) = 3.20x102 Kn=3.50 mola=4.17 atm·L2/mol2b= L/mol
14 Homework: Problem 5.89Calculate the pressure exerted by 2.50 moles of CO2 confined in a volume of 5.00 L at 450 K if the gas is behaving ideally. It has been shown that this gas exhibits non-ideal behavior. Calculate the actual pressure given a=3.59; b=
17 Apparatus for Studying Molecular Speed Distributiona
18 3RT urms = M The distribution of speeds of three different gases at the same temperatureThe distribution of speedsfor nitrogen gas moleculesat three different temperaturesurms =3RTM
19 Calculate the root mean squared speed of molecular chlorine in m/s at 20ºC.
20 Problem 5.78The temperature in the stratosphere is -23ºC. Calculate the root mean square speeds of N2 molecules in this region. N2=____
21 M2 M1 NH4Cl NH3 17 g/mol HCl 36 g/mol Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.r1r2M2M1=molecular pathNH4ClNH317 g/molHCl36 g/mol
22 Gas effusion is the is the process by which gas under pressure escapes from one compartment of a container to another by passing through a small opening.=r1r2t2t1M2M1Nickel forms a gaseous compound of the formula Ni(CO)x What is the value of x given that under the same conditions methane (CH4) effuses 3.3 times faster than the compound?M2 =r1r2()2x M1r1 = 3.3 x r2= (3.3)2 x 16 = 174.2M1 = 16 g/molx • 28 = 174.2x = 4.1 ~ 4
23 Justify the statement: A helium-filled rubber balloon deflates faster than an air-filled one.
24 Problem 5.83A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same condition of temperature and pressure, it takes an equal volume of N2 gas 12.0 min to effuse through the same barrier. Calculate the molar mass of the gas. What could this gas be?