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Combined Gas LawThe good news is that you dont have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!P1 V1 P2 V2 = T1 T2

No, its not related to R2D2Combined Gas LawIf you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! =

P1V1T1P2V2T2Boyles LawCharles LawGay-Lussacs LawCombined Gas Law ProblemA sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29C. What is the new temperature(C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?

Set up Data TableP1 = 0.800 atm V1 = 180 mL T1 = 302 KP2 = 3.20 atm V2= 90 mL T2 = ??*Make volume units the same!

CalculationP1 = 0.800 atm V1 = 180 mL T1 = 302 KP2 = 3.20 atm V2= 90 mL T2 = ??

P1 V1 P2 V2 = T1 T2

T2 = P2 V2 T1 P1 V1T2 = 3.20 atm x 90.0 mL x 302 K

0.800 atm x 180.0 mL

T2 = 604 K - 273 = 331 C

= 604 KLearning Check A gas has a volume of 675 mL at 35C and 0.850 atm pressure. What is the temperature in C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

Note: Volumes must be the same unit and pressures must be the same unit!1. List variables:V1 = 675 mL = 0.675 LT1 = 35C = 308 KP1 = 0.850 atmV2 = .315 LP2 = 802 mmHg = 1.06 atmDecide on the appropriate gas law:Everythings changing, so Combined!3. Rearrange to solve for unknown: T2 =

(P2) (V2) (T1)(P1) (V1)= 179.2 K = (178.4K)IF WE COMBINE ALL OF THE LAWS weve looked at TOGETHER - INCLUDING AVOGADROS LAW - WE GET: PV=nRTIdeal gas lawIdeal gas constant(R)R IS A CONSTANT THAT CONNECTS THE 4 VARIABLES

R IS DEPENDENT ON THE UNITS OF THE VARIABLE FOR PRESSURETEMP IS ALWAYS IN KELVINVOLUME IS ALWAYS IN LITERSPRESSURE IS IN EITHER atm OR mmHg OR kPaBecause of the different pressure units we use there are 3 different values for RR=.0821LatmmolKIF PRESSURE IS GIVEN IN mmHgR=62.4LmmHgmolKIF PRESSURE IS GIVEN IN kPaR=8.314LkPamolKIF PRESSURE IS GIVEN IN atmLearning CheckDinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23C, what is the pressure (in atm) in the tank in the dentist office?

Using Ideal gas law P V T ?20.0 L296K R =3.48 atm 0.0821LatmmolK(2.86 mol)(.0821)(296K)20.0 L PV = nRT1. List variables:2. Rearrange to solve for unknown:P = nRTV3, Plug & Chug:n = 2.86 molesGAS DIFFUSION AND EFFUSIONDiffusion is the movement of molecules to fill a containerEffusion is the movement of molecules through a small hole into an empty container.

Grahams Law

Thomas Graham, 1805-1869. Professor in Glasgow and London.Rates of effusion of gases are inversely proportional to the square root of their molar masses, at constant temp. & pressure.

M = molar mass & Gas B is the heavier gas!Grahams LawMolecules effuse thru holes in a rubber balloon thats the main reason they get whimpy after awhile! They do this at a rate that is inversely proportional to molar mass.Therefore, He (4 g/mol) effuses more rapidly than O2 (32 g/mol) at same T. (Its lighter!)

HeLighter gases effuse faster than heavier onesGrahams LawWe can use the entire equation to calculate the actual speed of gas particles, howeverWe will just use the square root side to COMPARE rates of effusion (speeds)Ex. Compare the rates of effusion of oxygen gas & hydrogen gas.1st find their molar masses!O2 = 32.0 g/mol H2 = 2.0 g/mol2nd -Put the heavier gas (Gas B) in the numerator!

432 g2.0 gYoure not done yet!Grahams LawThe number 4 is not much of a comparison!You must put your answer in sentence form!Try this:_______ gas travels (or effuses) at a rate ___ times faster than _________ gas.So, the answer isHydrogen gas travels (or effuses) at a rate 4 times faster than oxygen gas.(Lighter gas)(heavier)(#)Grahams LawYou try it!Compare the rates of effusion of Ar and nitrogen gas (N2)

39.9 g/mol28.0 g/mol39.928.01.19Nitrogen gas travels (or effuses) at a rate 1.19 times faster than argon gas.All of these gas laws work just ducky assuming the gases are ideal(Points with no volume & no mutual attractionMost of the time, gases conform to ideal conditions. So, when are gases not ideal?Under conditions of low temperature& high pressure (force molecules close enough to affect each other!)

Deviations from Ideal Gas LawReal Molecules have volumes and attractive forces between them.Gases are not Ideal under conditions of high pressure & low temperature which bring particles close enough together to affect each other!

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