2Gas PressureJust means that gas is “pushing” on something.
3Gas Pressure Tire What’s going on inside? Air: Nitrogen 78% Oxygen 21% Argon ~1%Carbon Dioxide <1%Each of these particles are constantly flying around. Like a lotto ball!They slam against the container and keep the tire “full”. The particles press against the walls.Tire
4Measuring Gas Pressure Air:Nitrogen 78%Oxygen 21%Argon ~1%Carbon Dioxide <1%Think of a giant ball pit miles and miles up.At the bottom of the ball pit, is like us walking around. That’s the atmospheric pressure.
5Measuring Gas Pressure VacuumVacuumU-TubeIt pushes down on this side, and it moves up on the other side.So how do we measure it?Can’t use it to measure atmospheric pressure, because atmospheric pressure presses on everything equally.
6Measuring Gas Pressure The fluid that is contained in this U tube, is mercury. If we measure this at sea level, we get. 760mmHg between the bottom and the top.Vacuum760 mmHgWe can measure that!Take a ruler and measure low to high in milimeters!
7Measuring Gas Pressure What if we go up a mountain or down into a mine?Think about that ball pit again. If you’re at the bottom of the ball pit will it weigh more or less than at the top?Sea LevelMore Pressure760mmHgLess Pressure
8Measuring Gas Pressure of Containers 760 mmHg800 mmHg40 mmHgWhat if I snap off the vacuum bulb?Because atmospheric pressure is pushing down!
10Gas Pressure Conversions How do we measure things? Lots of ways! Same goes with gas pressure.Gas Pressure UnitsmmHg atmosphere kilopascalTorratm kPaConversions760 mmHg = 1 atm = 101.3kpa
11Gas Pressure Conversions The pressure inside a car tire is 225 kPa.Express this value in both atm and mmHg.760 mmHg = 1 atm = kPa225 kPa x 1 atm101.3 kPa=2.22 atm225 kPa x 760 mmHg101.3 kPa=1688 mmHg
12Boyle’s LawIf we keep the temperature the same, we can predict what pressure and volume will do.
13Boyle’s Law Pressure and Volume What about volume? Gas particles have a bunch of room.Gas particles are squeezed into smaller space.P= LowV=HighP=HighV=LowAs pressure goes up, volume goes down. That means inverse relationship.
14Boyle’s Teeter Totter When volume is high, pressure is low When the volume is low, pressure is highAn Inverse relationship.
15Boyle’s Law Boyle’s law is explained by the equation P1V1=P2V2 Let’s get right to it!At 1.70 atm, a sample of gas takes up 4.35 L. If the pressure on the gas is increased to 2.40 atm, what will the new volume be?P1V1 = P2V2(before) (after)What do you know?Last p 2, 3, 5P1 (before pressure) =1.70 atm(1.70 atm)(4.35L)=(2.40 atm)V2V1 (before volume)=4.35 L7.40atm/L = (2.40atm)V2P2 (after pressure) =2.4 atmV2 =3.01LV2 = ??
16Boyle’s Law Does that answer make sense? At 1.70 atm, a sample of gas takes up 4.35 L. If the pressure on the gas is increased to 2.40 atm, what will the new volume be?We increased the pressure, so we pushed down that piston. We squeezed the molecules into a smaller space. So the volume should go down!
17Boyle’s LawIf I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?P1V1 = P2V2(before) (after)P1 (before pressure) =1.5 atmV1 (before volume)=5.6 L(1.5atm)(5.6L) = (P2)(4.8L)P2 (after pressure) =?8.4 atm/L = (4.8L)P2V2 =P 74.8L1.8 atm = P2
18Charles’ LawCharles’ law relates volume and temperature, while keeping pressure the sameV1 = V2T T2
19Charles’ LawHow could we test the theory that temperature and volume are related?Think about kinetic theory and molecules.
20Charles’ Law COLD HOT What’s going on with the temp? T= High T = Low V= HighV = LowPeriod 8Charles’ law says that as the temp increases, so does volume.A direct relationship.
21Charles’ Law So now we can relate volume and temperature. V1 = V2 T T2MUST ALWAYS USE KELVIN TEMPERATURE in gas lawsA balloon takes up 625 L at 0°C. If it is heated to 80°C, what will its new volume be?Must convert to Kelvin.0 °C = 273K80 °C = 353KV1 =625 LT1 =0 °CT2 =80 °CV2 =??
22Charles’ LawA balloon takes up 625 L at 0°C. If it is heated to 80°C, what will its new volume be?V1 = V2T T2V1 = 625 LT1 = 273KT2 = 353KV2 = ??L625L = V2273K K2.29L/K= V2353K808L = V2
23Charles’ LawAt °C a gas has a volume of 6.00 L. What will the volume be at °C?V1 = V2T T2What’s the equation?V1=6.00 LMust convert to Kelvin.27 °C = 300K150°C = 423KT1=27 °CV2=??T2=150.0 °C
24Charles’ LawAt °C a gas has a volume of 6.00 L. What will the volume be at °C?V1 = V2T T26.00L = V2300K KV1=6.00 LT1=300K0.02L/K = V2423KV2=??T2=423K8.46L = V2
25Avogadro’s Law Relationship between: Amount of gas (n) and the Volume. What happens to one, when I change the other?I start with the first balloon, and then blow more air into it…will the volume increase?Yes, a direct relationship
26Avogadro’s Law As the amount (in moles) goes up, so does the volume. If we double the amount, it doubles the volume.
27Avogadro’s Law We only changed TWO things. The volume and the amount of particles.We didn’t mess with the pressure or the temperature, they were held constant.V1 = V2n n2
28Avogadro’s Law V1 = V2 n1 n2 Let’s try! In a sample of gas, 50.0 g of oxygen gas (O2) take up 48L of volume. Keeping the pressure constant, the amount of gas is changed until the volume is 79 L. How many mols of gas are now in the container?n1= n2 =V1 = V2 =50gmol?79L40LWhen doing Avogadro's law, “n” MUST be in moles!
29Avogadro’s Law Before After n1=50g n2 = g? V1 = 48L V2 = 79L V1 = V2 n n21.6molWhen doing Avogadro's law, “n” MUST be in moles!50g O2 x 1 mol O232g O2= 1.6 mol O21.6 mol O248L= n279L0.03 = n279L2.6 mol = n2
30Gay-Lussac’s LawThe pressure and Kelvin temperature of a gas are directly proportional, when the volume remains constant.
31Gay Lussac’s LawThis law only applies to gases held at a constant volume. Only the pressure and temperature will change.Pi =initial pressurePf = final pressureTi = initial temperature (kelvin)Tf = final temperature (kelvin)P1 = P2T1 T2The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20C). If the can is warmed to 48C, what will the new pressure inside the can be?
32Gay Lussac’s LawThe pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20°C). If the can is warmed to 48°C, what will the new pressure inside the can be?P1 = P2T1 T2P1 =235 kPaMust convert to Kelvin20°C = 293K48°C = 321KP2 =?T1 =20°CT2 =48°C
33The pressure in a sealed can of gas is 235 kPa when it sits at room temperature (20°C). If the can is warmed to 48°C, what will the new pressure inside the can be?P1 = P2T1 T2P1 =235 kPa235293= Pf321P2 =?0.80 = Pf321T1 =293KT2 =321K257.5 kPa = Pf
34How to use these formulas Charle’s LawV1 = V2T T2They are all pretty much the same equation, just different variables!Avogadro’s LawV1 = V2n n2Gay Lussac’s LawP1 = P2T T2
35Combined Gas Law Charle’s Law V1 = V2 T T2What if I had a balloon. I wanted to increase the pressure and cool it down. What is the volume? Do we have an equation for that? P, T, V.Boyle’s Law(P1)(V1) = (P2)(V2)We can combine the laws!Gay Lussac’s LawP1 = P2T T2Combined Gas Law(P1)(V1) = (P2)(V2)T T2
36Combined Gas LawA 40.0L balloon is filled with air at sea level (1.00 atm, 25.0 °C). It's tied to a rock and thrown in a a cold body of water, and it sinks to the point where the temperature is 4.0 ° C and the pressure is atm. What will its new volume be?Convert to Kelvin25°C = 298K4°C = 277K(P1)(V1) = (P2)(V2)T T2P1 =1 atmP1= 1 atmP2= 11 atmV1= 40 LV2= ??T1= 298KT2= 277K(1)(40) = (11)(V2)298K 277KP2 =11 atmV1 =40 L0.13 = (11)(V2)277KV2 =??T1 =25°C36.01 = (11)(V2)T2 =4°C3.27 L = V2
37Ideal Gas LawHow can we describe what’s going on in this container? What variables can we think of?Temperature (T)313KPressure (P)3.18 atmVolume (V)95.2 LAmount of Gas (n)7.5 molDid you know that if we know 3 of the 4 variables, we can find the last one?
38Ideal Gas Law P =nRT V Ideal gas law: PV = nRT Temperature (T) 313K Pressure (P)3.18 atm??Volume (V)95.2 LAmount of Gas (n)7.5 mol??What if we needed the amount of gas (n)?How would we rearrange the problem to find P?P =nRTVPV = nRT
39Ideal Gas Law PV = nRT So what is R? R is a constant! For most cases, R = L▪atm/mol ▪KThose units look familiar.V = LP = atmT = Kn = molThe units on “R” MUST match the units in the problem!
40Ideal Gas Law “R” will come in many forms. R = 62.4 L▪mmHg /K ▪mol R = 8.31 L▪kPa /K ▪molNOT A BIG DEAL! The “R” constant will always be given, just use the right constant.
41Ideal Gas Law2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is volume of the gas?PV = nRTConvert to Kelvin41°C = 314KP =1.70 atmV =??n =2.3 molR =L▪atm/K ▪molT =41°C
42Ideal Gas Law2.3 moles of Helium gas are at a pressure of 1.70 atm, and the temperature is 41°C. What is volume of the gas?PV = nRTRearrange the equation.P =1.70 atmV = nRTPV =??V = (2.3 mol)(314K) x L ▪atm1.70 atm K ▪ moln =2.3 molR =L▪atm/K ▪molV = 59.31.7T =314KV = 34.9 L
43Ideal Gas LawAt a certain temperature, 3.24 moles of CO2 gas at 2.15 atm takes up a volume of L. What is this temperature (in Celsius)?Do the units given match the R?P =2.15 atmV =35.28 LT =??n =3.24 molR =L▪atm/K ▪mol
44Ideal Gas LawPV = nRTAt a certain temperature, 3.24 moles of CO2 gas at 2.15 atm takes up a volume of L. What is this temperature (in Celsius)?Rearrange the equation.P =2.15 atmT = PVnRV =35.28 LT =??n =3.24 molT = (2.15 atm)(35.28L) X K ▪ mol(3.24 mol) L ▪ atmR =L▪atm/K ▪mol
45Ideal Gas Law Charle’s Law V1 = V2 T1 T2 Who wants to memorize all of these?!?!Avogadro’s LawV1 = V2n n2Gay Lussac’s LawP1 = P2T T2Ideal Gas LawPV = nRTYou don’t have to!Combined Law(P1)(V1) = (P2)(V2)T T2
46Gas Law Just memorize one! Can use it for any of the gas law problems! Ideal Gas LawPV = nRTWarning:If this blows your mind and you get totally confused, just memorize the equations.
47Gas Law Rearrange the ideal equation so that the variables given are on the same “side”Before AfterP1 = 3 atm P2 = 7atmT1 = ?? T2 = 150kYou’ve found the equation you need to use. You don’t need “n, R, or V”.PV =nRTPV = nRTV VP = nRTT VTP1 = P2T T2P= nRT V
48Gas Law PV = nRT P1 = 1,217 mmHg P2 = 732 mmHg V1 = ?? V2 = 42L Rearrange the equation so the variables you’re looking for are on the same side of the equation.Easy! PV is already on the same side. Now just double it.P1V1 = P2V2
49Gas Law PV = nRT V1 = 7.5L V2 = 1.2L n1= 32 mol n2 = ? Rearrange the equation so V and n are on the same side.PV = nRTP PV = nRTPV = nRTn PnV1 = V2n1 n2
50Gas Law Before After V1 = ? V2 = 54L P1 = 96 kPa P2 = 112 kPa T1 = 12K T2 = 42KPV = nRTRearrange so V, T, P are on same side.PV = nRTT TP1V1 = P2V2T T2