1 Gas Law Unit Objectives 1. Understand the kinetic-molecular theory and how it explains certain properties of gases Assumptions of the kinetic theory. 3. Understand the differences between an ideal and real gas. 4. Understand the properties of gases

2 Kinetic Molecular Theory Based on the assumption that particles of matter are always in motion. Used to explain properties of substances by looking at the energy of the particles and the interaction between them.

3 The 5 Assumptions 1. Lots of tiny particles that are relatively far apart. 2. Elastic collisions- no loss of energy 3. Continuous, rapid, random motion 4. No interaction between molecules

4 Last One: Depends on the average kinetic energy of the particles. KE = 1/2mv 2 m= mass v=velocity How will this CO 2 React whe hated?

5 Physical Properties of Gases Expansion- Fill the container in which they are enclosed. Fluidity- particles slide easily past eachother Low Density- particles very far apart Compressibility- brings particles closer together

6 More Properties

7 Effusion- gas particles escape through a tiny opening.

8 How do gases behave? An Ideal gas perfectly fits the Kinetic- molecular theory of Gases (obeys all 5 assumptions!) The behavior of a gas is dependent on how “hot” it is. The temperature of a gas instigates the movement of the gas. un fa

9 The Variables- When talking about gases, we discuss the changes in three variables- Pressure Temperature Volume When we change one of the variables-- the other ones change too. It’s way cool!!

10 What is Pressure? Pressure Average force per unit area This force is from all the individual gas collisions (molecular collision = particles that go bump in the air) Pressure = force Area

11 Bet I can break this stick using one hand and a piece of newspaper!!

12 Measuring Pressure (Atmospheric pressure) Barometer - Measures atmospheric pressure. Air pressure is expressed in mmHg

13 Measuring Pressure (Important conversion factors!!) Pressure at sea level = 760 mmHg 1 atm = 760 mmHg = 760 torr =101.3 kPa = 14.7.lb/in 2 (psi) Just think about h ow much weight was pressing down on our newspaper!

14 Practice problem- In CB Express a pressure of 1.20 atm in mmHg ( Remember 1 atm = 760 mmHg)

15 Practice problems (CB) 5.60 atm to a)Torr b)psi (lb/sq. in) c)Pascal (Pa)

16 How did you do? 5.60 atm to a)4300 torr b)82 psi a)5.7 x 10 5 Pa Did you remember your sig figs? consider the numbers in the conversion factors!!

17 Question for you-- Why does it take longer to cook noodles here in Parker than it does in LA?? It’s all about PRESSURE!!

18 Increasing Temperature Temperature is the average kinetic energy of the molecules! Temperature molecules speed up. Temperature - molecules slow down. Think about when you leave your basketball outside in the fall

19 How is temperature measured? Three scales Farenheit Celsius Kelvin Conversion factor Kelvin = degrees Celsius

20 Temperature Conversions Convert the following Celsius degrees to Kelvin. a. 416 ºC b. 23 ºC c. 87 ºC All temperatures that we use in the gas law unit will need to be converted to Kelvin

21 Volume Volume = How big is the container containing the gas molecules? How do you think the size of the container affects how the particles move? Keep in mind that the number of molecules in the container stays the same.

22 Volume Larger volume- particles have more room to move around. Smaller volume- Particles have less room to move around.

23 How is Volume measured? You will usually see volume in milliliters (ml) or liters (L). Do you remember how many milliliters in a liter?

24 Gas Laws - An ideal gas What is STP? Standard Temperature and Pressure Standard Temp = 0 o C or 273 K (Kelvin) Standard Pressure = 1 atm

25 Killer Calculations- keep in mind P = Pressure T= Temperature V = Volume

IDEAL AND REAL GAS CALCULATIONS 26 STP (P = 1 atm and T = K). Law of Gay-Lussac: P 1 /T 1 = P 2 /T 2 Boyle's Law: P 1 V 1 = P 2 V 2 Charles' Law V 1 /T 1 = V 2 /T 2 Avogadro's Law V 1 /n 1 = V 2 /n 2 Combined gas P 1 V 1 /T 1 = P 1 V 2 /T 2 Ideal gas Law P 1 V 1 = nRT

Ideal gas equation PV = nRT 27

Pressure There is are many units of pressure, In the ideal gas equation R has very specific units Different units then the value of R changes Pressure can be measured in atms, Kilo Pascals, bar, mmHg or Torr these last two are pretty much the same thing. But look at the difference it make to the value of R 28

Pressure Different values of R 29 Values of RUnits (V P T −1 n −1 ) (V P T −1 n −1 ) Units of pressure L atm K −1 mol −1 atm Atmospheres L kPa K −1 mol −1LkPa kilopascals ×10 −2 L bar K −1 mol −1L Bar (11) L mmHg K −1 mol −1 mmHg (11) L Torr K −1 mol −1 Torr (10) ft lbf K −1 g-mol −1ft lbf g-mol Foot pounds

Pressure conversions 30 Converting mmHg or Torr into atm Divide by mmHg = 800 Atm mmHg = Atm So 1 Atm = 760 mmHg 760 torr kiloPascals bar

Temperature conversions Temperature must always be in Kelvin o C  K = +273 Eg 30 o C = 303K 31

Temperature conversions F  o C = (X -32) (5 /9) Eg 37 F = (37-32). (5/9) = 5.(5/9) = 25/9 = 2.78 o C 2.78 o C = K 32

Volume and amount of substance conversions V 1L = 1 dm ml = 1L 1cm 3 = 1 ml 1000cm 3 = 1L n The amount of substance must be measure in moles Mole = MIG/ GFM 33

34 Gas Law Problems- The Steps 1. Determine the correct equation. 2. Manipulate the equation to solve for the correct variable. 3. Plug in your known variables, cancel units and perform the calculation.

35 Gas Laws- 1. Boyle’s Law- Temperature is constant 2. The volume of a gas is inversely related to the pressure. P 1 V 1 = P 2 V 2

36 Charles Law- Charles’s Law- Pressure is constant. Kelvin temp & the volume are directly related. V 1 = V 2 T 1 T 2

37 Gas Laws- Gay Lussac’s Law- Volume remains constant Pressure is directly proportional to Kelvin temp. P1 = P2 T1T2

38 Let’s look at some problems Using the gas law packet, we’ll walk through several examples.

39 Example Problem 1. A sample of nitrogen gas occupies a volume of 200 ml at 740 torr. What will the pressure be if we change the size of the container to 500 ml? 2. A 230 ml sample of carbon monoxide experiences a change in pressure from 5atm to 3 atm. What is the new volume?

40 The Combined Gas Law- Putting all three gas laws together we come up with P 1 V 1 = P 2 V 2 T 1 T 2 Time for some practice problems!!!

41 TPS- Try these problems independently, then compare your answer with your table partner. How did you do? 1. If a balloon has a volume of 0.4 L and a temp of 20 o C, what will the volume of the balloon be after it’s heated to 25 o C ? 2. A cylinder of gas has a pressure of 4.40 atm at 25 o C. At what temp in Kelvins will it reach a pressure of 6.50 atm?

42 Same deal- work independently, then discuss with partner. 1.A gas has a volume of 3.6 liters when it is under a pressure of 1.05 atmospheres and a temp of –15 degrees Celsius. What will its volume be at STP? 2. A mL sample of gas at 40.0 degrees Celsius and 895 torr is transferred to a second vessel where the temperature is 0.0 degrees Celsius and the pressure is 745 torr. What is the volume of the second vessel?

43 The total pressure of gases equals the sum of the partial pressures of the component gases. P total = P gas 1 + P gas 2 + P gas 3 + P gas 4 + etc…… Dalton’s Law of Partial Pressure

44 Let’s try One! Example: If a gas canister contains 1.2 atm of oxygen, 3.5 atm of nitrogen and 5.1 atm of carbon dioxide. What is the total pressure?

45 Warm Up: TPS- Try it yourself…discuss with partner. A gas cylinder contains 770 torr of NO, 2.3 atm of O 2 and kPa of CO. a. Write the equation b. Convert all the values to a common unit. c. Add them up.

46 Take a couple of minutes and do the example problems in the packet. Compare answers with your table partner.

47 Avagadro’s Law Yes, it’s the same Avagadro that Came up with that big # 6.02x10 23 The volumes of gases (the amount of any given gas) is the same when the temperature and the pressure are the same. According to Avagadro’s Law-- one mole of any gas will occupy the same volume as one mole of any other gas, despite the mass differences (This is true only when temperature and pressure are constant. which means at STP.)

48 Avagadro’s Law cont…. Therefore, the volume occupied by one mole of a gas at STP is known as: Standard Molar Volume of a Gas = 22.4L To find the number of moles and/or mass of a given volume of a gas at STP, use As a conversion factor. 1 mole = 22.4 L

49 Ideal Gas Law PV=nRT n= number of moles R = constant The Ideal Gas Law can be applied to determine the conditions of a gas sample when three of the four variables are known.

50 The value of “R” changes depending on the pressure units. Given the following units of pressure. 1atm: R= L atm mol K kPa:R= L kPa mol K mmHg: R= 62.4 L mmHg mol K Ideal Gas Law: PV=nRT cont….

51 When do I use this one? Any problem that has the word “mole” Any problem that tells you how many “grams” you start with or that will result. Any problem that gives you the constant.