1. Unit 8 - Behavior of Gas Molecules

2. KEY TERMS Avogadro’s Law - Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules Boyle’s Law: P 1 V 1 = P 2 V 2 Charles’ Law: V 1 / T 1 = V 2 / T 2 Combined Gas Law: (P 1 V 1 )/T 1 = (P 2 V 2 )/T 2 Dalton’s Law of Partial Pressure - Total pressure experienced by a container containing more than one form of gas is the sum of the pressures of each individual gas Elastic Collision - The total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter Ideal Gas Concept - Hypothetical gas whose particles are in linear motion, occupy negligible space and have no interactions, and that consequently obeys the gas laws exactly Ideal Gas Law equation: PV= nRT Intermolecular Forces - The forces of attraction and repulsion between molecules

3. KEY TERMS Molar Volume - The volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure Kinetic Molecular Theory - The theory dealing with the ideal gas model (dimensionless particles moving in straight lines between elastic collisions with the container walls and not interacting with each other) Standard Temperature and Pressure (STP) - 273K and 1.00 atm pressure Volume Ratio – the ratio of the molar coefficients of a chemical reaction when comparing one gas to another within the chemical reaction

4. Solids Particles are held in a relative fixed position relative to each other Particle vibrate in place Solids have definitive shape. Particles are very tightly packed and have extremely low kinetic energy. Most effective attractive forces between particles Highest density Incompressible

5. Liquids Particles are not bound to a fixed position Particles flow freely (fluid) Liquids have no fixed shape Particles are still close together with slightly higher kinetic energy. Somewhat effective attractive forces between p articles causing liquids to have a fixed volume More dense than gases and less dense than solids Much less compressible than gases because liquid particles are already much closer together.

6. Gases Particles are not bound to a fixed position Particles flow freely (fluid) Gases have no shape. Particles are far apart and have high kinetic energy. Very Ineffective attractive forces between particles causing gases to have no fixed volume. Very low density Very compressible: lots of empty space.

7. KINETIC MOLECULAR THEORY Postulate 1 - Motion of gas particles is linear Postulate 2 - Collision between gas particles are elastic Postulate 3 - No intermolecular attraction between gas particles Postulate 4 - Gas particles have no volume

8. POSTULATE 1 – LINEAR MOTION Gas particles are in motion that is random Gas particles move in straight line (linear) motion until they collide with the boundary or with other gas particles

9. POSTULATE 2 – ELASTIC COLLISIONS Gas particles will collide with each other and the boundaries of the container All gas particle collisions are elastic Elastic collisions are collisions where there in no loss of energy Energy is transferred between particles and boundaries, but the total energy of the system remains unchanged

10. POSTULATE 3 – NO INTERMOLECULAR FORCES Even though gas molecules will be attracted to each other by both electrostatic and gravitational forces, the effects of these force is very small. The amount of attractive force is small enough to be ignored.

11. POSTULATE 4 – GAS PARTICLES HAVE NO VOLUME Gas molecules clearly have both some mass and some volume The volume of each molecule is so small that each gas molecule is said to be a point without volume. The whole gas occupies the space available and is called the volume of the gas, but the volume taken by the individual particles is ignored.

12. PROPERTIES OF GASES Temperature Volume Pressure

13. PROPERTIES OF GASES - TEMPERATURE Since all of the molecules are in linear motion, and therefore have a velocity, they possess kinetic energy as defined by the following equation: Kinetic Energy = ½ (mass) (velocity) 2 KE = ½ mv 2 Temperature is defined as the average kinetic energy of the molecules of the gas.

14. PROPERTIES OF GASES-TEMPERATURE Two scales to measure temperature: Celsius: 0°C - temperature at which water freezes 100°C - temperature at which water turns to gas Kelvin: 273 K - temperature at which water freezes 373 K - temperature at which water turns to gas “What is this Fahrenheit of which you speak” – not used in science

15. TEMPERATURE CONVERSION From Celsius → Kelvin Add 273 degrees 40ºC + 273 = 313K From Kelvin → Celsius Subtract 273 degrees 248 K - 273 = - 25ºC

16. PROPERTIES OF GASES - VOLUME Volume is defined as the space that matter occupies. The base unit for volume is the liter 1 liter (L) = 1000 milliliters (mL) 1 milliliter (mL) = 1 cubic centimeter (cm 3 )

17. PROPERTIES OF GASES-PRESSURE Pressure is defined as the amount of force applied to an area of matter: Force Pressure = ---------- Area Gas particles apply force on the container as particles collide with the boundary The area involved with pressure is the surface area of the container As Force ↑, Pressure ↑ As Surface Area ↓, Pressure ↑

18. PRESSURE CONVERSION Use the equivalent standard pressure values to set up proportionalities: Example: Convert 5.6 atm to KPa 5.6 atm 1atm ----------= --------------- x 101.325 KPa (5.6 atm) (101.325 KPa) = (1 atm) (x) (5.6 atm) (101.325 KPa) ------------------------------- = x 1 atm 567.4 KPa = x Thus, 5.6 atm is equivalent in pressure to 567.4 KPa

19. STANDARD PRESSURES & STANDARD TEMPERATURES Standard Pressures Standard Temperatures 1 atmosphere (1 atm) 0°C 760 millimeters of Mercury (760 mmHg) 273K 760 torr pressure (760 torr) 101.325 KiloPascals (101.325 KPa)

20. DALTON’S LAW OF PARTIAL PRESSURE A single container can, and normally does, contain more than one type of gas. John Dalton, attempting to describe the pressure exerted by each individual gas on the container, developed what is now called the Law of Partial Pressure. This law states that the total pressure experienced by a container containing more than one form of gas is the sum of the pressures of each individual gas. Total Pressure = Pressure of gas 1 + Pressure of gas 2 + … + Pressure of last gas P T = P 1 + P 2 + … + P n

21. DALTON’S LAW OF PARTIAL PRESSURE A special form of this law applies to any system where water vapor is one of the gases. In this form, the total pressure is equal to the sum of the pressure of the water vapor and the pressure of the other gas(es): P T = P vapor + P gas

22. IDEAL VS. REAL GAS IDEAL GAS MOTION IS TOTALLY RANDOM AND LINEAR ALL GAS PARTICLE COLLISIONS ARE ELASTIC GAS PARTICLES DO NOT HAVE ANY INTERMOLECULAR ATTRACTION GAS PARTICLES HAVE NO VOLUME REAL GAS MOTION IS BROWNIAN (ALMOST BUT NOT QUITE RANDOM) GAS PARTICLE COLLISIONS ARE NOT PERFECTLY ELASTIC GAS PARTICLES EXPERIENCE VERY SMALL INTERMOLECULAR ATTRACTION GAS PARTICLES HAVE VOLUME

23. APPLICATION TO GAS LAWS THE DIFFERENCE BETWEEN THE BEHAVIOR OF REAL AND IDEAL GASES IS SO SMALL THAT EXCEPT IN VERY SENSITIVE LABORATORY ENVIRONMENTS THE DIFFERENCE CAN BE IGNORED. FOR ALL OF THE GAS LAWS, THE GASES INVOLVED ARE ASSUMED TO BE IDEAL GASES.

24. BOYLE’S LAW Examines the behavior of gas under the condition of constant temperature. As the volume containing gas particles is reduced, the particles are forced closer together. The result is the particles exert the same amount of force (average kinetic energy hasn’t changed) over a smaller surface area. As surface area is reduced, the pressure of the gas on the container is increased. In similar fashion as the volume of the container is expanded, thereby increasing the surface area, the pressure of the gas on the container is decreased.

25. BOYLE’S LAW P 1 V 1 = P 2 V 2 As Pressure ↑, Volume ↓ As Pressure ↓, Volume ↑ Boyle’s Law is an Inverse Function

26. CHARLES’ LAW Examines the behavior of gas under the condition of constant pressure As the volume containing gas particles is reduced, the particles must move slower to exert the same force over a smaller surface area. or As temperature is decreased, the particles would exert less force on the available surface area. In order to restore the pressure lost through this process, the surface area has to be reduced to compensate.

27. CHARLES’ LAW V 1 V 2 -------- = --------- T 1 T 2 As Temperature ↑, Volume ↑ As Temperature ↓, Volume ↓ Charles’ Law is a Direct Function

28. COMBINED GAS LAW DIAGRAM V P T Boyle’s Law P x V Charles’ Law V/T Gay-Lussac’s Law P/T Combined Gas Law (P x V)/T

29. SAMPLE PROBLEM 1

30. SAMPLE PROBLEM 2

31. SAMPLE PROBLEM 3

32. IDEAL VS. REAL GAS Ideal Gas Motion is totally random and linear All gas particle collisions are elastic Gas particles do not have any intermolecular attraction Gas particles have no volume Real Gas Motion is Brownian (almost but not quite random) Gas particle collisions are not perfectly elastic Gas particles experience very small intermolecular attraction Gas particles have volume

33. APPLICATION TO GAS LAWS The difference between the behavior of Real and Ideal Gases is so small that except in very sensitive laboratory environments the difference can be ignored. For all of the Gas Laws, the gases involved are assumed to be Ideal Gases.

34. COMBINED GAS LAW DIAGRAM V P T Boyle’s Law P x V Charles’ Law V/T Gay-Lussac’s Law P/T Combined Gas Law (P x V)/T

35. COMBINED GAS LAW The behavior of gas molecules under changing circumstances can be explained by the mathematical relationship of the three defining properties of gases. That relationship is quantified through the following expression: (Pressure x Volume) is constant Temperature P 1 V 1 P 2 V 2 -------- = -------- T 1 T 2

36. AVOGADRO’S LAW States that equal volumes of gases at the same temperature and pressure contain the same number of particles 1 mol contains 6.02 x 10 23 particles STP is Standard Temperature and Pressure 273K and 1.00 atm pressure (STP) Avogadro’s Law states that one mole of any gas at Standard Temperature and Pressure (STP) occupies 22.4 Liters of volume @ STP, 1 mole = 22.4 L

37. Increasing the amount of gas in a sample will increase pressure if temperature and volume are constant Both volume and pressure are directly proportional to the number of moles so: PV is constant nT Combined & Avogadro’s Gas Laws

38. IDEAL GAS LAW While the Combined Gas Law deals with the relationship of gas properties under changing conditions The Ideal Gas Law uses the basis of that relationship and applies it to a known set of conditions of those properties and the amount of gas that is present using Avogadro’s Law. P V = n R T P = Pressure V = Volume n = Number of moles R = 0.0821 atm∙L/mole∙K T = Temperature

39. UNIVERSAL GAS CONSTANT - R By selecting the values for standard conditions, the value of the constant can be determined: Standard value for Temperature = 273K Standard value for Pressure = 1 atm Standard value for the amount of gas = 1 mole Standard value for volume = 22.4L This value is fixed for all gases: P V(1 atm) (22.4 L) 22.4 atm∙L 0.0821 atm∙L ------ = -------------------- = ----------------- = ---------------------- n T(1 mole) (273K) 273 mole∙K mole∙K R=0.0821 atm∙L/mole∙K

40. SUMMARY OF GAS LAWS LawEquationConditions Dalton’s Law of Partial Pressure P T = P 1 + P 2 +…+P n Mixture of gasses Boyle’s LawP 1 x V 1 = P 2 x V 2 Constant T Charles’ LawV 1 /T 1 = V 2 /T 2 Constant P Combined Gas Law(P 1 x V 1 )/T 1 = (P 2 x V 2 )/T 2 Constant amount Avogadro’s LawV 1 /n 1 = V 2 /n 2 Constant T & P Ideal Gas LawPV = nRTKMT or ideal gas

41. SAMPLE PROBLEM 1

42. MOLAR VOLUME Molar volume is the volume that 1 mol occupies at 273K and 1.00 atm pressure (STP) Avogadro’s Law states that one mole of any gas at Standard Temperature and Pressure (STP) occupies 22.4 Liters of volume. 1 mol of any gas occupies 22.4 L at STP 22.4 L/mol is a conversion factor

43. MOLAR VOLUME CONVERSIONS Example Find the number of moles in a sample of gas that has a volume of 5.32 L at STP Use the molar volume to convert from volume to moles 5.32 L X 1 mol = 0.238 mol 22.4 L

44. GAS STOICHIOMETRY The application of the Ideal Gas Law and Avogadro’s Law to stoichiometric calculations Avogadro’s Law allows for the application of volume ratio to replace mole ratio to compare any two gases in stoichiometric calculations The Ideal Gas Law allows for application of stoichiometric calculations to a volume of gas at any known condition of pressure and temperature For example, suppose you want to determine the mass relationships between reactants and products for a reaction involving gases. 1. You first convert the given mass to moles. 2. Then you use the mole ratio from the balanced equation to calculate the number of moles of the wanted substance. 3. Finally, you convert the moles of the wanted substance to mass.

45. VOLUME RATIO Works the same as Mole Ratio When more that one gas is present in a reaction, you can use the coefficients to mean volume because Avogadro’s Law applies because the gases both have the same temperature and pressure If the mole ratio is 1:1, the volume ratio is 1:1 If the volume ratio is 3:2, the mole ratio is 3:2 If the mole ratio is 4:5, the volume ratio is 4:5

46. SAMPLE PROBLEM 1 The main component of natural gas used for home heating and cooking is methane (CH 4 ). Calculate the volume that 5.00 kg of methane gas will occupy at STP. Known:Unknown: m = 5.00 kgV = ?L T = 273K P = 1.00 atm Determine molar mass of methane: 16.043 g/mol Determine number of moles of methane: 5.00 kg=5,000 grams 5,000 g x 1 mol = 311 mol 16.043 g Use the molar volume to determine the volume of methane at STP 311 mol x 22.4 L = 6.97 x 10 3 L 1 mol

47. SAMPLE PROBLEM 2

48. SAMPLE PROBLEM 2 CONTINUED

49. SAMPLE PROBLEM 3