1 KINETIC THEORY OF GASES MADE OF ATOMS OR MOLECULES THAT ARE CONSTANTLY AND RANDOMLY MOVING IN STRAIGHT LINES COLLIDE WITH EACH OTHER AND CONTAINER WALLS ENERGY IS TRANSFERRED DURING COLLISIONS, BUT NOT LOST

2 KT II GAS PARTICLES TAKE UP VERY LITTLE SPACE – MOSTLY EMPTY SPACE BETWEEN PARTICLES NO ATTRACTION OR REPULSION FORCES

3 KE, SPEED, AND TEMP KINETIC ENERGY IS DIRECTLY RELATED TO PARTICLE SPEED AND TO TEMPERATURE AS TEMP INCREASES, KE AND PARTICLE SPEED INCREASE AS TEMP DECREASES, KE AND PARTICLE SPEED DECREASE

4 PRESSURE COLLISIONS BETWEEN PARTICLES AND CONTAINER EXERT FORCE ON CONTAINER WALL THIS FORCES IS CALLED PRESSURE PHYSICAL PROPERTY OF ALL GASES IF # OF PARTICLES CHANGED, PRESSURE CHANGES

5 PRESSURE AND TEMP CHANGING TEMPERATURE CAUSES PARTICLE SPEED TO CHANGE FASTER PARTICLES CREATE MORE FORCE AND MORE PRESSURE SLOWER PARTICLES CREATE LESS FORCE AND LESS PRESSURE

6 PRESSURE OF MIXTURE IN A MIXTURE OF GASES, PRESSURE IS RELATED TO THE TOTAL NUMBER OF COLLISIONS EACH GAS CONTRIBUTES TO THE TOTAL PRESSURE THE PRESSURE CAUSED BY EACH GAS IS CALLED ITS PARTIAL PRESSURE

7 ATMOSPHERIC PRESSURE CAUSED BY COLLISIONS WITH PARTICLES MIXED IN AIR RELATED TO THE WEIGHT OF THE AIR ON US AS YOU TRAVEL UP, LESS AIR WEIGHS DOWN ON YOU, SO AIR PRESSURE IS LESS

8 BAROMETER DEVICE FOR MEASURING ATMOSPHERIC PRESSURE MECURY BAROMETER INVENTED BY TORRICELLI

9 BAROMETER AT DIFFERENT ELEVATIONS

10 PRESSURE UNITS POUNDS PER SQUARE INCH ATMOSPHERES TORR (ALSO CALLED mm Hg) PASCALS (SINCE PASCALS IS SO SMALL, kPa IS OFTEN USED)

11 PRESSURE CONVERSIONS 1 atm = 760 TORR (mm Hg) = kPa = psi = 29.9 in Hg USE FACTOR-LABEL TO DO CONVERSIONS

12 CONVERSION EXAMPLES CONVERT 740 mm Hg TO –ATMOSPHERES –kPa

13 PRESSURE GAUGE READS 0 WHEN NOT ATTACHED TO A PRESSURIZED OBJECT ABSOLUTE (TOTAL) PRESSURE = GAUGE + ATMOSPHERIC PRESSURE

14 TEMPERATURE A MEASURE OF THE AVERAGE KE OF THE MOLECULES IN A SUBSTANCE SCALES INCLUDE CELSIUS, KELVIN, AND FAHRENHEIT MUST USE KELVIN IN ALL GAS LAW EQUATIONS

15 CELSIUS BASED ON BOILING AND MELTING POINTS OF WATER MP OF WATER ASSIGNED A VALUE OF 0  C BP OF WATER ASSIGNED A VALUE OF 100  C 100 DIVISIONS BETWEEN THESE POINTS

16 KELVIN BASED ON ABSOLUTE ZERO (TEMPERATURE AT WHICH ALL MOLECULAR MOTION STOPS) MP OF WATER IS 273 K BP OF WATER IS 373 K DEGREE SIZE IS SAME AS CELSIUS NO NEGATIVE TEMPS! DON’T USE  SYMBOL

17 FAHRENHEIT MP OF WATER IS 32  F BP OF WATER IS 212  F 180 DIVISIONS BETWEEN THESE POINTS DEGREE SIZE IS SMALLER THAN C 

18 COMPARING SCALES

19 TEMPERATURE CONVERSION K =  C  C = K - 273

20 TEMP CONVERSION EXAMPLES CONVERT THE FOLLOWING: 25°C TO K 500 K TO  C

21 WATER VAPOR PRESSURE LIKE ANY OTHER GAS, WATER VAPOR CREATES PRESSURE

22 DALTON’S LAW TOTAL PRESSURE OF MIXTURE = SUM OF PARTIAL PRESSURE OF EACH GAS IN MIXTURE P TOTAL = P A + P B +... USEFUL IN FINDING PRESSURE OF GAS COLLECT BY WATER DISPLACEMENT

23 GAS COLLECTION BY WATER DISPLACEMENT GAS FROM A REACTION IS DIRECTED TO WATER FILLED CONTAINER GAS DISPLACES WATER AS IS BUBBLES THROUGH BUBBLES PICK UP WATER VAPOR CONTAINER HOLDS MIXTURE OF GAS AND WATER VAPOR P TOTAL = P GAS + P WATER P TOTAL = P ATM WHEN GAS COLLECTED

24 WATER VAPOR EXAMPLE GAS IS COLLECTED BY WATER DISPLACEMENT WHEN THE TEMPERATURE IS 20ºC AND ATMOSPHERIC PRESSURE IS 98.4 kPa FIND THE GAS PRESSURE

25 GAS LAWS DESCRIBE THE BEHAVIOR OF GASES WHEN PRESSURE, VOLUME, AND/OR TEMPERATURE CHANGE

26 BOYLE’S LAW PRESSURE AND VOLUME ARE INVERSELY RELATED IF TEMPERATURE AND # OF PARTICLES ARE CONSTANT

27 BOYLE’S LAW II

28 BOYLE’S LAW EXPLAINED AS VOLUME DECREASES, PARTICLES ARE CONFINED TO A SMALLER SPACE INCREASES # OF COLLISIONS WITH CONTAINER SINCE RANDOM MOTION UNAFFECTED MORE COLLSIONS CAUSES PRESSURE TO INCREASE

29 BOYLE’S LAW EQUATION P 1 V 1 = P 2 V 2

30 BOYLE’S EXAMPLE A BALLOON IS FILLED WITH GAS AND OCCUPIES 2.0 L AT 1.0 ATM. WHAT VOLUME WILL IT OCCUPY WHEN THE EXTERNAL PRESSURE IS INCREASED TO 2.5 ATM?

31 CHARLES’ LAW VOLUME AND TEMPERATURE ARE DIRECTLY RELATED IF PRESSURE AND # OF PARTICLES ARE CONSTANT

32 CHARLES’ LAW EXPLAINED AS TEMPERATURE INCREASES, PARTICLES MOVE FASTER THIS CAUSES A LARGER FORCE FROM COLLISIONS LARGER FORCE PUSHES CONTAINER WALLS OUT INCREASING VOLUME WHILE PRESSURE REMAINS CONSTANT

33 CHARLES’ LAW EQUATION V 1 /T 1 = V 2 /T 2 V 1 T 2 = V 2 T 1

34 CHARLES’ EXAMPLE A 3.0 L BALLOON IS AT 25  C. WHAT IS THE VOLUME WHEN THE BALLOON IS PUT INTO A FREEZER AT –10  C?

35 GAY-LUSSAC’S LAW PRESSURE AND TEMPERATURE ARE DIRECTLY RELATED IF VOLUME AND # OF PARTICLES ARE CONSTANT

36 GAY-LUSSAC’S LAW EXPLAINED AS TEMPERATURE INCREASES, PARTICLES MOVE FASTER THIS CAUSES A LARGER FORCE FROM COLLISIONS LARGER FORCE MEANS HIGHER PRESSURE

37 GAY-LUSSAC’S LAW EQUATION P 1 /T 1 = P 2 /T 2 P 1 T 2 = P 2 T 1

38 GAY-LUSSAC EXAMPLE THE PRESSURE IN A STEEL TANK IS 200 kPa AT 20  C. WHAT IS THE PRESSURE IF THE TANK IS IN THE SUN AND THE TEMPERATURE IS 90  C?

39 COMBINED GAS EQUATION P 1 V 1 /T 1 = P 2 V 2 /T 2 P 1 V 1 T 2 = P 2 V 2 T 1

40 GAS LAW MNEUMONIC P T V

41 COMBINED EXAMPLE A 2.0 L BALLOON IS AT 25  C AND 1.0 ATM. WHAT IS ITS VOLUME IN THE UPPER ATMOSPHERE WHERE THE PRESSURE IS 0.4 ATM AND THE TEMPERATURE IS -40  C?

42 IDEAL (OR PERFECT) GAS COMPLETELY OBEYS KT FOR GASES DOES NOT EXIST REAL GASES DEVIATE SLIGHTLY FROM IDEAL BEHAVIOR AT NORMAL PRESSURES AND TEMPS

43 IDEAL GAS EQUATION DESCRIBES AN IDEAL GAS FOR ONE SET OF CONDITIONS APPROXIMATES REAL GASES PV = nRT n IS THE NUMBER OF MOLES OF GAS

44 IDEAL GAS EQUATION II R IS THE UNIVERSAL GAS CONSTANT VARIES WITH PRESSURE UNITS = 8.31 kPa L/mol K = atm L/mol K = 62.3 Torr L/mol K CAN USE FACTOR LABEL TO CONVERT

45 IDEAL GAS EXAMPLES HOW MANY MOLES OF GAS FIT INTO A 5 L CONTAINER AT STP? WHAT VOLUME IS REQUIRED FOR 12.5 MOLES OF GAS AT 2.5 ATM AND 22  C? WHAT PRESSURE (IN kPa) IS NEEDED TO PUT 3.1 MOLES OF GAS INTO A 0.5 L TANK AT 25  C?

46 GAS PARTICLE ENERGIES DEPENDENT ON MASS, SPEED, AND TEMPERATURE AT A GIVEN TEMPERATURE, ALL GAS PARTICLES HAVE THE SAME AVERAGE KINETIC ENERGY THEY DO NOT HAVE THE SAME SPEED SINCE THEY HAVE DIFFERENT MASSES

47 GAS SPEEDS

48 DIFFUSION MOVEMENT OF GAS PARTICLES FROM AN AREA OF HIGH CONCENTRATION TO AN AREA OF LOW CONCENTRATION DUE TO ITS CONSTANT RANDOM MOTION MOLECULES OF DIFFERENT GASES WILL MIX TOGETHER DUE TO DIFFUSION THE RATE OF DIFFUSION DEPENDS ON SPEED

49 GRAHAM’S LAW FOR GASES AT THE SAME TEMP, GAS WITH SMALLER MOLAR MASS IS FASTER v 1 / v 2 = [M 2 / M 1 ] 1/2 v IS SPEED, M IS MOLAR MASS 1/2 POWER IS SQUARE ROOT SPEED RATIO HAS NO UNITS, DOES NOT GIVE SPECIFIC SPEED

50 GRAHAM’S EXAMPLE HOW MUCH FASTER IS WATER VAPOR COMPARED TO OXYGEN?

51 DIFFUSION EXAMPLE