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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
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KT II
• GAS PARTICLES TAKE UP VERY LITTLE SPACE – MOSTLY EMPTY SPACE BETWEEN PARTICLES
• NO ATTRACTION OR REPULSION FORCES
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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
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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
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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
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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
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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
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BAROMETER
• DEVICE FOR MEASURING ATMOSPHERIC PRESSURE
• MECURY BAROMETER INVENTED BY TORRICELLI
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BAROMETER AT DIFFERENT ELEVATIONS
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PRESSURE UNITS
• POUNDS PER SQUARE INCH
• ATMOSPHERES
• TORR (ALSO CALLED mm Hg)
• PASCALS (SINCE PASCALS IS SO SMALL, kPa IS OFTEN USED)
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PRESSURE CONVERSIONS
• 1 atm = 760 TORR (mm Hg) = 101.3 kPa = 14. 7 psi = 29.9 in Hg
• USE FACTOR-LABEL TO DO CONVERSIONS
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CONVERSION EXAMPLES
• CONVERT 740 mm Hg TO– ATMOSPHERES– kPa
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PRESSURE GAUGE
• READS 0 WHEN NOT ATTACHED TO A PRESSURIZED OBJECT
• ABSOLUTE (TOTAL) PRESSURE = GAUGE + ATMOSPHERIC PRESSURE
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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
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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
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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
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FAHRENHEIT
• MP OF WATER IS 32 F• BP OF WATER IS 212 F• 180 DIVISIONS BETWEEN THESE
POINTS• DEGREE SIZE IS SMALLER THAN C
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COMPARING SCALES
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TEMPERATURE CONVERSION
• K = C + 273C = K - 273
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TEMP CONVERSION EXAMPLES
• CONVERT THE FOLLOWING:
• 25°C TO K
• 500 K TO C
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WATER VAPOR PRESSURE• LIKE ANY OTHER GAS, WATER
VAPOR CREATES PRESSURE
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DALTON’S LAW
• TOTAL PRESSURE OF MIXTURE = SUM OF PARTIAL PRESSURE OF EACH GAS IN MIXTURE
• PTOTAL = PA + PB + ...
• USEFUL IN FINDING PRESSURE OF GAS COLLECT BY WATER DISPLACEMENT
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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• PTOTAL = PGAS + PWATER
• PTOTAL = PATM WHEN GAS COLLECTED
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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
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GAS LAWS
• DESCRIBE THE BEHAVIOR OF GASES WHEN PRESSURE, VOLUME, AND/OR TEMPERATURE CHANGE
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BOYLE’S LAW
• PRESSURE AND VOLUME ARE INVERSELY RELATED IF TEMPERATURE AND # OF PARTICLES ARE CONSTANT
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BOYLE’S LAW II
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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
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BOYLE’S LAW EQUATION
• P1V1 = P2V2
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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?
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CHARLES’ LAW
• VOLUME AND TEMPERATURE ARE DIRECTLY RELATED IF PRESSURE AND # OF PARTICLES ARE CONSTANT
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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
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CHARLES’ LAW EQUATION
• V1/T1 = V2/T2
• V1T2 = V2T1
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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?
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GAY-LUSSAC’S LAW
• PRESSURE AND TEMPERATURE ARE DIRECTLY RELATED IF VOLUME AND # OF PARTICLES ARE CONSTANT
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GAY-LUSSAC’S LAW EXPLAINED
• AS TEMPERATURE INCREASES, PARTICLES MOVE FASTER
• THIS CAUSES A LARGER FORCE FROM COLLISIONS
• LARGER FORCE MEANS HIGHER PRESSURE
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GAY-LUSSAC’S LAW EQUATION
• P1/T1 = P2/T2
• P1T2 = P2T1
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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?
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COMBINED GAS EQUATION
• P1V1/T1 = P2V2/T2
• P1V1T2 = P2V2T1
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GAS LAW MNEUMONIC
P T V
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COMBINED EXAMPLE
• A 2.0 L BALLOON IS AT 25C 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?
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IDEAL (OR PERFECT) GAS
• COMPLETELY OBEYS KT FOR GASES
• DOES NOT EXIST
• REAL GASES DEVIATE SLIGHTLY FROM IDEAL BEHAVIOR AT NORMAL PRESSURES AND TEMPS
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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
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IDEAL GAS EQUATION II
• R IS THE UNIVERSAL GAS CONSTANT
• VARIES WITH PRESSURE UNITS• = 8.31 kPa L/mol K • = 0.082 atm L/mol K • = 62.3 Torr L/mol K • CAN USE FACTOR LABEL TO
CONVERT
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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 22C?
• WHAT PRESSURE (IN kPa) IS NEEDED TO PUT 3.1 MOLES OF GAS INTO A 0.5 L TANK AT 25C?
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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
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GAS SPEEDS
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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
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GRAHAM’S LAW
• FOR GASES AT THE SAME TEMP, GAS WITH SMALLER MOLAR MASS IS FASTER
• v1 / v2 = [M2 / M1]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
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GRAHAM’S EXAMPLE
• HOW MUCH FASTER IS WATER VAPOR COMPARED TO OXYGEN?
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DIFFUSION EXAMPLE