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

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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

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

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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