Unit 12: Gas Laws. The Kinetic Theory of Gases Gases aren’t attracted or repelled by each other. Gas particles are super tiny, but the space between each

Unit 12: Gas LawsUnit 12: Gas Laws

The Kinetic Theory of GasesThe Kinetic Theory of Gases Gases aren’t attracted or repelled by each

other. Gas particles are super tiny, but the space Gas particles are super tiny, but the space

between each particle is huge. between each particle is huge. Most of the volume of a gas is empty space!Most of the volume of a gas is empty space!

Gas particles move constantly and randomly.Gas particles move constantly and randomly.

The Kinetic Theory of GasesThe Kinetic Theory of Gases

No kinetic energy is lost when gas No kinetic energy is lost when gas particles collide! This is called an particles collide! This is called an elastic elastic collisioncollision..

Inelastic Collision Elastic Collision

The Kinetic Theory of GasesThe Kinetic Theory of Gases

All gases have the same amount of kinetic All gases have the same amount of kinetic energy at a given temperature. So…energy at a given temperature. So…As the temperature increases, so does the As the temperature increases, so does the

energy!energy!

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=296.0

Click for animation

Characteristics of GasesCharacteristics of GasesCharacteristics of GasesCharacteristics of Gases Gases Gases expand expand to fill any container.to fill any container.

random motion, no attractionrandom motion, no attraction

Gases have very Gases have very lowlow densities. densities.no volume = lots of empty spaceno volume = lots of empty space

Characteristics of GasesCharacteristics of GasesCharacteristics of GasesCharacteristics of Gases Gases can be compressed.Gases can be compressed.

no volume = lots of empty spaceno volume = lots of empty space

Gases undergo diffusion.Gases undergo diffusion. random motionrandom motion

PressurePressurePressurePressure

Which shoes create the most pressure?

Atmospheric PressureAtmospheric Pressure

Here is the earth’s Here is the earth’s atmosphere. atmosphere. This blanket of This blanket of air is pushing down on us at air is pushing down on us at all times!all times!

Atmospheric pressure is Atmospheric pressure is equal to 14.7 psi (pounds per equal to 14.7 psi (pounds per square inch) at sea level square inch) at sea level (Houston).(Houston).

Torricelli’s barometer:

Atmospheric pressure Atmospheric pressure is measured with a is measured with a barometer.barometer.

It was invented by It was invented by Evangelista Torricelli Evangelista Torricelli back in the 1600s.back in the 1600s.

The The higherhigher the altitude the altitude, the , the lowerlower the the atmospheric pressure.atmospheric pressure.This is because you have less atmosphere This is because you have less atmosphere

pushing down on you the higher you go up.pushing down on you the higher you go up. ““The air is thinner”…The air is thinner”… The higher you go , the The higher you go , the

less gas molecules. Less oxygen for you.less gas molecules. Less oxygen for you.

LocationLocation ElevationElevation Atmospheric Atmospheric Pressure inPressure in

pounds per square pounds per square inch (psi)inch (psi)

Galveston, TXGalveston, TX Sea levelSea level 14.7 psi14.7 psi

Denver, CODenver, CO 5280 ft5280 ft 12.2 psi12.2 psi

Pike’s Peak, COPike’s Peak, CO 14,000 ft14,000 ft 8.8 psi8.8 psi

Top of Mt. EverestTop of Mt. Everest 29,000 ft29,000 ft 4.9 psi4.9 psi

Pressure Units and Pressure Units and ConversionsConversions

Pressure Units and Pressure Units and ConversionsConversions

Pressure units can look a bit strange. Here is an Pressure units can look a bit strange. Here is an explanation of the ones you will most commonly explanation of the ones you will most commonly use:use:

Pounds per square inchPounds per square inch = = psipsi;; simply expresses the simply expresses the force in pounds over an area in inchesforce in pounds over an area in inches22

AtmosphereAtmosphere = = atmatm; 1 atm; 1 atm is the pressure at sea level (the is the pressure at sea level (the entire atmosphere is pushing down)entire atmosphere is pushing down)

Millimeters of mercuryMillimeters of mercury or or inches of mercuryinches of mercury = = mm Hgmm Hg or or in Hgin Hg;; comes from the height that Hg climbs in a comes from the height that Hg climbs in a barometerbarometer

TorrTorr;; named after Torricelli and is equal to mm Hg named after Torricelli and is equal to mm Hg PascalPascal = = PaPa;; named after Blaise Pascal, a famous scientist named after Blaise Pascal, a famous scientist

who studied gas pressurewho studied gas pressure

ConversionsConversionsKilopascalKilopascal = = kPakPa; ; just 1000 times greater than a Pascaljust 1000 times greater than a Pascal

Relationships between pressure unitsRelationships between pressure units: : **important for conversions!!!**important for conversions!!!

1 atm = 14.7 psi = 760 mm Hg = 29.9 in Hg 1 atm = 14.7 psi = 760 mm Hg = 29.9 in Hg = 760 Torr = 101,300 Pa = 101.3 kPa = 760 Torr = 101,300 Pa = 101.3 kPa

Try these pressure conversions:Try these pressure conversions:

1. 0.50 atm = ? kPa1. 0.50 atm = ? kPa

0.50 atm x 0.50 atm x 101.3 kPa 101.3 kPa = 50.65 kPa= 50.65 kPa

1 atm1 atm2. 744 Torr = ? mm Hg2. 744 Torr = ? mm Hg

744 Torr x 744 Torr x 760 mm Hg 760 mm Hg = 744 mmHg = 744 mmHg

760 Torr760 Torr

Pressure and Temperature Pressure and Temperature Relationship Relationship

As long as the volume stays As long as the volume stays the same…the same…

As temperature increases, As temperature increases, the pressure increases.the pressure increases.

Why? The higher the temp, the more Why? The higher the temp, the more energy they have and they bounce off energy they have and they bounce off the walls more often and with more the walls more often and with more force, creating the pressure.force, creating the pressure.

Pressure and Temperature Pressure and Temperature RelationshipRelationship

Click for animation.Click for animation.

http://phet.colorado.edu/en/simulation/gas-http://phet.colorado.edu/en/simulation/gas-propertiesproperties

Pressure and Temperature Pressure and Temperature RelationshipRelationship

DIRECTDIRECT relationship. P is directly relationship. P is directly

proportional to T.proportional to T. Graph:Graph:

P

T

Volume and Temperature Volume and Temperature RelationshipRelationship

As long as the As long as the pressurepressure remains the same remains the same, , as as the temperature increases, the the temperature increases, the volume increases.volume increases.

Why? Why? The higher the The higher the temperature, the more energy temperature, the more energy the particles get. The the particles get. The increased motion causes the increased motion causes the volume to expand.volume to expand.

Temperature and Volume Temperature and Volume RelationshipRelationship


http://http://phet.colorado.eduphet.colorado.edu/en/simulation/gas-properties/en/simulation/gas-properties

Temperature and Volume Temperature and Volume RelationshipRelationship

DIRECTDIRECT relationship. V is directly relationship. V is directly proportional to T.proportional to T.

V

T

Pressure and Volume RelationshipPressure and Volume Relationship

As long as the temperature doesn’t As long as the temperature doesn’t change,change,As volume increases, pressure As volume increases, pressure

decreases.decreases.Why?Why? When there is more volume, When there is more volume,

the particles are less crowded, so the particles are less crowded, so they have space to move around. they have space to move around. The pressure will drop.The pressure will drop.



http://http://phet.colorado.eduphet.colorado.edu/en/simulation/gas-properties/en/simulation/gas-properties


INVERSE INVERSE relationship. P is inversely relationship. P is inversely proportional to V.proportional to V.

Graph: Graph:

P

V

TemperatureTemperatureTemperatureTemperature

ºF

ºC

K

-459 32 212

-273 0 100

0 273 373

32FC 95 K = ºC + 273

Always use absolute temperature Always use absolute temperature (Kelvin) when working with gases.(Kelvin) when working with gases.

STPSTPSTPSTP

Standard Temperature & PressureStandard Temperature & Pressure

0°C0°C 273 K273 K

1 atm1 atm 101.3 kPa101.3 kPa-OR--OR-

STP

Boyle’s LawBoyle’s LawBoyle’s LawBoyle’s Law

The pressure and volume of a The pressure and volume of a gas are inversely related gas are inversely related at constant mass & tempat constant mass & temp

P

V

P1V1 =P2V2

Example:Example: A 5.0 L container of nitrogen gas is at a pressure of 1.0 atm. What A 5.0 L container of nitrogen gas is at a pressure of 1.0 atm. What

is the new pressure if the volume is decreased to 500 mL, and the is the new pressure if the volume is decreased to 500 mL, and the

temperature remains constant?temperature remains constant?

Formula Formula neededneeded

Rearrange Rearrange for for unknownunknown

Plug-in to formulaPlug-in to formulaInclude units and cancellation!Include units and cancellation!

Final answer Final answer UnitUnit

Unit conversion(s) needed:Unit conversion(s) needed:

1 2

1 2

V V

T TV

T

Charles’ LawCharles’ LawCharles’ LawCharles’ Law

The volume and absolute The volume and absolute temperature (K) of a gas are temperature (K) of a gas are directly related directly related at constant mass & pressureat constant mass & pressure

Example:Example: A container of helium gas at 25A container of helium gas at 25°°C in an expandable 500 mL C in an expandable 500 mL

container is heated to 80.container is heated to 80.°°C. What is the new volume if the C. What is the new volume if the pressure remains constant? pressure remains constant?


Rearrange Rearrange for unknownfor unknown




1 2

1 2

P P

T TP

T

Gay-Lussac’s LawGay-Lussac’s LawGay-Lussac’s LawGay-Lussac’s Law

The pressure and absolute The pressure and absolute temperature (K) of a gas are temperature (K) of a gas are directly related directly related at constant mass & volumeat constant mass & volume

Example:Example: A tank of propane gas at a pressure of 3.0 atm is cooled from 90.A tank of propane gas at a pressure of 3.0 atm is cooled from 90.°°C C

to 30.oC. What is the new pressure if the volume remains to 30.oC. What is the new pressure if the volume remains constant?constant?






Combined Gas LawCombined Gas LawCombined Gas LawCombined Gas LawWe use the We use the Combined Gas LawCombined Gas Law when when

nothing remains constant.nothing remains constant.

PP11VV11 = = PP22VV22

TT11 T T22

Example:Example:

A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 3636ooC. If it is released and rises to an elevation at which the pressure is C. If it is released and rises to an elevation at which the pressure is 0.900 atm and the temperature is 280.900 atm and the temperature is 28ooC, what will be the new volume of the C, what will be the new volume of the

balloon?balloon?






Ideal Gas LawIdeal Gas Law

Used when there are only one set of Used when there are only one set of conditions. We also use MOLES!! conditions. We also use MOLES!!

You will also need the ideal gas constant, You will also need the ideal gas constant, R. R. R = R = 0.0821 L atm0.0821 L atm

K molK molThe units in your problemThe units in your problem must must

matchmatch the units in R.the units in R.

A. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas Law

UNIVERSAL GAS CONSTANT

R=0.0821 Latm/molK

PV=nRT

You don’t need to memorize these values!

YOU MUST CONVERT:YOU MUST CONVERT:YOU MUST CONVERT:YOU MUST CONVERT:P into atmP into atm

Use pressure conversionsUse pressure conversionsV into LV into L

Divide by 1000 if mLDivide by 1000 if mLn into moles n into moles

divide by molecular weightdivide by molecular weightT into KT into K

Add 273 to CelciusAdd 273 to Celcius

Example:Example:

32.0 g of oxygen gas is at a pressure of 760 32.0 g of oxygen gas is at a pressure of 760 mm Hg and a temperature of 0mm Hg and a temperature of 0ooC. What is the C. What is the volume of the gas? volume of the gas?






Example:Example:

A sample of helium gas is in a 500. mL container at a pressure of A sample of helium gas is in a 500. mL container at a pressure of

2.00 atm. The temperature is 272.00 atm. The temperature is 27ooC. What is the mass of the gas?C. What is the mass of the gas?






Gas StoichiometryGas Stoichiometry

Review the 4 basic steps in stoichiometryReview the 4 basic steps in stoichiometry: : 1) Identify the given.1) Identify the given. 2) convert it to moles if not already in moles. 2) convert it to moles if not already in moles. 3) Identify the unknown, and do a mole-to-mole 3) Identify the unknown, and do a mole-to-mole

ratio between given and unknown using the ratio between given and unknown using the

coefficientscoefficients from the balanced equation. from the balanced equation. This is This is the key stepthe key step: it gets you from moles of given to : it gets you from moles of given to

moles of unknown.moles of unknown. 4) Convert the unknown to the unit specified in 4) Convert the unknown to the unit specified in

the problem. the problem.

Example:Example:

4 Fe(s) + 3 O4 Fe(s) + 3 O22(g) (g) 2 Fe 2 Fe22OO33(s) (s)

Calculate the volume of oxygen gas at STP that is Calculate the volume of oxygen gas at STP that is

required to completely react with 52.0 g of iron.required to completely react with 52.0 g of iron.

Example:Example:

4 Fe(s) + 3 O4 Fe(s) + 3 O22(g) (g) 2 Fe 2 Fe22OO33(s)(s) Refer to the equation above. If 22.4 L of oxygen Refer to the equation above. If 22.4 L of oxygen

gas is reacted at STP (with an excess of iron), gas is reacted at STP (with an excess of iron), how many grams of iron (III) oxide will be how many grams of iron (III) oxide will be formed?formed?

Avogadro’s LawAvogadro’s Law

Avogadro’s Law says that Avogadro’s Law says that equal volumes equal volumes of gases at the same temperature and of gases at the same temperature and pressure contain equal numbers of pressure contain equal numbers of molesmoles. .

This means that the coefficients in the This means that the coefficients in the balanced equation stand for balanced equation stand for volumevolume as as well as moleswell as moles, , but only for the gasesbut only for the gases..

ExampleExample

N2(g) + 3 H2(g) N2(g) + 3 H2(g) 2 NH3(g) 2 NH3(g) If 25.0 L of nitrogen gas is reacted with an If 25.0 L of nitrogen gas is reacted with an

excess of hydrogen, what volume of excess of hydrogen, what volume of ammonia is produced?ammonia is produced?

ExampleExample

2 H2 H22(g) + O(g) + O22(g) (g) 2 H 2 H22O(g)O(g) If 300. mL of water vapor is produced in If 300. mL of water vapor is produced in

the above reaction, how many mL of the above reaction, how many mL of oxygen reacted? oxygen reacted?

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Unit 12: Gas Laws. The Kinetic Theory of Gases Gases aren’t attracted or repelled by each other. Gas particles are super tiny, but the space between each