The Kinetic Theory Chapter 13

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Kinetic Theory The Kinetic Molecular Theory of Matter is a

concept that basically states that atoms and molecules possess an energy of motion (kinetic energy) that we perceive as temperature.

In other words, atoms and molecules are constantly in motion, and we measure the energy of these movements as the temperature of that substance.

This means if there is an increase in temperature, the atoms and molecules will gain more energy (kinetic energy) and move even faster.

The Kinetic Theory of Gases

1. Gases consist of hard, small spheres

2. Gas particles have insignificant volume because they are so small and so spread out.

Explains…

Compressibility – measure of how much the volume of matter decreases under pressure

Kinetic Theory

3. No attractive or repulsive forces exist between particles

As a result…

Gases are free to move in their containers

Kinetic Theory4. Gas particles

move rapidly in constant random motion

Affected by…Temperature and Volume

The effect of volume on temperature…Smaller Volume = Faster Movement of Particles (more collisions) = Increase in Temperature (HOT!)

The effect of volume on temperature…Larger Volume = Slower Movement of Particles (fewer collisions) = Decrease in Temperature (COLD!)

Real Life Example

Smoke out of a chimney on a cold winter day hangs in the air because the gas particles are moving so slowly (in the summer smoke travels very quickly through the air)

Kinetic Theory

5. All collisions are perfectly ELASTIC (the total kinetic energy remain CONSTANT)

Video Demonstration http://accad.osu.edu/~midori/GasLaw.html

Quick Check

Summarize the kinetic theory in the space provided.

Share your responses with a shoulder partner.Partner A shares for 30 seconds and then

Partner B shares for 30 seconds.Partner A is the student with the most pets.

Gas PressureGas pressure results from the

collisions of particles with the walls of a container

If there are no particles, there cannot be collisions, which means there would be no pressure. This explains why there is no pressure in a vacuum.

Gas Pressure

Air exerts pressure on Earth because the gases in our atmosphere push down (collide with) the Earth’s surface.

This is called atmospheric pressure.  Atmospheric pressure decreases as

you climb a mountain because there is less air pressing down on you.

Quick Check

Think of a pressure in your life. How does it relate to pressure as we’ve discussed here?

Think About it…

What is the relationship between kinetic energy and temperature?

Absolute ZeroThe temperature of an

object depends on how fast the particles in it are moving

Absolute ZeroAbsolute Zero (0 K) is the lowest possible temperature that can be reached – it is when motion of particles STOPS!

Absolute Zero

Temperature and Particle Movement Web Demonstration

Changes of StateChange of State Phases Example

Boiling (Vaporization/Evaporation)

Liquid → Gas   

Melting 

 Solid → Liquid  

Condensation  

 Gas → Liquid  

Freezing 

Liquid → Solid 

 

Sublimation 

 Solid → Gas   

Deposition 

 Gas → Solid   

Phase Diagram

A phase diagram tells you the state of matter at each temperature and pressure for a substance.

Triple point – when all three states of matter occur simultaneously in a container.

Phase Diagram

Phase Diagrams

Two phases exist on the linesWater is in a single phase in each

of the colored regions.At the triple point, water is a solid,

liquid, and a gas at the same time!

Phase Diagram

Real Life Applications

Cooking at high altitudes.Demo – boiling water in a

syringe

Quick Check Quick Check – Look at the phase diagram for CO2.

Label which state of matter is occurring at each point. A = B = C = Which change of state occurs when you go from point C

to point B? Which change of state occurs when you go from point A

to point B?  

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The Behavior of Gases

Variables to describe gases

Variables Used to Describe GasesPressureMeasured in atm, torr, mm

Hg or PascalsBarometer

Variables Used to Describe Gases

TemperatureMeasured in Kelvin, Fahrenheit, or Celsius

Thermometer

Variables Used to Describe Gases

VolumeMeasured in Liters or m3

Variables Used to Describe Gases

Amount of Gas

Measured in Moles

STPStands for Standard

Temperature and PressureStandard Conditions of 1

atm pressure and 0 degrees Celsius

Temperature Conversion Factors

K = C + 273F = 9/5(C) + 32C = 5/9 (F – 32)

Other Conversion FactorsConversion Factors

1 cm3 = 1 mL

1 dm3 = 1 L

1000 Pa = 1 kPa

1000 mL = 1 L

1 atm = 760 mm Hg

1 atm = 101 kPa

1 torr = 1 mm Hg

1000 L = 1 kL

ASSIGNMENTComplete Worksheet #1 – Conversions!

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Our Plan:Online Inquiry LabsNotesWorksheet #2Clicker Review - Scenarios

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Online Inquiry Lab

Go to Mrs. C’s website, Unit 9, Resources

Find 4 “Dates”

Fill out your date card on p. 8 of your booklet. People at your table are your family and we don’t date family!

Gas Laws Challenge!What happens to a bag of

potato chips when it is placed in the freezer?

What happens when it is left in a hot car?

Gas Laws Challenge!Aerosol cans have a warning

on them, indicating not to incinerate them or to store them above a certain temperature. Explain why this is the case and what will happen if they are exposed to extreme temperatures.

Boyle’s Law

Boyle’s Law

Named after its founder Robert Boyle

English

The Original ExperimentRobert Boyle – 1662Used a manometer – J-shaped piece

of tubing with one end closedSealed a certain volume of air in the

closed end of the tubeVaried the pressure (mm Hg) and

watched the change in volume

The Original Experiment

The Relationship

As pressure increases, volume decreases

ORAs pressure decreases, volume increases

Variables that are ConstantThe amount of gas (moles)

ANDThe temperature of the gas

The Equation

P1V1 = P2V2

Where P = Pressure and V = Volume

Where 1 = Initially (1st) and 2 = Finally (2nd)

The Graph

The Graph

This is called an inverse relationship

Practice Problem A sample of gas has a volume of 12.0

L and a pressure of 1.00 atm. If the pressure of gas is increased to 2.00 atm, what is the new volume of the gas?

MATH ALERT!

Practice Problem

Try it Out!A sample of gas has a pressure

of 3.00 atm and a volume of 4.6 L. If the volume of gas is decreased to 3.2 L, what is the new pressure of the gas? Enter in Clicker!

Quick Check

Come up with at least 1 real-life application for this gas law and write it in the appropriate spot.

Find your 3:00 date and share your answers.

Real-Life ApplicationsSYRINGES

To draw fluids in: the volume is increased in the syringe, which causes the pressure inside to be less than that outside, so the liquid is forced in

To force fluid out: the volume is decreased, so the pressure inside is greater than outside, so the fluid is forced out

Real-life ApplicationsLUNGS & DIAPHRAGM

When we breathe in (inspire), the diaphragm is lowered and the chest wall is expanded, increasing the volume for the chest cavity. Outside air enters the lungs because it is at a higher pressure than the air in the chest cavity. When we breathe out (expire), the diaphragm rises and the chest wall contracts, decreasing the volume of the chest cavity. The pressure is increased, and some air is forced out.

Real-life Applications

Tire PumpAir-filled

Automotive Shock Absorbers

Tire Pressure Gauge

Real Life Applications

AirplanesAutomobile Pistons

MeteorologyStraws

Scuba Diving – “The Bends”

Real-Life Applications

Diving – “The Bends”As a diver descends, the water

exerts greater pressure. More gas pressure is required to keep the lungs expanded. This increased gas pressure causes more nitrogen to dissolve in the divers blood.

Real-Life Applications

Diving – “The Bends”Below a depth of about 30 meters,

dissolved nitrogen interferes with the transmission of nerve impulses. The effects are similar to those of alcohol and include dizziness, slowed reaction time, and an inability to think clearly.

Real-Life Applications

Diving – “The Bends”As the diver returns to the surface,

pressure decreases and dissolved nitrogen is released from the blood. Bubbles of nitrogen can block small blood vessels and reduce the supply of oxygen to cells, causing severe pain in the joints, dizziness, vomiting, or even death.

QuestionWhy are gases transported under great pressure?

Charles’ Law

The Inventor Named after Jacques Charles,

but actually discovered by Joseph Louis Gay-Lussac when he was only 23 years old.

Gay-Lussac named it after Charles because of his previous work with gases.

The InventorHot air balloons were very

popular at the time, so the two men decided to do studies on the relationship between volume and temperature.

The Original Experiment Used a manometer – immersed the

J-shaped tube in a water bath. By adjusting the temperature of the water they changed the temperature of the gas in the tube.

Charles and Gay-Lussac watched what happened to the volume of the gas when they changed the temperature

The Relationship

As temperature is increased, volume increases.

OR

As temperature is decreased, volume decreases.

Variables that are constantPressure

ANDAmount of gas

(moles)

The Equation

V1 / T1 = V2 / T2

Where V = volume and T = Temperature

The Graph

The Graph

This is called a direct relationship

Practice Problem The temperature of a 4.00 L sample

of gas is changed from 10.0 degrees Celsius to 20.0 degrees Celsius. What will the volume of this gas be at the new temperature if the pressure is held constant?

IMPORTANT!

When solving gas law problems, all temperatures must be in KELVIN!

Practice Problem

Try it Out! The volume of a tire at 32○C

is 2 L. What is the temperature if the volume of the tire is 5.4 L? Enter in Clicker!

Quick Check

Come up with at lest 1 real-life application for this gas law and write it in the appropriate spot.

Find your 6:00 date and share your answers.

Real-life Applications Hot Air Balloons

A propane heater is used to heat the air in the balloon. As the air is heated, the gas expands, becoming less dense. Because the density of the air inside the balloon is less than the density outside the balloon, the balloon is buoyant.

Real-life Applications Hot Air Balloons

As the air cools, it contracts and becomes more dense and less buoyant. Thus the balloonist can control altitude by heating or cooling the gas to increase or decrease buoyancy.

Real-life Applications

Tire VolumeBridgesFood in a freezer

Gay-Lussac’s Law

The Experiment

Discovered by Joseph Louis Gay-Lussac in 1802

He did experimentation on hot air balloons

The RelationshipAs the temperature

increases, the pressure increases

ORAs the temperature

decreases, the pressure decreases

The Relationship To understand the relationship, think

about the kinetic theory – if you increase the temperature, the particles move faster and thus hit the side of the container more often. This causes the pressure to increase. If the container is solid, the volume doesn’t change

Variables that are constantVolume

ANDNumber of Moles

The Equation

P1/T1 = P2/T2

Where P = Pressure and T = Temperature

The Graph

The Graph

The Graph

This is a direct relationship

Practice Problem

A gas has a pressure of 0.370 atm at 50 degrees Celsius. What is the pressure at standard temperature?

Practice Problem

Remember to convert all temperatures to Kelvin!

Practice Problem

Try it Out A gas has a pressure of 0.891 atm at 120 K. What is the temperature at 0.428 atm? Enter in Clicker!

Quick Check

Come up with at lest 1 real-life application for this gas law and write it in the appropriate spot.

Find your 12:00 date and share your answers.

Real-Life Applications

Aerosol CansAutoclave – machine that

sterilizes medical equipment

Tire Pressure

Quick Check

Which gas law describes each situation on p. 11 of your notebooklet?

Share your answers with your 9:00 partner.

STOP!Worksheet Time!Complete Worksheet #2 by next class

Wrap Up

Clicker Review

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Magic Squares Review ActivityNotesWS #3Gases Reading

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Gas Laws Review

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Helpful Reminders!1. All Temperatures must be in KELVIN!

2. Measurements of the same variable must be in the same units

Can’t have 1 mL and 2 L Can’t have 123 kPa and 0.9 atm CONVERT to one or the other

3. STP (Standard Temperature & Pressure) Standard Temp = 0 Celsius Standard Pressure = 1 atm

Review Time

Complete the Review Worksheet with a partner. Be sure to each use 2 different colored writing utensils and take turns writing!

The Combined Gas Law

Put all of the Gas Law Equations together to form one!

P1V1 = P2V2

T1 T2

Practice Problem If a balloon containing 1000L of

gas at 50 degrees Celsius and 101 kPa rises to an altitude where the pressure is 50.5 kPa and the temperature is 10 degrees Celsius, what would the volume of the balloon be under these new conditions?

Practice Problem

Practice Problem 2A container of krypton

occupies a volume of 15.0 L at a pressure of 210 kPa and a temperature of 110 K. Find the new temperature when the volume is 25.0 L and the pressure is 790 kPa.

Practice Problem

Try it Out!

A sample of gas at 47○C and 1.03 atm occupies a volume of 2.20 L. What volume would this gas occupy at 107○C and 0.789 atm? (3.41 L)

Try it Out!A gas has a volume of 1.75

L at -23○C and 150 kPa. At what temperature would the gas occupy 1.30 L at 210. kPa? (260 K)

STOP!

Complete Worksheet #3 by next class.

When you finish choose a gas reading to complete by next class.

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Review Problem If 10.0 liters of oxygen at STP are heated

to 512 °C, what will be the new volume of gas if the pressure is also increased to 1520.0 mm Hg? 14.4 L

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Our Plan:Penny Mystery LabFinish Gas Laws Lab – DUE TODAY

Homework (Write in Planner):Labs if you don’t finish in class!

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Password Vocabulary ReviewNotes – Ideal Gas LawWorksheet #4Clicker Review

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The Ideal Gas Law

Ideal Gas Law DefinitionMathematical relationship between pressure, volume, temperature, and the number of moles of gas.

The effect of changing moles on volume

The effect of changing moles on pressure

The Ideal Gas Law ConstantR = 0.0821 L x atm

mol x K The numbers from the problem must be

in those units to solve!Volume in LitersPressure in atmTemperature in Kelvin

The EquationPV = nRT

Where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

Practice ProblemWhat is the volume, in Liters, of 0.250 mole of oxygen gas at 20oC and 0.974 atm of pressure?

Practice Problem

Practice Problem

What is the pressure, in atmospheres, of 12 grams of neon gas at 32○C that fills a 2L gas tube?

Practice Problem

STOP!Begin working on WS #4

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Demo Time…

Ideal Gases vs. Real Gases

An ideal gas is one that follows the gas laws at all conditions of pressure and temperature and conforms precisely to the assumption of the kinetic theory.

Ideal gases do not exist Real gases:

Do have volumeThere are attractions between particles

Ideal Gas Law & Stoichiometry Last unit we calculated volumes of gas

produced in chemical reactions using the molar volume of a gas (22.4 L).

Remember, this only works if the reaction is carried out at STP (0 degrees C and 1 atm pressure)

Under any other conditions, you must use stoichiometry in combination with the ideal gas law.

Example 1 An air sample containing H2S at 0.989 atm

and 29 degrees C is treated with a catalyst to promote the reaction, H2S (g) + O2 (g) → H2O (g) + S(s). If 3.2 g of solid S was collected, calculate the volume of H2S in the original sample.

Example 2 How much NaN3 is needed to inflate a 50.0

L air bag containing N2 to 1.15 atm at 25.0 ºC given the following chemical reaction?

2 NaN3 (s) → 2 Na (s) + 3 N2 (g)

Try It Out!In the chemical reaction used in automotive air-bag safety systems, N2(g) is produced by the decomposition of sodium azide, NaN3(s), at a somewhat elevated temperature:

2 NaN3(s) --> 2 Na(l) + 3 N2(g)

What volume of N2(g), measured at 25 °C and 0.980 atm, is produced by the decomposition of 62.5 g NaN3?

35.9 L

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures

Partial Pressure: the pressure of each gas in a mixture

Dalton’s Law: the total pressure of a mixture of gases is equal to the sum of the partial pressures of each component gas

Dalton’s Equation

PT = P1 + P2 + P3 + ….

Practice ProblemA mixture of three gases, A, B,

and C, is at a total pressure of 6.11 atm. The partial pressure of gas A is 1.68 atm; that of gas B is 3.89 atm. What is the partial pressure of gas C?

Practice Problem

6.11 =1.68 + 3.89 + Pc

Pc = 0.54 atm

Graham’s Law

DiffusionSpontaneous mixing of the particles of

2 substances caused by their random motion

Quick Check – Think of examplesExamples:

SmellsSteam/SmokeOthers?

EffusionProcess by

which gas particles pass through a tiny opening

Video

Graham’s Law of EffusionThe rate of effusion of a gas

depends on its size.The more massive a molecule,

the slower it effuses.Can also be applied to the

diffusion of gases.Video

Quick Check

Think of examples of effusion.

STOP!Complete WS #5 Begin Test Review

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Enjoy your Spring Break

Boyle’s Law P1V1 = P2V2

Charles’ Law V1/T1 = V2/T2

Gay-Lussac Law P1/T1 = P2/T2

Combined Gas Law (P1V1)/T1 = (P2V2)/T2

Ideal Gas Law PV = nRT

Dalton’s Law PT = P1 + P2 + P3 +…

Gases Collected Over Water

Patm = Pgas + PH2O

Graham’s Law rate = √M2/M1

When to Convert…

Kelvin ALWAYSPV=nRTOtherwise, as long as the

variables are in the same unit you’re fine.

How to do the problems on the test…. A gas occupies 11.2 L at 0.860 atm. What

is the pressure if the volume becomes 15,000 mL? (0.64 atm)

How to do the problems on the test…. A sample of hydrogen gas has a volume of

65.0 mL at a pressure of 0.992 atm and a temperature of 16.0 ○C. What volume will the hydrogen occupy at 747.84 mm Hg and 25○C? (67.6 mL)

How to do the problems on the test…. An engineer pumps 5.00 mol of carbon

monoxide gas into a cylinder that has a capacity of 20.0 L. What is the pressure in kPa of CO inside the cylinder at 25.0○C? (618 kPa)