KMT and Gas Laws States of Matter, Kinetic Molecular Theory, Diffusion, Properties of Gases, and Gas...

KMT and Gas Laws

States of Matter, Kinetic Molecular Theory, Diffusion,

Properties of Gases, and

Gas Laws

Standards4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of

gases. As a basis for understanding this concept: a. Students know the random motion of molecules and their collisions with a surface create the observable

pressure on that surface.

4. b. Students know the random motion of molecules explains the diffusion of gases.

4. c. Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

4. d. Students know the values and meanings of standard temperature and pressure (STP).

4. e. Students know how to convert between the Celsius and Kelvin temperature scales.

4. f. Students know there is no temperature lower than 0 Kelvin.

4. g.* Students know the kinetic theory of gases relates the absolute temperature of a gas to the average kinetic energy of its molecules or atoms.

4. h.* Students know how to solve problems by using the ideal gas law in the form PV = nRT.

4. i. * Students know how to apply Dalton’s law of partial pressures to describe the composition of gases and Graham’s law to predict diffusion of gases.

States of Matter

Solid

Liquid

Gas

Plasma

Freezing

MeltingDep

ositi

onSu

blim

ation

CondensationBoiling

Deionization

Ionization

Condensation (Gas Liquid)

Boiling(Liquid Gas)

Sublimation (Solid Gas)

Deposition (Gas Solid)

Freezing (Liquid Solid)

Melting (Solid Liquid)

Molecular Motion of Gases

KMT

• The path of any individual molecule could best be described as random.

KMT – Kinetic Molecular Theory

Molecular Motion• The state of matter depends

on how much energy (motion) the molecules, atoms, or ions have.

• The state of matter also depends on how attracted the atoms, molecules, or ions are to each other.

Molecular MotionState of Matter

O O

Na+ Cl–

OHH

+ +

–

Gas

Liquid

Solid

Nonpolar molecules

O O O O

Polar molecules

OHH

+ +

–

OH

H+

+

–

O

HH+

+

–

Ionic compounds

Na+ Cl–

Na+ Cl–

Na+ Cl–

Na+ Cl–

Cl–

Na+

Na+Cl–

Molecular Twist and Stretch

Diffusion• Diffusion – when a substance spreads out in a

gas or liquid.

• Examples: 1. Perfume eventually reaching the far side of a

room. 2. Kool-Aid dissolving into water.

Diffusion of Gases

Diffusion of Liquids

Temperature (T)• Kinetic energy is the energy of motion.

• Temperature is defined as a measure of the average kinetic energy of the atoms or molecules.

Temperature (T)

• There are two scales and an absolute unit. (degrees Fahrenheit, degrees Celsius, and Kelvin)

Temperature Scales

Water Boils

Human Body

Water Freezes

212°F

98.7°F

32°F

100°C

37°C

0°C

373K

310K

273K

Temperature ScalesSurface of Sun

Room Temp.

Absolute Zero

9,941°F

70°F

-460°F

5,505°C

21°C

-273°C

5,778K

294K

0K

Converting Temperatures• Fahrenheit Celsius

°C = (°F – 32)×(5/9)

• Celsius Fahrenheit°F = °C ×(9/5) + 32

• Celsius KelvinK = °C + 273.15

Absolute Zero• At Zero Kelvin (0 K or –273.15 °C), atoms

and molecules stop moving.

• There is no temperature lower than absolute zero (0 K).

Volume (V)• How much space is occupied by a fluid.

Liquid Gas • Usually gases are measured in Liters (L)

Pressure (P)• Defined as force divided by area. • The force comes from atoms’ or molecules’

collisions with the wall of the container. • The greater the number of collisions or the

more energy with each collision, the greater the pressure.

Pressure Units

UnitUnit

Symbol 1 atm =Atmospheres atm --

Pascals Pa 101,325 Pa

Kilopascals kPa 101.3 kPa

Pounds per square inch

lbs. or psi 14.7 psi

Millimeters mercury

mm Hg 760 mm Hgin.2

Pressure0 atmOuter Space (a vacuum)

1,072 atmAt the Bottom of Mariana Trench

1 atmRegular Atmosphere (at sea level)

0.33 atmTop of Mt. Everest

Gas Properties

Property SymbolUsualUnit

Unit Symbol

Pressure P kilopascal kPa

Volume V liters L

Temperature T Kelvin K

Moles n moles mol

STP = Standard Temperature and Pressure

Temperature is 0°C = 273.15 Kand

Pressure is 1 atm = 101.3 kPa

Gas Laws• Most of the gas laws deal with taking a

quantity of gas and changing one property (pressure, temperature, or volume) and predicting how the other properties will change in response.

Boyle’s LawWhen given a certain amount of gas, if you

increase the pressure, the volume decreases. If you decrease the pressure, the volume

increases.Mathematically: P1V1 = P2V2

P1V1 = P2 V2

Boyle’s LawWhen given a certain amount of gas, if you

increase the pressure, the volume decreases. If you decrease the pressure, the volume

increases.Mathematically: P1V1 = P2V2

P1V1 = P2 V2

This assumes a constant temperature (T)

Boyle’s Law ExampleYour nephew is playing with a balloon in the car as

your family drives over a mountain pass. The balloon initially had a volume of 1 L when the car was at the bottom of the mountain (and the air pressure was 100 kPa).

Now that your family is at the top the air pressure is 70 kPa. What is the new volume of the balloon?

P1V1 = P2 V2

Boyle’s Law ExampleP1 = 100 kPa P2 = 70 kPa

V1 = 1 L V2 = ?

(100 kPa)(1 L) = (70 kPa)•V2

100 kPa•L = 70 kPa•V2

1.43 L = V2

P1V1 = P2V2

70 kPa 70 kPa

Boyle’s Law Example

Normal P

Low P

Boyle’s Law Example

Normal P Low P

V1 = 1 LV2 = 1.43 L

Charles’ LawWhen given a certain amount of gas, if you increase

the temperature, the volume increases. If you decrease the temperature, the volume

decreases.Mathematically: V1 V2

T1 T2

=

V1

T1

V2

T2

=

You must use Kelvin temperatures!

Charles’ LawWhen given a certain amount of gas, if you increase

the temperature, the volume increases. If you decrease the temperature, the volume

decreases.Mathematically: V1 V2

T1 T2

=

V1

T1

V2

T2

=

This assumes a constant pressure (P)


Charles’ Law ExampleIf 1.0 L of gas is contained within a piston at 27 ˚C (300 K), what will new volume be if the gas is cooled to -23 ˚C (250 K)? Assume that the pressure is constant.

V1

T1

V2

T2

=

Charles’ Law Example

V1

T1

V2

T2

=

V1 = 1.0 L V2 = ?

T1 = 300 K T2 = 250 K

1.0 L300 K

V2

250 K=

1.0300

V2

250= (250)(250) V2 = 0.83 L

Charles’ Law

This assumes a constant pressure (P)

Which Law?

7) Oxygen gas at 47 ˚C occupies a volume of 0.5 L. To what temperature should the oxygen gas be lowered to bring the volume to 0.2 L? Assume constant pressure.

V1 V2

T1 T2

=

Charles’ Law

V1

T1

V2

T2

Which Law?

9) A nitrous oxide sample (N2O) occupies a volume of 360 mL when under 70 kPa of pressure. How much volume will it occupy at 420 kPa? Assume constant temperature.

Boyle’s Law

P1V1

P2

V2

P1V1 = P2V2

Gay–Lussac’s LawWhen given a certain amount of gas, if you increase

the temperature, the pressure increases. If you decrease the temperature, the pressure

decreases.Mathematically: P1 P2

T1 T2

=

P1

T1

P2

T2

=


Gay–Lussac’s LawWhen given a certain amount of gas, if you increase

the temperature, the pressure increases. If you decrease the temperature, the pressure

decreases.Mathematically: P1 P2

T1 T2

=

P1

T1

P2

T2

=

This assumes a constant volume (V)


Gay–Lussac’s Law ExampleA tire that has already been inflated to its maximum volume, begins a drive at a temperature of 300K with an air pressure of 36 psi. During the hot day the air in the tire’s pressure increases to 42 psi. What will the new temperature be?

P2

T1

P1

T2

Gay–Lussac’s Law ExampleA tire that has already been inflated to its maximum volume, begins a drive at a temperature of 300K with an air pressure of 36 psi. During the hot day the air in the tire’s pressure increases to 42 psi. What will the new temperature be?

P2

T1

P1

T2

P1

T1

P2

T2

=

Gay–Lussac’s Law Example

P1 T1

P2 T2

=

P1 = 36 psi P2 = 42 psiT1 = 300 K T2 = ?

36 psi 300 K

42 psi T2

=

0.12 42 T2

= (T2)(T2)

T2 = 350 K0.12 (T2) = 42

0.12 0.12

Before

T1 = 300 K

P1 = 36 psi

After

P2 = 42 psi

T2 = 350 K

Avogadro’s LawThe volume of a gas at Standard Temperature

and Pressure (STP) is directly proportional to the moles of the gas.

V = k n

At STP there are 22.4 L per mole of gas.

# of moles

Avogadro’s Law ExampleHow many liters will 3 moles of gas occupy

at STP?

V = k n

V = 67.2 LV = (22.4 )(3 mol) L

mol

Combined Gas LawThis combines Boyle’s, Charles’, and Gay-Lussac’s

Gas Laws. Mathematically:

P1 V1 P2 V2

T1 T2

=

Cancel out the properties that remain constant.

Combined Gas Law Example

P1V1 T1

P2V2 T2

=

P1 = 50 kPa P2 = 200 kPaV1 = ? V2 = 0.12 LT1 = 300 K T2 = 400 K

(50)V1

300(200)(0.12) (400)=

(V1)0.167 = 0.06 V1 = 0.36 L 0.167 0.167

Ideal Gas LawIf we know 3 of the 4 gas properties (P, V, T, and n)

we can solve for the missing one by using the formula:

PV = nRT

R is called the gas constant. R = 8.314 kPa•L

mol•K

Ideal Gas LawA cylinder is filled with 0.2 moles of gas. The sealed

cylinder has a volume 3.0 L and is heated with 3,000 J to a temperature of 300K. What is the pressure inside the cylinder?

PV = nRT kPa•Lmol•K

P•(3.0 L) = (0.2 mol)(8.314 )(300 K)

P•(3.0 L) = 499 kPa•L

P = 166 kPa

3.0 L 3.0 L

Gas Laws SummaryGas Law FormulaBoyle’s Law P1V1 = P2V2

Charles’ Law

Gay-Lussac’s Law

Avogadro’s Law V = k nCombined Gas Law

Ideal Gas Law PV = nRT

V1 V2

T1 T2

=

P1 P2

T1 T2

=

P1 V1 P2 V2

T1 T2

=

What is the change in volume?

CH4(g) + H2O (g) CO (g) + 3 H2 (g)Methane water carbon hydrogen

monoxide

+ +

Vapor PressureFor a liquid as the temperature increases, its vapor pressure increases.

When the vapor pressure is equal to the external pressure, the liquid has reached its boiling point.

Effects of Vapor Pressure: • Warm water evaporates faster than cold water. • At higher altitudes, water boils at a lower

temperature.

Dynamic EquilibriumDynamic equilibrium occurs when the rate of condensation equals the rate of evaporation.

LiquidVapor

(or gas)

evaporation

condensation

Note: the amounts of liquid and vapor can be completely different.

Dalton’s Law of Partial PressuresThe total pressure exerted by a mixture of gases is equal to the sum of all partial pressures exerted by each individual gas.

Ptot = P1 + P2 + P3 + …

For example: our classroom

Ptot = PN2 + PO2 + PAr + PCO2 + PH2O + …1 atm = 0.79 atm + 0.19 atm + 0.01 atm + 0.003 atm + …

Graham’s Law of Diffusion• From the simulations we saw, that lighter gas

molecules move faster than heavier gas molecules.

• If we want to directly compare the speeds of gas molecules we can use:

These are the molar masses

vA MB

vB MA

=These are the average molecular speeds

NeFONCBBe

He

Li

H

Kr

ArCl

Br

XeI

SPSiMg Al

Ca

Na

K

4 e– in valence shell

Gas Laws SummaryGas Law Formula

Boyle’s Law P1V1 = P2V2

Charles’ Law V1 V2

T1 T2

Gay-Lussac’s Law P1 P2

T1 T2

Avogadro’s Law V = k n

Ideal Gas Law PV = nRT

=

=

KMT and Gas Laws States of Matter, Kinetic Molecular Theory, Diffusion, Properties of Gases, and Gas...

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