KMT and Gas Laws

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KMT and Gas Laws. States of Matter, Kinetic Molecular Theory, Diffusion, Properties of Gases, and Gas Laws. Standards. 4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of gases. As a basis for understanding this concept:

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### KMT and Gas Laws

States of Matter, Kinetic Molecular Theory, Diffusion,

Properties of Gases,

and

Gas Laws

Standards

4. 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

Deionization

Plasma

Ionization

Condensation

Gas

Boiling

Liquid

Sublimation

Deposition

Freezing

Solid

Melting

KMT
• KMT – Kinetic Molecular Theory
• The path of any individual molecule could best be described as random.
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 Motion

State of Matter

Gas

Liquid

+

+

H

O

O

+

Na

Solid

Cl

O

H

Polar molecules

+

+

+

+

+

+

H

H

H

O

O

O

H

H

H

Ionic compounds

+

+

+

+

+

+

Na

Na

Na

Na

Na

Na

Cl

Cl

Cl

Cl

Cl

Cl

Diffusion
• Diffusion – when a substance spreads out in a gas or liquid.
• Examples:
• Perfume eventually reaching the far side of a room.
• Kool-Aid dissolving into water.
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 Scales
• 9,941°F
• 70°F
• -460°F
• 5,505°C
• 21°C
• -273°C
• 5,778K
• 294K
• 0K

Surface of Sun

Room Temp.

Absolute Zero

Converting Temperatures
• Fahrenheit Celsius

°C = (°F – 32)×(5/9)

• Celsius  Fahrenheit

°F = °C ×(9/5) + 32

• Celsius Kelvin

K = °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 (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

0 atm

Outer Space (a vacuum)

0.33 atm

Top of Mt. Everest

1 atm

Regular Atmosphere

(at sea level)

1,072 atm

At the Bottom of

Mariana Trench

STP = Standard Temperature and Pressure

Temperature is 0°C = 273.15 K

and

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 Law

When 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 Law

When 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 Example

Your 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 Example

P1 = 100 kPa P2 = 70 kPa

V1 = 1 L V2 = ?

P1V1 = P2V2

(100 kPa)(1 L) = (70 kPa)•V2

100 kPa•L = 70 kPa•V2

70 kPa 70 kPa

1.43 L = V2

Boyle’s Law Example

Normal P

Low P

V1 = 1 L

V2 = 1.43 L

Charles’ Law

When 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

=

You must use Kelvin temperatures!

T1 T2

• V2
• T2
• V1
• T1

=

Charles’ Law

When 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

=

You must use Kelvin temperatures!

T1 T2

• V2
• T2
• V1
• T1

=

This assumes a constant pressure (P)

Charles’ Law Example

If 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.

• V2
• T2
• V1
• T1

=

Charles’ Law Example

V1= 1.0 LV2= ?

T1= 300 KT2= 250 K

• V2
• T2
• V1
• T1
• V2
• 250 K
• V2
• 250
• 1.0 L
• 300 K
• 1.0
• 300

=

=

=

• V2= 0.83 L

(250)

(250)

Charles’ Law

This assumes a constant pressure (P)

Charles’ Law

This assumes a constant pressure (P)

Gay–Lussac’s Law

When 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

• P2
• T2
• P1
• T1

=

Gay–Lussac’s Law

When 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

• P2
• T2
• P1
• T1

=

This assumes a constant volume (V)

The 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.

How many liters will 3 moles of gas occupy at STP?

V = k n

V = (22.4 )(3 mol)

V = 67.2 L

L

mol

Combined Gas Law

This combines Boyle’s, Charles’, and Gay-Lussac’s Gas Laws.

Mathematically:

• P1 V1P2 V2

=

T1 T2

Cancel out the properties that remain constant.

Combined Gas Law

This combines Boyle’s, Charles’, and Gay-Lussac’s Gas Laws.

Mathematically:

• P1 V1P2 V2

=

T1 T2

Cancel out the properties that remain constant.

Ideal Gas Law

If 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 Law

A 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

• P•(3.0 L) = (0.2 mol)(8.314 )(300 K)
• P•(3.0 L) = 499kPa•L
• 3.0 L 3.0 L

kPa•L

• mol•K
• P = 166kPa
What is the change in volume?

CH4(g) + H2O(g) CO (g) + 3 H2(g)

Methane water carbon hydrogen monoxide

+

+

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:

vA MB

vB MA

These are the molar masses

These are the average molecular speeds

=

K

H

Na

Li

Mg

Ca

Be

He

O

S

Cl

Ar

F

P

N

Br

Kr

C

Si

Al

Ne

B

I

Xe

K

H

Na

Li

Mg

Ca

Be

He

O

S

Cl

Ar

F

P

N

Br

Kr

C

Si

Al

Ne

B

I

Xe