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### Unit 8: The Kinetic Molecular Theory and Gas Laws

Chapters 10, 13, and 14

Demo – Vacuum Pump

- Can water boil at room temperature? Why/why not?
- Water boils when vapor pressure = atmospheric pressure
- Yes! If we lower the air/atmospheric pressure below the vapor pressure, the molecules don’t have to move as fast, bringing water to a boil at a much lower temp.
- Can we inflate a balloon by taking out air in its surrounding? Why/why not?
- Yes! In a fixed container, if you vacuum out air, the size of the balloon expands to make up for the missing air.

Kinetic Molecular Theory of Gases

- Gases consist of tiny molecules
- Gases are in constantrandom motion
- Gases collide into each other and the walls of the container; this creates Gas Pressure
- Collisions are elastic – KE is transferred
- As the temperature increases so does the KE; gas molecules move faster!

States of Matter

- How can matter change from one state to another?
- Temperature =
- A temperature increase = a kinetic energy ___________
- Kinetic Energy = Potential Energy =
- Remember – energy must be conserved – it cannot be created or destroyed!
- If we add heat energy, either the kinetic or potential energy of molecules must change
- If kinetic energy ↑, what must potential energy do? _____

150

100

Temperature in Celsius

0

-50

0

2

4

6

8

10

12

Time in minutes

What letter is at the melting point? _______What letter is at the boiling point? _______What might the cooling curve of water look like?

What letter is at the freezing point? _______What letter is at the condensation point? _______

kilojoules

What units are used to measure energy?___________, abbreviated ___

If the prefix –kilo is put in front you multiply by ______ and abbreviate it _____

What is a rate?

If you know the heating rate, how can you use a heating curve to calculate an amount of heat?

Physical Properties Used to Model the Behavior of Gases

- Temperature
- Pressure
- Volume and Compressibility
- number of moles (n)

Air Pressure

- Force applied to an area
- Pressure = force

area

- If force increases, pressure ?
- If area increases, pressure ?

Increases.

Decreases.

Compressibility

- Gases are easily compressed because of the large space between the particles in a gas.
- Under pressure (added force), the particles in a gas are forced closer together, decreasing the volume.

Factors Affecting Gas Pressure

- Amount of Gas – increasing # of particles will increase the pressure (and vv)

Factors Affecting Gas Pressure

- Volume –
- increasing the volume in which the gases can move will decrease the pressure (more room to move)
- Decreasing the volume in which gases can move will increase the pressure.

Factors Affecting Gas Pressure

- Temperature
- Increasing the temperature will increase the pressure (more KE, more collisions with container and other gas particles)
- Decreasing the temperature will decrease the pressure (less KE, less collisions with container and other gas particles)

The Gas Laws - Overview

- Boyle’s Law – Pressure and Volume
- Charles’ Law – Temperature and Volume
- Gay – Lussac’s Law – Temperature and Pressure

Boyle’s Law

- Relates Pressure (P) and Volume (V)
- Measures the pressure and volume under one set of conditions (P1 and V1) and then changes the conditions (P2 and V2)
- It is an inverse relationship meaning:
- When the volume decreases, the pressure increases
- When the volume increases, the pressure decreases.
- Equation:

P1V1 = P2V2

The Relationship between

volume and pressure

Boyle Example #1

A balloon initially occupies 12.4 L at 1.00 atm. What will be the volume at 0.800 atm?

1. Write the equation: P1V1 = P2V2

- List the variables:

V1 = 12.4 L

P1 = 1.00 atm

V2 = ?

P2 = 0.800 atm

- Plug in the numbers and solve!

(1.00 atm) (12.4 L) = (0.800 atm) V2

V2 = 12.4 atm · L

0.800 atm

= 15.5 L

Boyle Example #2

5.00 L of a gas is at 1.08 atm. What pressure is obtained when the volume is 10.0 L?

1. Write the equation: P1V1 = P2V2

2. List the variables:

V1 = 5.00 L

P1 = 1.08 atm

V2 = 10.0 L

P2 = ?

3. Plug in the numbers and solve!

- (1.08 atm) (5.00 L) =(P2) (10.0 L)

P2 = 0.54 atm (don’t forget the units!)

Hints

- Know the units for Pressure
- Know the units for Volume
- Keep all Units
- Standard Pressure = 1 atm = 760 mm Hg
- BIG Hint:

Peter V. Boyle likes to “Play” on “Vacation”!

Using the KMT…

- Use the kinetic theory of gases to answer this question.

If the volume decreases, why does the pressure increase?

- Smaller volume means more collisions. More collisions will increase the pressure.

Charles’s Law

- Relates Temperature (T) and Volume (V)
- Temperature must be measured in Kelvin
- Kelvin = °C + 273
- Equation:

T1V2 = T2V1 notice the numbers!

Charles’s Law

- Direct Relationship – as one variable goes up, the other goes UP
- Temperature increased, the volume will increase and v.v.

Charles Example #1

Given 17 L of a gas at 358 K. What is its volume at 283 K? – work through the problem on your own first before proceeding

1. Write the equation: T1V2 = T2V1

2. List the variables:

T1 = 358 Kelvin

V1 = 17 L

T2 = 283 Kelvin

V2 = ?

3. Plug in the numbers and solve!

T1V2 = T2V1

(358K)V2 = (283K)(17L)

V2 = (283K)(17L)

358K

V2 = 13.4 L

Given 200 mL of a gas at 364 K. What is the temperature when the volume is increased to 500 mL? work through the problem on your own first

Write the equation: T1V2 = T2V1

2. List the variables:

T1 = 364 Kelvin

V1 = 200 mL

T2 = ?

V2 = 500 mL

3. Plug in the numbers and solve!

T1V2 = T2V1

(364 K)(500 mL) = T2(200 mL)

T2 = (364 K) (500 mL)

200 mL

T2 = 910 K

In degrees Celsius:

910 K – 273 = 637°C = T2

Charles’ Example #2Hints

- Temperature must be in Kelvin
- Recall: K = °C + 273
- Volume is measured in:
- L or mL 1L = 1000 mL
- Always keep your units in the problem and of course the answer
- Hint:

“Charles in Charge” was on T.V.!

Using the KMT…

- Use the kinetic theory of gases to answer this question.

If the temperature increases, why does the volume also increase? – think and write your answer

The particles are moving faster as the temperature increases and hit the walls of the container with more force causing the volume to increase

Gay-Lussac’s Law

- Relates Temperature (T) and Pressure (P)
- Temperature must be measured in Kelvin
- Kelvin = °C + 273
- T1P2 = T2P1 - notice the numbers

Gay-Lussac’s Law

- Direct Relationship – as one variable goes up, the other goes UP
- Temperature increased, the pressure will increase
- Draw a sample graph of pressure and temperature.

Example Problems

A container filled with a gas at 1.00 atm at 273 K. What will be the new pressure if the temperature increases to 298 K? work through the problem on your own before proceeding

- Write the equation: T1P2 = T2P1
- List the variables:

T1 = 273 K

P1 = 1.00 atm

T2 = 298 K

P2 = ?

3. Plug in the numbers and solve!

T1P2 = T2P1

(273 K)P2 = (298 K)(1.00 atm)

P2 = 1.09 atm

A gas has a pressure of 535 mm Hg at 40.0 °C. What is

the temperature in Kelvin and degrees Celsius at

760 mm Hg? work through the problem on your own before proceeding

1. Write the equation: T1P2 = T2P1

2. List the variables:

T1 = 40°C + 273 = 313 K

P1 = 535 mm Hg

P2 = 760 mm Hg

T2 = ? in K and °C

3. Plug in the numbers and solve!

T1P2 = T2P1

(313 K)(760 mm Hg) = T2(535 mm Hg)

T2 = 445 K or

°C = 444 – 273 = 171°C

ExampleHints

- Temperature must be in Kelvin
- Always keep your units
- Read the problem
- Standard temperature is 273 K
- Standard pressure is 1 atm = 760 mm Hg
- Hint:

Good Landscaping makes Pretty Tulips!

Using the KMT…

- Use the kinetic theory of gases to answer this question.
- If the temperature decreases, why does the pressure also decrease?

When the temperature decreases the particles are moving with less kinetic energy (slower). The collisions are less frequent and with less force, so the pressure decreases too!

Formula

- PV = nRT

P = Pressure in atmospheres

V = Volume in Liters

n = number of moles

R = Ideal Gas Constant 0.0821 L x atm

K x mol

T = Temperature in Kelvin

Example #1

At what pressure would 0.150 mole of nitrogen gas at 23.0 °C occupy 8.90 L?

- Write the equation: PV = nRT

2. List the variables:

P = ?

V = 8.90 L

n = 0.150 mol

R = 0.0821 L*atm/K*mol

T = 23 + 273 = 296 K

3. Plug in the numbers and solve!

PV = nRT or P = nRT

V

P = (0.150 mol)(.0821L*atm/K*mol)(296 K) = 0.41 atm

8.90L

Example #2

How many moles of gas are contained in a 20.0 L cylinder at a pressure of 100.0 atm and a temperature of 35.0 °C?

- Write the equation: PV = nRT

2. List the variables:

P = 100.0 atm

V = 20.0 L

n = ?

R = R = 0.0821 L*atm/K*mol

T = 35.0 + 273 =308 K

3. Plug in the numbers and solve!

PV = nRT or n = PV

RT

n = (100.0 atm) (20.0 L) = 79.1 mol

(0.0821L*atm/K*mol) (308 K)

Hints

- Rearrange the equation before you plug in your variables. Ex: Solve for Temperature

PV = nRT

T = P V

n R now plug in the variables

- Units! Keep them!
- Memorize R = 0.0821 L *atm / mol * K

When you are asked to solve for grams…

- Sometimes you will be asked to solve for grams. First solve for n = moles, then convert to grams using the molar mass.
- Remember Molar Mass – multiply the number of atoms by the mass and add up all the elements in the compound.

Ex. What is the molar mass of water?

H2O = 2 ( 1.0g) + 1(16.0g) = 18.0 g H2O

If you had 4.5 moles of water, how many grams would you have?

4.5 moles x 18.0 g = 81 g. of H2O

1mol

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