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.

Properties of the States of Matter

Phase Changes

Kinetic Molecular Theory of Gases

• Gases consist of tiny molecules• Gases are in constant random 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? _____

Heating Curve of Water

A

B C

D E

F

Time in minutes

Tem

per

atur

e in

Ce

lsiu

s

0

100

0 2 6 8 104 12

150

-50

Section Time (min)

Temp. (°C)

State Potential Energy

Kinetic Energy

A-B

B-C

C-D

D-E

E-F

What letter is at the melting point? _______

What letter is at the boiling point? _______

What might the cooling curve of water look like?

Time in minutes

Tem

per

atur

e in

Ce

lsiu

s

0

100

0 2 6 8 104 12

150

-50

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.

Units for PressureUnit Abbreviation

Pascal Pa

Kilopascal kPa (1 kPa = 1000 Pa)

Atmospheres atm

Millimeters of mercury mm Hg

torr torr (same as mm Hg)

Pounds per square inch psi

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 #1A 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

2. List the variables: V1 = 12.4 LP1 = 1.00 atmV2 = ?P2 = 0.800 atm

3. 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 LP1 = 1.08 atmV2 = 10.0 LP2 = ?

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 #1Given 17 L of a gas at 358 K. What is its volume at 283 K? –

work through the problem on your own first before proceeding1. Write the equation: T1V2 = T2V1

2. List the variables: T1 = 358 KelvinV1 = 17 LT2 = 283 KelvinV2 = ?

3. Plug in the numbers and solve!T1V2 = T2V1

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

358KV2 = 13.4 L

Charles’ Example #2Given 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 first1. Write the equation: T1V2 = T2V1

2. List the variables: T1 = 364 KelvinV1 = 200 mLT2 = ?V2 = 500 mL3. 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

Hints

• 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 ProblemsA 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

1. Write the equation: T1P2 = T2P12. List the variables: T1 = 273 KP1 = 1.00 atmT2 = 298 KP2 = ?3. Plug in the numbers and solve!

T1P2 = T2P1

(273 K)P2 = (298 K)(1.00 atm)P2 = 1.09 atm

ExampleA gas has a pressure of 535 mm Hg at 40.0 °C. What isthe temperature in Kelvin and degrees Celsius at 760 mm Hg? work through the problem on your own before proceeding1. Write the equation: T1P2 = T2P1

2. List the variables: T1 = 40°C + 273 = 313 KP1 = 535 mm HgP2 = 760 mm HgT2 = ? 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

Hints

• 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!

Combined Gas Laws

• When you combine Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law, you get the Combined Gas Law:

P1V1 = P2V2

T1 T2

Example #1: A balloon contains 2 L of air at 300K (68oF) and 1 atm.

What will be the pressure if the volume is 3 L and the temperature is 250 K?

1. Write the equation:2. List the variables:P1= P2=V1= V2=T2= T2=3. Plug in the numbers and solve!

P1V1 = P2V2 T1 T2

1 x 2 = P2 x 3 300 250

.0067 = P2 x .012

.0067 = P2

.012

P2= .558 atm

Example #2: A balloon contains 4 L of air at 280 K (45oF) and 1.02 atm.

What will be the volume at 297 K and 1.5 atm?

1. Write the equation:2. List the variables:P1= P2=V1= V2=T2= T2=3. Plug in the numbers and solve!

P1V1 = P2V2 T1 T2

1.02 x 4 = 1.5 x V2

280 297 .0145= .005 x V2

.0145= V2

.005

= 2.9 L

Example #3: A balloon contains 4 L of air at 280 K (45oF) and 1.02 atm.

What will be the temperature if the volume is 7 L and the pressure is 0.9 atm?

1. Write the equation:2. List the variables:P1= P2=V1= V2=T2= T2=3. Plug in the numbers and solve!

P1V1 = P2V2 T1 T2

1.02 x 4 = .9 x 7 280 T2

.01457 = 6.3T2

.01457 x T2 = 6.3

T2 = 6.3 .01457

= 432.4 K

Ideal Gas Law

• This gas law is the only law that considers the number of gas molecules (in units of moles)

Formula

• PV = nRT

P = Pressure in atmospheresV = Volume in Litersn = number of molesR = Ideal Gas Constant 0.0821 L x atm

K x molT = Temperature in Kelvin

Example #1At what pressure would 0.150 mole of nitrogen gas

at 23.0 °C occupy 8.90 L?

1. Write the equation: PV = nRT 2. List the variables:

P = ?V = 8.90 Ln = 0.150 molR = 0.0821 L*atm/K*molT = 23 + 273 = 296 K

3. Plug in the numbers and solve!PV = nRT or P = nRT

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

8.90L

Example #2How 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?

1. Write the equation: PV = nRT 2. List the variables:

P = 100.0 atmV = 20.0 Ln = ?R = R = 0.0821 L*atm/K*molT = 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