The Gas Laws During this unit you will be able to answer the following questions: 1)Why does pumping...

The Gas LawsDuring this unit you will be able to answer the following questions:

1) Why does pumping a tire become difficult as it becomes more inflated?

2) Why does a hot air balloon lift off the ground and the air inside is heated?

3) Why does soda eventually go flat, and what could you do to slow that process down?

4) Why do your car ties seem like they have lost air, or go flat in the cold winter months, but then as spring/summer approaches, they seem to have re-inflated on their own?

What do you know?

What is the name of the gas, mostly responsible for the

greenhouse effect?

Carbon Dioxide

The Atmosphere

1. Made of a sea of gasesA. The air is made of 78% nitrogen, 21% oxygen, 0.9%

argon, and 0.033% carbon dioxide.

2. The trapping of heat energy in the atmosphere is called the greenhouse effect.

3. Increasing the greenhouse gases could be increasing the worlds average temperature.

A. Warmer temps. mean the ice caps would melt and cause coastal flooding

B. CO2 in the atmosphere is increasing due to the combustion of fossil fuels and loss of forests

4. The ozone is another main component of our atmosphere.

A. Ozone is the molecule O3

B. Shields us from UV rays given off by the sun. These UV rays cause cancer, and are called a mutagen.

C. The ozone is approximately 3 mm thick

D. Ozone is being depleted by chlorofluorocarbons (CFC’s)

i. CFC’s can be found in air conditioners, refrigerators, and aerosol cans

E. 1 CFC molecule can destroy millions of ozone molecules

F. The hole of the ozone is centered over Antarctica

G. CFC’s have been banned, but it’s estimated they won’t be completely out of the atmosphere until 2060

Sept 13, 2007 March 3, 2012

Kinetic Molecular Theory

1. Predicts the behavior of gases and assumes that gases are ideal gases

A. Ideal gases are gases that travel in a straight line and only change direction when they collide another gas molecule.

B. There is no attractive forces between ideal gases.

2. The average kinetic energy of gas particles is directly proportional to temperature in Kelvin. –THIS IS WHY WE USE KELVIN FOR ALL GAS LAW PROBLEMS

A. Meaning: if gas molecules move faster, and hit each other more often, then thetemperature will increase. If the moleculesmove slowly and hit each other less often, thetemperature will decrease. Temperature depends onhow often and how hard molecules hit each other.

3. Different gases at the same temperature move at different speeds. Why?

A. They have different masses.

B. Lighter molecules/compounds, such as H2, move faster than heavier molecules/compounds such as N2 or CO2

4. Temperatures for gases are always given in Kelvin. Remember that if the temperature is given in Celsius use the equation K = ºC + 273.

Fluidity

1. Gases are in constant motions and flow like liquids

2. Gases are in constant motion and collide with each other and their container.

3. The kinetic molecular theory assumes that the collisions are elastic

A. This means energy is not lost after a collision happens.

Density

1. Gases have a density that is less than solids and liquids because there’s more space between atoms.

2. The kinetic molecular theory says that the volumes of the individual molecules can be ignored when compared to the total volume of the gas

Volume and Compressibility 1. Remember, volume is the amount of space

something takes up. A. If you apply a pressure to a gas, the gas molecules

come closer together.

B. This decreases the volume of the gas.

2. Volume = length * width * height

3. Common units of volume include: liters (L), milliliters (mL), cubic meters (m3), or cubic centimeters (cm3)

4. Avogadro’s principle states that equal volumes of gases under the same conditions have equal numbers of molecules. The volume of 1 mole of any gas at STP is 22.4 liters.

A. This is called molar volume

Pressure

1. When a gas fills a container it puts a pressure on the container in all directions.

Think of blowing air in a balloon.

2. Pressure is caused by the collision of gases running into each other

A. The more collisions occurring, the more the pressure increases

3. Pressure is defined as force exerted over a specific area

4. Pressure = force/unit area

5. The metric unit of force is the pascal (Pa)

A. 1 pascal = 1 Newton/meter2

6. All the air above your exerts (gives) a pressure.

A. This is called atmospheric pressure

B. 1 atmosphere of pressure causes the a column of mercury 760 mm high.

C. 1 atmosphere = 760 mmHg

Pressure Abbreviation Equivalant

Pascel Pa

Bar bar 1 bar = 100,025 Pa

Millimeter of mercury

mmHg 1 mmHg = 133.3 Pa

Pound per square inch

psi 1 psi = 6894.76 Pa

Torr torr 1 torr = 133.3 Pa

Atmosphere atm 1 atm = 101,325 Pa

7. STP = standard temperature and pressure

A. Values include 0ºC and 1 atm OR 273 K and 101.3 kPa.

What do you know?The average kinetic energy

(temperature) of a gas molecule depends on

_____________________.

Pressure is caused by the ___________________ of gas

molecules against each other and the container.

HOW FAST THE MOLECULES MOVE

Collisions

Properties of Gases

1. They don’t always behave ideallyA. At high pressures gas molecules get close

and attractive forces are significant.

B. Same thing occurs at low temperatures

2. Two assumptions that the kinetic

molecular theory doesn’t always follow:A. The volume of gas molecules is negligible

B. There are no attractive forces between gas molecules.

3. Low temperatures & high pressure cause gases to misbehave.

c) If the temperature is low enough, and the pressure is high enough, then molecules can condense.

4. Depending on the temperature and the amount of water in the air, water can be in a gas form and a liquid form at almost the same time. Water changes from liquid to gas and back to liquid. This is called fog. H2O(l) H2O(g)

A. The two opposing arrows tells us that the system is in equilibrium.

5. In a closed container the pressure caused from water evaporating reaches a maximum value

A. Ex: butane lighter. Gas evaporates until it can’t

6. Equilibrium vapor pressure is just called vapor pressure.

A. As temperature increases, vapor pressure increases

7. Liquids boil when its vapor pressure equals the atmospheric pressure.

A. The higher you are, the smaller the atmospheric pressure, so it takes less heat to boil water on top of a mountain than sea level.

Water boils at 94ºC in the mountains of Denver.

Water boils instantly in outer space.

Which substance from the graph has the highest boiling point? Which ahs the lowest?

Evaporation Vs. Boiling point

1. Evaporation happens at temperatures lower than boiling point

A. Evaporation happens at the surface of the liquid.

B. Random molecules gain enough energy to break free of intermolecular forces

2. Boiling happens when bubbles of vapor form inside the liquid.

A. The pressure inside the liquid has to be greater than the pressure outside the liquid.

Phase Diagram1. Shows the

temperatures and pressures a substance exists in different phases.

A. X-axis is temperature and Y-axis is pressure

B. Phases are in equilibrium with one another at each line

i. Equilibrium means that the phases are changing back and forth at equal times.

2. In each region the substance exists in one phase

3. If you increase the temperature, vapor increases.

A. At the same time the density of liquid decreases.

B. Over time, the liquid and vapor will have the same density, so vapor won’t exist

C. This is called the critical point

4. At one point of the diagram, solid liquid and gas all exist at the same point (point A)

A. This is called the triple point

4. The normal boiling point is where the liquid-gas line crosses 1 atm of pressure.

Phase Diagrams Practice

Label the diagram:

a. triple point

b. solid-vapor equilibrium

c. solid-liquid equilibrium

d. critical point

e. normal boiling point

f. normal freezing point

Phase Diagrams Practice

What’s Happening?:

77. A?

78. D?

79. E?

80. F?

Triple point- all three phases exist in equilibrium

Critical point- no longer tell diff btween L and G, vapor not exist…

Normal boiling point- liquid-gas line crosses 1atm

Normal freezing/melting point- solid/liquid line crosses 1atm

Phase Diagrams Practices, l or g ?:

81.

82.

83.

84.

85.

86.

gas

liquid

solid

liquid

gas

liquid

Simple Gas Laws

1. You MUST know what these variables represent

A. P = Pressure ( what are units for pressure? )

B. V = Volume ( what are units for volume? )

C. n = moles

D. T = Temperature in Kelvini. Calculations with temperature must be made in

Kelvin

Charles’ Law

1. Relates temperature and volume

2. If the temperature increases, then the volume must increase

A. The opposite is also true. If the volume decreases, the temperature must also decrease

B. This is called a direct relationship

Charles’ Law

• Heating a gas will make it expand. • Gas molecules move faster when heat is

added, striking the container walls with more force.

• More frequent and forceful collisions make the volume of a flexible container like a balloon increase.

If heating a gas makes it expand, what will cooling it do?

3. Charles’ equationA.

B. V1 = starting volume

C. V2 = ending volume

D. T1 = starting temp.

E. T2 = ending temp.

2

2

1

1

T

V

T

V

4. T1 and T2 must have the same units

5. V1 and V2 must also have the same units

6. Beware: some problems will give you extra information that you don’t need, such as how many moles are in the container or what the pressure is

Charles Law Example 1:

7. Basic Charles Law example:

A chamber has an initial temperature of 298 K and is 2.5 L. The chamber volume changes to 1.75 L. What is the new temperature?

2

2

1

1

T

V

T

V

2

75.1

298

5.2

T

L

K

L

)5.2(

)298)(75.1(2

L

KLT

KT 6.2082

8. Intermediate problem:

A container has an initial volume of 17 L at a temperature of 313 K and a pressure of 1 atm. If the temperature changes to 350K and the pressure stays the same, what would the new volume have to be?

A. Since the pressure didn’t change, we don’t have to worry about it. We use the same equation!

Charles Law Example 2:

2

2

1

1

T

V

T

V

K

V

K

L

350313

172 2313

)17)(350(V

K

LK

LV 192

9. Advanced problem:

A chamber has 12 moles of a gas, a volume of 25 L, and a temperature of 300 K. Assuming the number of moles stays the same, what is the new volume if the temperature increases 25ºC?

(K = ºC + 273)(ºC = K – 273)

Charles Law Example 3:

A. To solve this problem, you’ll need to convert ºC to K in order to make the units the same. Once the units are the same, you need to use your new T2 temperature in the equation. The number of moles is unnecessary information.

2

2

1

1

T

V

T

V

K

V

K

L

598300

252

2300

)25)(598(V

K

LK

LV 83.492

25ºC = X - 273

298 = X

300K + 298 K = 598 K

Boyle’s Law1. Relates pressure and volume

2. If pressure increases, then volume will decrease

3. If pressure decreases, then volume will increase

A. This is called an inverse relationship

P

1/V

If we plot the same information, but with the inverse of volume, we get a straight line…. THUS the relationship

is INVERSE!!!

4. Equation for Boyle’s Law:

P1V1 = P2V2

Boyle’s Law Example 1:

5. Basic example problem:

A container has a volume of 6 L and under 3 atm of pressure. If the atmospheric pressure is cut in half, then what is the final volume?

P1V1 = P2V2 (3 atm)(6 L) = (1.5 atm)(V2)

25.1

)6)(3(V

atm

Latm 12 L = V2

Boyle’s Law Example 2:

6. Intermediate problem:

A container with an unknown pressure has a 12 moles of gas and a volume of 35 L. When the volume is decreased to 20 L, the pressure is 5 atm. What is the initial pressure?

A. The number of moles is not important in this problem

P1V1 = P2V2 (P1)(35 L) = (5 atm)(20 L)

L

LatmP

35

)20)(5(1 P1 = 2.9 atm

Boyle’s Law Example 3:

7. Advanced problem:

A container is 2.7 L and is under 2017 torr of pressure. If the volume changes to 1500 mL, what is the new pressure in units of atm? (760 torr = 1 atm)(1000 mL = 1 L)

A. To solve, convert 2017 torr to atm, then convert 1500 mL to L. Once done, plug into the Boyle’s Law equation.

torr

atmtorr

760

12017 atmtorr 654.22017

mL

LmL

1000

11500 LmL 500.11500

P1V1 = P2V2

(2.654 atm)(2.7 L) =(P2)(1.5 L)

25.1

)7.2)(654.2(P

L

Latm 4.8 atm = P2

Other Simple Gas Equations to Know

Gay-Lussac • There is a direct relationship between

pressure and temperature, when other variables are constant.

Avogadro’s Law• There is a direct relationship between

moles and volume, when other variables are constant.

2

2

1

1

T

P

T

P

2

2

1

1

n

V

n

V

Daltons Gas Law1. The total pressure of the

gas in a mixture can be found.

2. The pressure of a single gas in a mixture is called its partial pressure.

3. Adding up all the partial pressures gives the total pressure.

4. Simply add up the pressures of the other gasses in the mixture.

Ptotal=PA+PB+PC…

Combined Gas Laws

1. As long as the number of molecules in the gas doesn’t change (the moles stay constant) the combined gas law can be used to find a missing volume, temperature, or pressure.

2. Combined Gas Law Equation:

2

22

1

11

T

VP

T

VP

Combined Gas Law Example 1:

3. Example problem:

A weather balloon containing helium with a volume of 410.0 L rises in the atmosphere and is cooled from 27°C to -27°C. The pressure on the gas is reduced from 110.0 kPa to 25.0 kPa. What is the volume of the gas at the lower temperature and pressure?

A. Remember to convert ºC to K

P1= P2=

V1= V2=

T1= T2=

410.0 L

300 K 246 K

110.0 kPa 25.0 kPa

?

)246(

))(0.25(

)300(

)0.410)(0.110( 2

K

VkPa

K

LkPa

2)0.25)(300(

)246)(0.410)(0.110(V

kPaK

KLkPa

1479.28 L = V2

Ideal Gas Law

1. When you combine all the gas laws together you get the ideal gas law

2. PV = nRTA. n = moles

B. R = gas constant

3. Gas constant:

4. Number was determined by using STP values and solving for R

5. Due to the units of R, all variables must be in atm OR kPa, L, mol, and K

Kmol

LatmR

*

*0821.

Kmol

kPaLR

314.8

Ideal Gas Law Example 1:

A sample of carbon dioxide with a mass of 0.250 grams is placed in a 350.0 mL container at 400.0K. What is the pressure exerted by the gas?

A. You need pressure, volume, moles, and temperature. Your missing variable is pressure. Find moles by converting your grams of CO2 to moles (use the molar mass of CO2) and then convert 350.0 mL to L

2

22 CO grams 44

CO mol 1 CO grams 0.250 5.68x10-3 mol of CO2

=

mL 1000

L 1 mL 350 = 0.350 L

PV = nRT

)350(.

)400)(0821)(.1068.5( 3

L

KmolxP

P = 0.533 atm

Volume Conversions

1. Equal volumes of gases contain equal volumes of molecules at the same temperature and pressure. The chemical equation gives a conversion factor or mole ratio to solve the problem. The mole ratio from the chemical equation is the same as the volume ratio.

1 N2 (g) + 3 H2 (g) 2 NH3 (g)

2. 3L of H2 will contain 3 times as many molecules as 1 L of N2.

3. 2L of NH3 will contain twice as many molecules as 1 L of N2.

Volume Conversion Example 1:

N2 (g) + 3 H2 (g) 2 NH3 (g)

How many liters of H2 are needed to react completely

with 22L of N2?

2

22 N L 1

H L 3 N L 22 = 66 L H2

Quick Review

Volume vs. ________ or ________?

Inverse or Direct?

What Law/s does this represent?

V

Charle’s Law – with TemperatureORAvogadro’s Law – with molesBoth are DIRECT

Quick Review

Volume vs. ______________?

Inverse or Direct?

What Law does this represent?

V

Boyle’s Law- PressureInverse

Quick Review

Pressure vs. ______________?

Inverse or Direct?

What Law does this represent?

Gay-Lussac’s Law- TemperatureDirect