ahcc14 chapter 14 objectives and notes - v20web.eccrsd.us/harrison/public/science/ahc_chapter... ·...

1

ADVANCED HONORS CHEMISTRY - CHAPTER 14 NAME:

THE BEHAVIOR OF GASES DATE:

OBJECTIVES AND NOTES - V21 PAGE:

THE BIG IDEA: KINETIC THEORY

Essential Questions

1. How do gases respond to changes in pressure, volume, and temperature?

2. Why is the ideal gas law useful even though ideal gases do not exist?

Chapter Objectives

1. Describe the properties of gas particles. (14.1)

2. Describe the kinetic-molecular theory and explain how it accounts for observed gas behavior. (14.1)

3. Explain what gas pressure means and describe how it is measured. (14.1)

4. Describe how the behavior of gases relates to changes in amount of the gas, and changes in temperature,

pressure, and volume. (14.1 - 14.3)

5. State Boyle's law and use it to qualitatively and quantitatively account for pressure-volume changes in a gas.

(14.1 and 14.2)

6. State Charles' law and use it to qualitatively and quantitatively account for temperature-volume changes in a

gas. (14.1 and 14.2)

7. State Amontons’s Law (Also called Gay-Lussac's Law) and use it to qualitatively and quantitatively account

for temperature-pressure changes in a gas. (14.1 and 14.2)

8. State the combined gas law and use it to solve gas law problems involving changes in temperature, pressure,

and volume. (14.2)

9. State and solve problems involving the ideal gas law equation. (14.3)

10. Solve problems involving gas density and molar mass. (3.2, 10.1, 10.2, 14.2, and 14.3)

11. Distinguish between ideal and real gases. (14.3)

2 - AHC - Chapter 14 - Objectives and Notes - V21

12. State and solve problems involving Dalton's law of partial pressures. (14.4)

13. Derive and solve problems using Graham's law of diffusion. (14.4)

14. Demonstrate and be able to describe all aspects of laboratory safety rules and procedures. (Applicable every

chapter)

14.1 Properties of Gases

B. Factors Affecting Gas Pressure

1. Amount of Gas: Changing the amount of gas changes the number of collisions and, thus, changes the

pressure.

a. Example: Doubling the amount of particles doubles the pressure.

n1 = 10.0 mol

P1 = 1 atm

n2 = 20.0 mol

P2 = 2 atm

2. Volume: See Boyle’s law in section 14.2 below.

3. Temperature: See Amontons’s law (Gay-Lussac's Law) in section 14.2 below.


14.2 The Gas Laws

A. Boyle's Law: The Pressure - Volume Relationship

1. Proposed by Robert Boyle in 1662 (Don’t memorize any dates).

2. When temperature is held constant, the pressure and volume of a gas are inversely proportional.

3. While the external pressure is what was changed in Boyle’s experiment, the piston in the picture below

stops going down when the internal pressure equals external pressure.

4. For a sample of any gas at constant temperature and moles of the gas:

P1V1 = k and P2V2 = k

∴ P1V1 = P2V2

P1 = 1 atm

V1 = 1 L

P2 = 2 atm

V2 = 0.5 L

P3 = 0.5 atm

V3 = 2 L


5. While Boyle experimentally changed the external pressure to see what occurred to the volume of the gas,

his law allows us to study what happens to internal pressure when volume is changed.

V1 = 1 L

P1 = 1 atm

V2 = 0.5 L

P2 = 2 atm

V3 = 1.5 L

P3 = 0.67 atm


B. Charles's Law: The Temperature - Volume Relationship

1. Proposed by Jacques Charles in 1787 (Don’t you dare memorize any dates).

2. When pressure is held constant, the volume of a gas is directly proportional to its absolute temperature.

3. For a sample of any gas at constant pressure and moles of the gas:

V1

T1

= k and

V2

T2

= k

∴

V1

T1

= V2

T2

T1 = 250 K

V1 = 1 L

T2 = 500 K

V2 = 2 L


C. Amontons’s Law (Gay-Lussac's Law): The Temperature - Pressure Relationship

1. Proposed by Guillaume Amontons in the late 1600’s (Don’t even think about it).

2. When volume is held constant, the pressure of a gas is directly proportional to its absolute temperature.

3. For a sample of any gas at constant temperature and moles of the gas:

P1

T1

= k and

P2

T2

= k

∴

P1

T1

= P2

T2

T1 = 250 K

P1 = 1 atm

T2 = 500 K

P2 = 2 atm

D. The Combined Gas Law

1. Boyles, Charles's, and Amontons's gas laws can be combined to form the combined gas law.

a.

P1V1

T1

= P2V2

T2 1. All of the above three gas laws can be solved using the combined gas law.


14.3 Ideal Gases

A. Ideal Gas Law

1. A way to derive the ideal gas law is to take any sample of any gas and multiply the pressure of that gas by

its volume and then divide that product by the product of the number of moles of the gas times its

temperature, the answer always equals a constant (k), i.e., the gas law constant.

PVnT

= k

The constant k is normally written as R

PVnT

= R

However, writing the equation this way makes as much sense as writing an equation for π where π is

isolated. Who cares? We never solve for the constant! The ideal gas law equation is normally written as:

PV = nRT

2. R is called the ideal gas law constant, or the universal gas law constant, or just the gas law constant.

a. R =

PVnT

= 0.0821 atm•Lmol•K

= 8.31kPa•Lmol•K

= 62.4mm•Lmol•K

1. Note that all of the expressions above are equal.

2. The different numerical values are based on expressing pressure in different units.

3. As you study chemistry it will be interesting to see in exactly how many different situations, other

than systems involving gases, that this constant is found.

3. This equation is based on the sample of gas being studied acting as an ideal gas. This is a reasonable

assumption under normal conditions.

4. The combined gas law can be derived from the ideal gas law.

PV = nRT

nR =

P1V1

T1

and nR =

P2V2

T2

The moles of gas are constant

∴ nR = k

k =

P1V1

T1

and k =

P2V2

T2

∴

P1V1

T1

= P2V2

T2


B. Ideal Gases and Real Gases

1. The ideal gas law obeys the kinetic-molecular theory.

a. Pressure increases if the number of moles of gas is increased.

b. Pressure increases if the temperature is increased.

c. Pressure increases if the volume is decreased.

2. Real gas molecules have volume, ideal gases do not. Therefore, for ideal gases, the volume of the

container is the volume that the molecules have to move. For real gases we should have to take into

account the volume of all of the gas molecules.

3. Real gas molecules are slightly attracted to the other gas molecules. Ideal gas molecules have no

intermolecular forces and therefore they have no friends.

4. Gases deviate from the ideal gas law at very low temperature or very high pressure.

a. At very low temperatures the gas particles have so little kinetic energy that the intermolecular forces are

strong enough to affect the behavior of the gas particles.

b. Very high pressure at low temperature can only be achieved if the volume of the gas container is very

small.

1. This results in the volume of the actual gas particles being significant in relationship to the volume of

the container.

a. Therefore, at this condition, the volume of the gas particles needs to be taken into consideration.

14.4 Ideal Gases

A. Dalton's Law

1. Proposed by John Dalton in 1801 (Don’t . . . ).

2. Dalton's law of partial pressure: The pressure exerted by a mixture of gases is the sum of all of the

component partial pressures of the gases in the mixture.

a. partial pressure: The pressure exerted by each type of gas in a mixture of gases. This pressure is the

pressure the gas would exhibit if it was alone in the container.


3. PT = P1 + P2 + P3 . . .

a. PTotal is the total pressure of the mixture. (See the picture on the left below.)

b. P1 is the partial pressure of the first gas in the mixture.

4. Dalton's law is often used in the collection of gases over water, where the water vapor present must be

taken into consideration.

PTotal = PDry Gas + PWater Vapor

PDry Gas = PTotal - PWater Vapor

a. PTotal is the total pressure of the mixture.

b. PDry Gas is the partial pressure of the gas being studied in the mixture. (See the pix on the right above.)

c. PWater Vapor is the partial pressure of the water vapor in the system.

VAPOR PRESSURE OF WATER Temperature

(oC) Pressure

(kPa) Temperature

(oC) Pressure

(kPa) Temperature

(oC) Pressure

(kPa)

0 0.6 21 2.5 30 4.2 5 0.9 22 2.6 35 5.6 8 1.1 23 2.8 40 7.4 10 1.2 24 3.0 50 12.3 12 1.4 25 3.2 60 19.9 14 1.6 26 3.4 70 31.2 16 1.8 27 3.6 80 47.3 18 2.1 28 3.8 90 70.1 20 2.3 29 4.0 100 101.3


B. Graham's Law

1. diffusion: The movement of one substance through space or another substance. Substances diffuse from

areas of higher concentration to areas of lower concentration until the concentration is uniform throughout

the container. The diffusion of gases obeys Graham's law.

2. effusion: Movement of a gas through an opening so small that only one particle can pass through at a time.

a. Effusion, like diffusion, follows Graham's law.

3. Graham's law: The rate of effusion of a gas is inversely proportional to the square root of the mass of the

gas particle (the molar mass of the gas). It was proposed by Thomas Graham in 1830. (D . . . ).

a. On the test you will forget to take the square root of the masses, you will only take the ratio of the

masses. When you get the questions wrong you will blame me, your mama will blame me, but the

good news is I . . .

4. Graham's law can be derived from the mathematical definition of kinetic energy, as seen below.

KE = 1

2mv2

If two gases are at the same temperature, than their average KE is the same.

KEGas A = KEGas B

12

mGas A( ) vGas A( )2= 1

2mGas B( ) vGas B( )2

12

molecular massGas A( ) velocityGas A( )2=

12

molecular massGas B( ) velocityGas B( )2

2( ) 1

2!

"#$

%&molecular massGas A( ) velocityGas A( )2

= 2( ) 12

!

"#$

%&molecular massGas B( ) velocityGas B( )2

molecular massGas A( ) velocityGas A( )2

= molecular massGas B( ) velocityGas B( )2

molecular massGas A( ) velocityGas A( )2

molecular massGas A


molecular massGas A

velocityGas A( )2


molecular massGas A


velocityGas A( )2

velocityGas B( )2 = molecular massGas B( ) velocityGas B( ) 2

molecular massGas A( ) velocityGas B( ) 2

velocityGas A( )2

velocityGas B( )2 = molecular massGas B( )molecular massGas A( )

velocityGas A( )2

velocityGas B( )2 = molecular massGas B( )molecular massGas A( )

velocityGas A

velocityGas B

= molecular massGas B( )molecular massGas A( )

or velocityGas A

velocityGas B


a. The velocity of the gas can also be replaced by speed of the gas, rate of diffusion, rate of effusion, or

just rate.

b. Note in the Graham's law equation that the molar mass of gas B is in the numerator on the right side of

the equation.

c. When solving this type of problem always make sure that the lighter gas is the one that travels faster!!!

d. In one type of Graham’s Law problems we are solving for one of the four variables. In this type of

problem the equation is generally written:

velocityGas A

velocityGas B


e. The left side of the equation sometimes acts as one variable, such as in a problem that asks for the ratio

of the velocities of the gases. In this type of problem the equation is generally written:

Ratio of Velocities =

molecular massGas B( )molecular massGas A( )

1. When solving this type of problem, we usually compare the faster gas to the slower gas, therefore the

faster gas, and thus the lighter gas, is gas A.

ahcc14 chapter 14 objectives and notes - v20web.eccrsd.us/harrison/public/science/ahc_chapter... ·...

Documents