Gases Notes

12.1 A. Physical Properties:1. Gases have mass. The density is much

smaller than solids or liquids, but they have mass. (A full balloon weighs more than an empty one.)

2. Gases can be compressed. It is very easy to reduce the volume of a gas.

Example: air in a bicycle tire

3. Unlike liquids, gases completely fill their containers.

4. Gases can move through each other

rapidly. Example: the diffusion of food

smells and perfume.

5. Gases exert pressure.

6. The pressure of a gas depends upon

temperature.

high temp. = high pressure,

low temp. = low pressure

B. Kinetic-Molecular Theory:1. Gases are small particles that have mass.

These particles are usually molecules, except for the Noble Gases.

2. The particles in gases are separated

by relatively large distances.

3. The particles in gases are in constant rapid motion (random).

4. Gases exert pressure because their particles frequently collide with the walls of their container and each other.

5. Collisions of gas particles are perfectly elastic.

Inelastic Collision

Elastic Collision

Gas particles do not slow down when hitting each other or the walls of their container… How do we know?

6. Temperature of a gas is simply a measure of the average kinetic energy of the gas particles. High temp. = high KE, Low temp. = low KE

7. Gas particles exert no force on one another. Attractive forces are so weak between particles they are assumed to be zero.

C. Measuring Gases:1. The following 4 variables will be used to do gas calculations:

n - amount of a gas, it is measured in molesV - volume of a gas, it is measured in L (dm3) or mL (cm3)

“STP” = Standard Temperature & Pressure:T- Standard Temperature: 0 oC = 273 K

Taken in oC converted to Kelvin (K) T(K) = °C + 273

Ex #1) 22°C = 295 K 100.°C = 373 K -27.3°C = 245.7 K -273°C = 0 K

P - Standard Pressure: can be measured using the following units:

(sea level pressure)

1 atm (atmospheres) 760 mm Hg

101,325 Pa (Pascals) 760 torr

101.325 kPa (kilopascals) 14.7 lb/in2 (psi)

Ex #2) Convert 1.026 atm to kPa:

Ex #3) Convert 98,500 Pa to mm Hg:

104.0 kPa101.325 kPa1.026 atm =

1 atm

739 mm Hg760 mm Hg98,500 Pa = 101,325 Pa

2. Atmospheric pressure is the pressure exerted by the air in the atmosphere. This pressure varies with altitude and water vapor content.

3. Atmospheric pressure is measured with a barometer. This is a glass tube sealed at one end and filled with Hg.

Why toxic mercury and not water?

Atmospheric Pressure• Affects Weather:

• Changes with Altitude:

Boiling Point Changes w/Altitude & Pressure

12.2 The Gas LawsA. Boyle’s Law: Pressure - Volume

Relationship. The pressure & volume of a sample of gas at constant temperature are inversely proportional to each other.

Indirect

P1V1 = P2V2

Doubling Pressure = ½ VolumeQuadrupling Pressure = ¼

Volume

Boyle’s Law

Ex #4) A gas has a volume of 300. mL under a pressure of 740. mm of mercury. If the temperature remains constant, calculate the volume when under a pressure of 750. mm Hg.

P1V1 = P2V2

2740. mm 300. mL = 750. mm V

740. mm 300. mL

750. mm

750. mm =

2V

750. mm

2296 mL = V

B. Charles’ Law: Temperature - Volume Relationship. At constant pressure the volume of a fixed amount of gas is directly proportional to its absolute temperature.

Direct1 2

1 2

V V =

T T

*Temperatures must be in Kelvin!

K = °C + 273

Ballon in cool and cold water:

Ex #5)

What is the Celsius temperature of

68.20 mL of methane, if it occupies a volume of 0.02200 L at 50.0°C?

1 2

1 2

V V =

T T

1

68.20 mL 22.00 mL = T 323.0 K

168.20 mL 323.0 K T 22.00 mL=

22.00 mL22.00 mL

1T = 1001 K

-273 C

728 C

C. Avogadro’s Law: Amount - Volume Relationship. Equal volumes of gases at the same temperature and pressure contain an equal number of particles.

1 mole gas = 22.4 L = 6.02 x 1023 particles at STP (273 K & 1 atm)

molar mass

volume

4 He 222 Rn

constant

22.4L

Therefore because of Avogadro’s Law if these three gases have the same number of particles and are at the same temperature and pressure, they must take up the same volume.

He RnO2

Molar Mass does not affect volume of a gas

D. Dalton’s Law of Partial Pressures: The sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas mixture.

Ex #6) A flask contains a mixture of oxygen, argon, and carbon dioxide with partial pressures of 745 torr, 0.278 atm, and 391 torr respectively. What is the total pressure in the flask?

PT = Pa + Pb + Pc + …

760 torr.278 atm = 211 torr

1 atm

+ 745 torr

+ 391 torr

1347 torr

Dalton’s Law of Partial Pressures

Ex #7) The total pressure of a mixture of helium and neon is 498 mm Hg. If helium is 20.0 % of the mixture, what is the partial pressure of helium in mm Hg?

498 mm Hg 0.200 He 99.6 mm Hg for He

E. The Combined Gas Law: “Choyles” This law can be used to determine how changing two variables at a time affects a third variable.

1 1 2 2

1 2

P V P V =

T T

Ex #8) A gas occupies 72.0 mL at 25 °C and 198 kPa. Convert these to standard conditions. What is the new volume?

P1 = 198 kPa P2 = 101.325 kPa

V1 = 72.0 mL V2 = ?

T1 = 298 K T2 = 273 K

2

2

198 kPa 72.0 mL 101.325 kPa V =

298 K 273 K129 mL = V

1 1 2 2

1 2

P V P V =

T T

(273 K)

(101.325 kPa)

12.3 A. Ideal Gas LawAlthough no “ideal gas” exists, this law can be

used to explain the behavior of real gases under ordinary conditions.

P = pressure (atm)

V = volume (L or dm3)

n = number of moles

R = 0.0821 L•atm/mol•K

universal gas constant

T = Kelvin temperature

PV = nRT

B. Ideal Gas Law & The Kinetic – Molecular Theory:

Under normal conditions (temperature and pressure) gases behave ideally.

n ____ P ____ (more gas, ____________)more collisions

T ____ P ____ (moves faster, ______________)more collisions

V ____P ____ (smaller volume, ____________)more collisions

2. Gases at low temperatures and high pressures do NOT behave ideally. As you decrease the volume of a gas, the volume of the particles themselves becomes significant. The Kinectic-Molecular Theory & Ideal Gas Law assumes the gas particles have no volume of their own.

3. Second, the attractive forces which are very small when the particles are moving fast, become larger as they slow down.

Ex #9) How many grams of carbon dioxide occupy a volume of 36.9 mL at 158 kPa and 72 oC?

36.9 mL = 0.0369 L

1 atm158 kPa =

101.325 kPa1.56 atm

72 C + 273 = 345 K

PV = nRT

1.56 atm 0.0369L = n 0.0821 L atm/mol K 345 K

1st convert units to “R” units

(0.0821 L•atm/mol•K) (345 K)(0.0821 L•atm/mol•K) (345 K)

n = 0.00203 mol CO2

22 2

2

44.0 g CO0.00203 mol CO = 0.0893 g CO

1 mol CO

C. Lifting Power of Gases: 1. Uses a gas “lighter” than air (smaller molar mass.)

Ex) The Hindenburg used hydrogen

Ex) Today’s blimps use helium

2. Hot Air balloons heat air to lower its density.

3. Effusion is the movement of gas atoms or molecules through a hole so tiny they move one particle at a time. Smaller particles effuse faster than larger particles.

Ex) → →H2

fastest

He

rare/expensive

N2

(air) plentiful/ cheap/slowest

Effusion

Effusion

The Hindenburg was a Dirigible (a balloon that has engines to control its horizontal movement)

PassengerQuarters had 25

two-berth cabins

Titanic - 882 feetHindenberg – 804 feet

May 6, 1937 Lakehurst, NJ

Memorial in Lakehurst, NJ