The Behavior ofGases

Ch. 12

The Properties of Gases

12-1

Kinetic Theory (Revisited)• Kinetic Theory of Gases

1) Gases are composed of hard, spherical particles in constant, rapid, random, straight-line motion.

2) There are no attractive forces between particles. All collisions are perfectly elastic (no energy lost).

3) Kinetic Energy is directly proportional to Kelvin temperature.

4) A gas expands to fill the container. There is empty space between gas particles (explains compressibility). Gas particles occupy negligible volume.

Variables describing a gas

• 4 Variables are used to describe a gas:

– Pressure (P) in kilopascals (kPa)

– Volume (V) in liters (L)

– Temperature (T) in Kelvin (K)

– Number of moles (n) – amount of gas particles

Factors affecting Gas Pressure

12-2

1) Amount of Gas

• (Review) Pressure of a gas = force per unit area that gas particles exert on the walls of their container– Gas particles Pressure– Ex: Inflating a basketball adds more gas

molecules which increases the pressure in the ball

2) Volume

• Volume Pressure • Ex: piston in car engine, forces gas in cylinder to

reduce in volume, creating more pressure.

3) Temperature– Remember…as

temperature increases kinetic energy increases…

– temperature pressure

– Ex: heat up a propane tank, gas molecules will move faster and faster… and finally blow up

Gas Laws

12-3

Boyle’s Law (Pressure vs. Volume)

• Boyle’s Law = the pressure and volume of a gas are inversely proportional at a constant temperature.

– Pressure Volume

– Calculation:

P1V1 = P2V2

DRAW!

Calculating Boyle’s Law

• Calculation:– P1V1 = P2V2 (P= pressure, V = volume)

– Ex: The volume of a scuba tank is 10.0 L. It contains 290 atm of gas pressure in it. What would be the volume of gas at 2.40 atm?

P1 = 290 atm P2 = 2.40 atm

V1 = 10.0 L V2 = ?

290atm(10.0L) = 2.40atm(V2)

V2 = 1208 L

Charles’ Law(Temperature vs. Volume)

• Charles’ Law = at constant pressure, the volume of a gas is directly proportional to temperature (K).– Volume Temperature– Ex: if you put a balloon in the freezer, it will

shrink in size, take it out and it will expand!• Calculation:

– V1 = V2

T1 T2

DRAW!

Calculating Charles’ Law

• Calculation:– V1 = V2 V = volume, T = temperature (K) T1 T2

– Ex: A balloon is filled with 3.0 L of helium at 22°C and 760 mm Hg. It is then placed outdoors at 31°C, what will the new volume be? (convert °C to K first!)3.0 L = V2

295 K 304K V2 = 3.1 L

Gay-Lussac’s Law(Temperature vs. Pressure)

• Gay-Lussac’s Law = the pressure of a gas is directly proportional to the temperature, in Kelvin, at a constant volume.– Pressure Temperature– Calculation:

P1 = P2

T1 T2

DRAW!

Calculating Gay-Lussac’s Law

• Calculation:– P1 = P2 P = pressure, T = temperature (K) T1 T2

– Ex: If a can at a of pressure is 103kPa at 25°C is thrown into a fire, what will the resulting pressure be at 928°C?

– 103 kPa = P2

298 K 1201 K

– P2 = 415 kPa

Combined Gas Law

• Combined Gas Law: P1V1 = P2V2

T1 T2

• Ex: A 2.7 L sample of nitrogen is at 121kPa and 288K. If the pressure increases to 202kPa and the temp. rises to 303K, what is the new volume?121kPa(2.7L) = 202kPa(V2)

288K 303KV2 = 1.7L

Gas Law Overview

Gas Law Proportion Variable Constant Calculation

Boyle

Charles

Gay-Lussac

Combined

Gas Law OverviewGas Law Proportion Variable Constant Calculation

Boyle Inverse Pressure, volume

Temp P1V1=P2V2

Charles Direct Volume, temp

Pressure V1 = V2

T1 T2

Gay-Lussac

Direct Pressure, temp

Volume P1 = P2

T1 T2

Combined Pressure, temp,

volume

P1V1 = P2V2 T1

T2

Ideal Gases

12-4

Ideal Gas Law Calculation

• Ideal Gas Constant (R) = 8.31 L•kPa/K•mol

• Ideal Gas Law = PV = nRT; n = # of moles

• Ex: You fill a rigid cylinder will a volume of 20.0L with N2 gas to a pressure of 2.00x104 kPa at 28°C. How many moles of N2 gas does the cylinder contain?

2.00x104 kPa x 20.0L = n x 8.31 L•kPa/K•mol x 301K

n = 160 mol N2

Ideal Gas Law + Kinetic Theory

• Kinetic theory assumes all gases are ideal gases.

• An ideal gas follows all of the gas laws under ALL conditions of pressure and temperature.

• An ideal gas does NOT exist; however, the behavior of real gases is very similar.

Departures from the Ideal Gas Law

• Main 2 differences between real + ideal behavior:

1. Gas molecules ARE attracted to each other (otherwise could not become a liquid)

2. Gas particles DO have volume (made up of particles, must have volume)

Gas Molecules:Mixtures + Movements

12-5

Avogadro’s Hypothesis

• Avogadro’s Hypothesis = equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

• Thus, at STP, 1 mol = 6.02x1023 atoms, of any gas regardless of size, occupies a volume of 22.4 L

At STP!!

Dalton’s Law• Partial Pressure = the contribution each

gas in a mixture adds to the total pressure.

• Dalton’s Law of partial pressures = at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases.

• Dalton’s Calculation:Ptotal = P1 + P2 + P3 + …

Dalton’s Law Practice

• Ex: Air contains O2, N2, CO2, and trace amounts of other gases. What is the partial pressure of O2 if the total pressure is 101.30 kPa and the partial pressures of N2 = 79.10 kPa, CO2 = 0.040 kPa, and other gases = 0.94 kPa?

• Ptotal = PN2 + PO2 + PCO2 + Pother

• 101.30 = PO2 + 79.10 + 0.040 + 0.94

• PO2 = 21.22 kPa

Graham’s Law• Diffusion = the tendency

of molecules to move from areas of high concentration to areas of low concentration until the concentration is uniform throughout.

• Effusion = process in which a gas escapes through a tiny hole in a container.

• Graham’s Law of Effusion/Diffusion = the rate of effusion of a gas is inversely proportional to the square root of a gas’s molar mass.

• Graham’s Law Calculation:

Rate A = √molar massB

Rate B √molar massA

• What?! Gases with lower molar mass move faster than gases with higher molar mass.

• Ex: A balloon filled with helium

deflates faster than a balloon

filled with air –

which has a larger mass?

Calculating Graham’s Law

• Ex: Compare the rates of effusion of nitrogen (B) (molar mass = 28.0g) to helium (A) (molar mass = 4.0g).

RateHe = √28.0g = 5.3g = 2.7

RateN2 √4.0g 2.0g

Helium effuses/diffuses 2.7 times faster than nitrogen at the same temperature!!