The Behavior ofGases

The kinetic theory of gases describes a gas ● as a large number of submicroscopic particles, ● all of which are in constant, rapid & random motion. ● The randomness arises from the particles' many

collisions with each other and with the walls of the container.

Factors Describing a Gas

1. Four Variables are used to describe a gas:

a. Pressure (P) in kilopascals(kPa),atmosphere(atm), milimeterMercury(mmHg), Pounds per Square Inch(psi)

b. Volume (V) in liters (L)c. Temperature (T) in Kelvin (K)d. Number of moles (n) – amount of

gas particles

1) PressurePressure of a gas = force per unit area that gas particles exert on the walls of their container. Pressure= Force

Area– # of Gas particles Pressure

– Ex: Inflating a ball 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) TemperatureRemember…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

4. Amount of gas • Gas particles in a

container are in constant motion because of the negligible space between them.

• The amount of particles will influence the amount of pressure against each other & against the container.

Gas Laws

A.Boyle’s Law (Pressure vs. Volume)

1. Boyle’s Law = the pressure and volume of a gas are inversely proportional at a constant temperature.2.Pressure Volume3..Calculation: P1V1 = P2V2

4.DRAW!

Calculating Boyle’s Law1.Calculation:

P1V1 = P2V2 (P= pressure, V = volume)2.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 atmV1 = 10.0 L V2 = ?290 atm(10.0L) = 2.40atm(V2)

V2 = 1208 L

B.Charles’ Law(Temperature vs. Volume)

• 1.Charles’ Law = at constant pressure, the volume of a gas is directly proportional to temperature (K).2.Volume Temperature3.Ex: if you put a balloon in the freezer, it will shrink in size, take it out and it will expand!

4. Calculation: V1 = V2 T1 T2

5. DRAW!

Calculating Charles’ Law

1.Calculation:– V1 = V2 V = volume, T = temperature (K) T1 T22.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!) K= 273+31=304 K= 273+22=295

3.0 L = V2295 K 304K V2 = 3.1 L

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

1. Gay-Lussac’s Law = the pressure of a gas is directly proportional to the temperature, in Kelvin, at a constant volume.2.Pressure Temperature3.Calculation:

P1 = P2T1 T2

4. DRAW!

Calculating Gay-Lussac’s Law1.Calculation:

P1 = P2 P = pressure, T = temperature (K) T1 T22.Ex: If a can at a of pressure is 103 kPa at 25°C is thrown into a fire, what will the resulting pressure be at 928°C? K= 273+25= 298 103 kPa = _P2_

298 K 1201 K P2 = 415 kPa

D.) Combined Gas Law Combines the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law. 1.Combined Gas Law: P1V1 = P2V2

T1 T22.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 303K

V2 = 1.7L (

STPStandard Temperature & PressureUsed when performing calculations on gases. • The standard temperature is

273 K (0°C or 32°F) &

• Standard pressure is 1 atm.

Converting from 0°C(Celcius) to K(Kelvin)

K= 273 + °CEx: Given temp. is 25°C.K=273+25= 298

(Stop here)

Gas Law OverviewGas Law Proportion Variable Constant Calculation Graph

Boyle

Charles

Gay-Lussac

Combined

Gas Law OverviewGas Law Proportion Variable Constant Formula Graph

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

Gas Law OverviewGas Law Proportion Variable Constant Formula

Boyle Inverse Pressure, volume

Temp P1V1=P2V2

Charles Direct Volume, temp

Pressure V1 = V2 T1 T2

Gay-Lussac Direct Pressure, temp

Volume P1 = P2T1 T2

Combined Pressure, temp,

volume

P1V1 = P2V2 T1 T2

Ideal Gases

E.Ideal Gas Law Calculation

• Ideal Gas Constant (R) = 8.31 L•kPa/K•mol• 1. Ideal Gas Law = PV = nRT; n = # of

moles2.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

Gas Molecules:Mixtures + Movements

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

(Standard Temp is 0 0C. & Pressure is 1atm, 70mmHg,...)

At STP!!