U NIT 7 “T HE B EHAVIOR OF G ASES ” Chemistry CDO High School

V ARIABLES THAT DESCRIBE A G AS The four variables and their common units: 1. pressure (P) in kilopascals 2. volume (V) in Liters 3. temperature (T) in Kelvin 4. amount (n) in moles

1. P RESSURE OF G AS a measure of the force exerted by the gas on the walls of a container The greater the number of collisions between gas particles and the wall the greater the pressure

P RESSURE C ONVERSIONS 1 atm = kPa = 760 mmHg = 760 torr The pressure in Tucson 668 mmHg, what is that pressure in: atm kPa torr

2. A MOUNT OF G AS Increasing the number of gas particles increases the number of collisions thus, the pressure increases

P RESSURE AND THE NUMBER OF MOLECULES ARE DIRECTLY RELATED Gases naturally move from areas of high pressure to low pressure, because there is empty space to move into

3. V OLUME OF G AS As volume decreases, pressure increases. Thus, volume and pressure are inversely related to each other

4. T EMPERATURE OF G AS Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly related)

T HE G AS L AWS

#1. B OYLE ’ S L AW Pressure x Volume = a constant Equation: P 1 V 1 = P 2 V 2 (T = constant) P 1 = initial pressure V 1 = initial volume P 2 = final pressure V 2 = final volume Gas pressure is inversely proportional to the volume, when temperature is held constant.

#2. C HARLES ’ S L AW The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant.

C ONVERTING C ELSIUS TO K ELVIN Gas law problems involving temperature will always require that the temperature be in Kelvin. Kelvin =  C °C = Kelvin and

#3. G AY -L USSAC ’ S L AW The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. V is constant

#4. A VOGADRO ’ S L AW

#5. T HE C OMBINED G AS L AW The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

The combined gas law contains all the other gas laws! If the temperature remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Boyle’s Law

The combined gas law contains all the other gas laws! If the pressure remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Charles’s Law

u The combined gas law contains all the other gas laws! u If the volume remains constant... P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Gay-Lussac’s Law

#6. T HE I DEAL G AS L AW #1 Equation: PV = nRT Ideal Gas Constant (R) R = (L kPa) / (mol K) The other units must match the value of the constant, in order to cancel out.

#7. I DEAL G AS L AW 2 PVmm = gRT g = mass, in grams mm = molar mass, in g/mol

I DEAL G AS E QUATION #3 Density is mass divided by volume Pmm = dRT d = density

#8 D ALTON ’ S L AW OF P ARTIAL P RESSURES For a mixture of gases in a container, P Total = P 1 + P 2 + P P 1 represents the “partial pressure”, or the contribution by that gas. Dalton’s Law is particularly useful in calculating the pressure of gases collected over water.

Collecting a gas over water – one of the experiments in this unit involves this. Connected to gas generator

If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3: 2 atm + 1 atm + 3 atm = 6 atm Sample Problem 14.6, page

I DEAL G ASES DON ’ T EXIST, BECAUSE : 1. Molecules do take up space 2. There are attractive forces between particles - otherwise there would be no liquids formed

R EAL G ASES BEHAVE LIKE I DEAL G ASES... When the molecules are far apart. The molecules do not take up as big a percentage of the space We can ignore the particle volume. This is at low pressure

R EAL G ASES BEHAVE LIKE I DEAL G ASES … When molecules are moving fast This is at high temperature Collisions are harder and faster. Molecules are not next to each other very long. Attractive forces can’t play a role.

D IFFUSION IS : Effusion: Gas escaping through a tiny hole in a container. Both of these depend on the molar mass of the particle, which determines the speed. u Molecules moving from areas of high concentration to low concentration. u Example: perfume molecules spreading across the room.

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Molecules move from areas of high concentration to low concentration. Fig , p. 435

Effusion: a gas escapes through a tiny hole in its container -Think of a nail in your car tire… Diffusion and effusion are explained by the next gas law: Graham’s