“The Behavior of Gases”

CompressibilityGases can expand to fill its

container, unlike solids or liquidsThe reverse is also true:

They are easily compressed, or squeezed into a smaller volume

Compressibility This is the idea behind placing “air

bags” in automobilesIn an accident, the air compresses

more than the steering wheel or dash when you strike it

The impact forces the gas particles closer together, because there is a lot of empty space between them.

Variables that describe a Gas

The four variables: ( STP)

1. Pressure (P) in 101.3 kilopascals, 760 mmHg, 760 Torr, and 1 Atm

2. Volume (V) in Liters, ml

3. Temperature (T) in 273 Kelvin

4. Amount (n) in moles

Volume

Pressure

TemperatureAmount of space enclosed by a shape or object

Force exerted on a surface per unit area.

Measure of the average heat or thermal energy of the particles in a substance.

1. Amount of GasWhen we inflate a balloon, we are

adding gas molecules. Increasing the number of gas

particles increases the number of collisions

thus, the pressure increases If temperature is constant, then

doubling the number of particles doubles the pressure

2. Volume of Gas In a smaller container, the

molecules have less room to move.

The particles hit the sides of the container more often.

As volume decreases, pressure increases. (think of a syringe)Thus, volume and pressure are

inversely proportional to each other

3. Temperature of Gas

Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly proportional)The molecules hit the walls harder, and

more frequently!

1. The volume of a gas particle is miniscule compared to the distance between themselves and other molecules.

2. Gas particles undergo no intermolecular attractions or repulsions.

3. Gas particles are in continuous, random motion.

4. Collisions between gas particles are perfectly elastic.

5. The average kinetic energy is the same for all gases at a given temperature, regardless of the identity of the gas.

The Gas Laws

Robert Boyle(1627-1691)

Boyle’s Law

Equation: P1V1 = P2V2

Gas pressure is inversely proportional to the volume, when temperature is held constant.

Graph of Boyle’s Law – page 418

Boyle’s Law says the pressure is inverse to the volume.

Note that when the volume goes up, the pressure goes down

A balloon contains 7.2 L of He. The pressure is reduced to 2.00 atm and theballoon expands to occupy a volume of 25.1 L. What was the initial pressureexerted on the balloon?

Jacques Charles (1746-1823)

Charles’s Law The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant.

VT

VT

P1

1

2

2 ( constant)

Temperature Must Be in Kelvin.

Converting Celsius to Kelvin•Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.)

Kelvin = C + 273 °C = Kelvin - 273

A balloon is filled with 3.0 L of helium at 310 K. The balloon is placed in an oven where the temperature reaches 340 K. What is the new volume of the balloon?

Joseph Louis Gay-Lussac (1778 – 1850)

Gay-Lussac’s Law •The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.

2

2

1

1

T

P

T

P

#4. The Combined Gas LawThe combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

2

22

1

11

T

VP

T

VP

The equation for Avogadro's Law is V/n=k. V is the volume of the gas, n is the amount of substance of the gas, and k is a proportionality constant.

5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?

Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

•P1 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.

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 434

1 2 3 4

8. Graham’s Law

The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.

Derived from: Kinetic energy = 1/2 mv2

m = the molar mass, and v = the velocity.

RateA MassB

RateB MassA

=

Ideal Gas Law

The Ideal Gas Law

Equation: P x V = n x R x T

Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the Temperature in Kelvin. R= .0821

What volume is occupied by 5.03 g of O2 at 28°C and a pressure of 422 mmHg?

Density Density is mass divided by volume

m

V

so,

m M P

V R T

D =

D = =

Ideal Gases don’t exist, because:

1. Molecules do take up space

2. There are attractive forces between particles

- otherwise there would be no liquids formed

Real Gases behave like Ideal Gases...

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

Real Gases behave like Ideal Gases…

When molecules are moving fastThis 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.

Diffusion 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.

Molecules moving from areas of high concentration to low concentration.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. 14.18, 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

Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436

With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and

effuse faster than gases of higher molar mass.

Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases!

Graham’s Law