The Gas Laws

1.Boyle’s Law

2.Charles’ Law

3.Gay-Lussac’s Law

4.Avogadro’s Law

Boyle’s Law

Boyle’s Law – at constant temperature, the

volume of the gas increases as the pressure

decreases. The volume of the gas decreases and

the pressure increases.V↑ P↓

V

o

l

u

m

e

L

Pressure (kPa)

If you squeeze a

gas sample, you

make its volume

smaller.

Moveable

piston

↕

Now . . . a

container where

the volume can

change (syringe)

Same

temperature

Volume is 100 mL at

25°C

Volume is 50 mL at

25°C

In which system is the pressure higher? (Which has the greater number

of collisions with the walls and each other?)

Charles’ Law

Charles’ Law – at a constant pressure, the

volume of a gas increases as the temperature of the

gas increases and the volume decreases when the

temperature decreases.

V

o

l

u

m

e

L

Temperature (K)

V1 V2

T1 T2=

• increase AKE

• increase the speed of

the particles

• the walls of a flexible

container expand –

think of hot air balloons!

Steel cylinder (2L)

contains 500

molecules of O2 at

400 K

Steel cylinder (2L)

contains 500

molecules of O2 at

800 K

1. In which system do the O2 molecules have the highest average kinetic

energy?

2. In which system will the particles collide with the container walls with the

greatest force?

3. In which system is the pressure higher? B

B

B

Gay-Lussac’s LawGay-Lussac’s Law – the pressure of a gas is

directly proportional to its absolute temperature at

a constant volume.

Pressure

(atm)

Temperature (K)

P1 P2

T1 T2

=

Volume Units:

Volume

Liter (L)

Milliliter (mL)

1000 mL = 1L

1mL= 1cm3

Temperature Units :Fahrenheit -(Based on the freezing point of brine) ……….i.e.

useless and dumb

Celsius- (Based on the freezing point of water)

Kelvin- Based on the theoretical concept of absolute zero

0K=-273.15°C

***This is the only acceptable unit for temperature***

To convert temperatures:

[°C] = ([°F] - 32) × 5/9

[°F] = [°C] × 9/5 + 32

_____________________

[°C] + 273.15= °K

Pressure Units:Atmosphere (atm)- Based of the pressure of the atmosphere of

planet earth

Kilopascal (kPa)- Based on the pressure of 1 newton/square meter

*1 atm = 101.3 kPa

Millimeters Mercury (mm Hg)- Based on the volume of mercury in a

baromoter.

*1 atm = 760 mm Hg

Torr- the mm Hg measurement is named after the scientist that

discovered it Torricelli

1 torr= 1mm Hg

Combined Gas Law

P1V1 P2V2

T1 T2=

The equation is found on Note that all

temperatures must be in Kelvin!

Similar measurements must have the

same units.

Avogadro’s LawAvogadro’s Law – equal volumes of gases

at the same temperature and pressure

contain equal numbers of molecules.

1 mole of ANY gas takes up a volume of

22.4 L at STP.

H2 O2 CO2

Ideal Gases

• Gases whose behavior can be predicted

by the kinetic molecular theory are called

ideal, or perfect, gases. No gases are

truly ideal because no gas totally obeys all

of the gas laws.

• An ideal gas is an imaginary gas that is

perfect and does follow everything

perfectly.

Ideal Gases, continued

An ideal gas does not condense to a

liquid at low temperatures

An ideal gas does not have forces of

attraction or repulsion between

particles

An ideal gas is composed of particles

that have no volume.

Real Gas Vs. Ideal Gas

A real gas is most like an ideal

gas when the real gas is at a low

pressure and a high temperature.

The gases that act most like ideal

gases are the small mass ones –

hydrogen and helium.

Ideal Gas Equation

P V = n R T

Universal Gas ConstantVolume

No. of moles

Temperature

Pressure

R = 0.0821 atm * L / mol K

**All units must match R from

here on out.**

Diffusion

• movement of particles from areas of high

concentrations to areas of low concentration.

•Gases diffuse and mix with other gases very rapidly

due to their rapid motion. (Think ammonia, tuna or

skunk smell.)

•It eventually reaches equilibrium and the mixture is

homogeneous.

Entropy is the randomness of particles.

Effusion – the passage of gas under pressure

through a small opening. (Gases effuse through

a hole in your tire!)

Two More Laws!!Graham’s Law – Particles of low molar mass travel

faster than heavier particles.

Hydrogen effuses 4 times faster than oxygen.

Dalton’s Law of Partial Pressure -

In a mixture of gases, each gas exerts a certain pressure

as if it were alone. The pressure of each one of these

gases is called the partial pressure. The total pressure of

a mixture of gases is the sum of all of the partial

pressures.

Example:

A closed cylinder contains 3L of He, 1L of H2

and the total pressure in the system is 800 torr.

What is the partial pressure of the He?

Ptotal = PA + PB + PC

3L + 1L = 4L AND 4L = 800 torr

4L = 800 torr

4 4 → 1L = 200 torr

1L H2 200 torr

3L He 600 torr

4L gas 800 torr