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The Gas Laws

- Boyle’s Law
- Charles’ Law
- Gay-Lussac’s Law
- 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↓

Volume

L

P1V1 = P2V2

If you squeeze a gas sample, you make its volume smaller.

Pressure (kPa)

Now . . . a container where the volume can change (syringe)

Moveable piston

↕

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.

V1V2

T1 T2

=

- increase AKE
- increase the speed of
- the particles
- the walls of a flexible
- container expand –
- think of hot air balloons!

Volume

L

Temperature (K)

B

Steel cylinder (2L)

contains 500 molecules of O2 at 400 K

Steel cylinder (2L) contains 500 molecules of O2 at 800 K

- In which system do the O2 molecules have the highest average kinetic energy?
- In which system will the particles collide with the container walls with the greatest force?
- In which system is the pressure higher?

B

B

B

Gay-Lussac’s Law

Gay-Lussac’s Law – the pressure of a gas is directly proportional to its absolute temperature at a constant volume.

P1P2

T1 T2

Pressure

(atm)

=

Temperature (K)

To remember which constants go with which law . . .

Boyle’s Law – Temperature is constant

Charles’ Law – Pressure is constant

Gay-Lussac’s Law – Volume is constant

BLT

Cheese Pizza

Green Veggies

Combined Gas Law

P1V1P2V2

T1 T2

=

The equation is found on Table T. Note that all temperatures must be in Kelvin!

Units used to describe gas samples:

Volume

Liter (L)

Milliliter (mL)

1000 mL = 1L

Temperature

Kelvin ONLY

Pressure

Atmosphere (atm)

Kilopascale (kPa)

1 atm = 101.3 kPa

1 atm = 760 mm Hg

1 atm = 760 torr

Avogadro’s Law

Avogadro’s Law – equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

H2

O2

CO2

1 mole of ANY gas takes up a volume of 22.4 L at STP.

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.

- 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.

Ptotal = PA + PB + PC

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

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