GASES and the Kinetic Molecular Theory

A.Gas particles DO NOT attract or repel each other

B. Gas particles are much smaller than the distances between them

C. Gas particles are in constant, random motion

D. No kinetic energy is lost when gas particles collide

E. All gases have the same average kinetic energy at a given temperature

Kinetic energy is the energy of motion. The higher the temperature the higher the kinetic energy.

IDEAL GAS

AN IMAGINARY GAS THAT PERFECTLY FITS ALL THE ASSUMPTIONS OF THE KINETIC-MOLECULAR THEORY.

REAL GASA GAS THAT DOES NOT

BEHAVE COMPLETELY ACCORDING TO THE ASSUMPTIONS OF THE KINETIC-MOLECULAR THEORY.

The Kinetic Molecular Theory and the NATURE OF GASES

A. Gases expand and spread to take the shape and volume of their container

B. Gases are FLUIDS – they are able to flow (just like liquids)

C. Gases have a low density compared to liquids and solids

D. Gases are compressible

E. Gases are able to diffuse and effuse

DIFFUSION AND EFFUSION

• DIFFUSION IS SPONTANEOUS MIXING OF PARTICLES OF TWO SUBSTANCES CAUSED BY THEIR RANDOM MOTION.

• EFFUSION IS A PROCESS BY WHICH GAS PARTICLES PASS THROUGH A TINY OPENING.

Gas Solubility

• Solvent – substance doing the dissolving (often water)

• Solute – substance being dissolved

• To dissolve a gas in a liquid certain conditions must be met.– Low temperature of the solvent– High pressure above the solvent

Relationships for solubility of a gas:

• As the temperature increases the solubility of a gas decreases (inversely related)

• As pressure above the solvent increases the solubility of the gas increases (directly related)

Examples of Solubility of Gases

• Thermal pollution – fish die because oxygen does not dissolve in the water, because the water is too hot.

• Carbonated drinks - the carbon dioxide must be pressurized to stay in the drink. Once the can is open pressure decreases; and the drink goes flat.

• Scuba diving – if you rise too fast and do not adjust for the decrease in pressure, you get bubbles of gas in your blood. This is called “the bends.”

DESCRIBING A GAS

You need:

• Volume

• Temperature

• Number of molecules

• Pressure

PRESSURE

• Force per unit area on a surface

• Pressure = force / area

• Atmospheric pressure is measured using a barometer.

UNITS for PRESSURE• Millimeters of Mercury (mm Hg)

because we use a mercury barometer• Torr named after Torricelli who invented the

barometer.• Atmosphere of pressure (atm)• Pascals (Pa) – named after Blaise Pascal

Relationships• 1 mm Hg = 1 torr• 1 atm = 760 torr = 760 mm Hg • 1 atm = 1.013 x 105 Pa = 101.35 kilopascals (kPa)

STPStandard Temperature &

Pressure• For purposes of comparison, scientists use

standard conditions to compare gases.

• 1 atm & 0oC (273 Kelvin)

• We must use Kelvin for the temperature instead of oC.

• Remember K = oC + 273

Graphing Relationships

• Direct Relationship – graph will be a straight line – As one goes up the other goes up

• Inverse Relationship – graph will be a hyperbola (curve)– As one goes up the other goes down

Remember

• Gases act least ideal under high pressure and low temperatures

GAS LAWS

BOYLE’S LAW

The VOLUME of a given amount of gas held at constant temperature varies INVERSELY with the PRESSURE

2211 VPVP

• Example:

• 4.0 liters of helium gas at a pressure of 1.2 atm is compressed to 2.5 liters, what is the new pressure?

V1 = 4.0 liters

P1 = 1.2 atm

V2 = 2.5 liters

P2 = ?

 

(1.2 atm)(4.0L) = (X)(2.5 L)

X = 1.9 atm

CHARLES’ LAW

The VOLUME of a given mass of gas is DIRECTLY proportional to its Kelvin TEMPERATURE

2

2

1

1

T

V

T

V

• A sample of gas at 40.0oC occupies a volume of 2.32 L. If the temperature is raised to 75.0oC, what will the volume be? Pressure is held constant.

• T1 = 40.0oC = 313 K

• V1 = 2.32 L

• T2 = 75.0oC = 348 K

• V2 = ?

• V2 = 2.58 Liters

GAY-LUSSAC’S LAW

The PRESSURE of a given mass of gas varies DIRECTLY with the Kelvin TEMPERATURE when the volume remains constant

2

2

1

1

T

P

T

P

The pressure of a gas in a tank is 3.20 atm at 22.0oC. If the temperature rises to 60.0oC, what will be the gas pressure in the tank?

P1 = 3.20 atm

T1 = 22.0oC = 295 K

P2 = ?

T2 = 60.0oC = 333 K

 

  

P2 = 3.61 atm

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

A gas at 110 kPa and 30.0oC fills a flexible container with an initial volume of 2.00 liters. If the temperature is raised to 80.0oC and the pressure increased to 440 kPa, what is the new volume?

P1 = 110 kPa

T1 = 30.0oC = 303 K

V1= 2.00 liters

P2 = 440 kPa

T2 = 80.0oC = 353 K

V2 = ?

 

• V2 = 0.58 Liters

DALTON’S LAW of PARTIAL PRESSURE

States that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the gases.

PT = P1 + P2 + P3 + . . .

Dalton’s Law Continued

Example: Air contains oxygen, nitrogen, carbon dioxide, & trace amounts of other gases. What is the partial pressure of oxygen at sea level if the total pressure is 760 mm Hg, PN2 = 593.4 mm Hg, PCO2 = 0.3 mm Hg, and Pothers = 7.1 mm Hg?

PT = P1 + P2 + P3 + . . .

Graham’s Law of Effusion

• Gases at the same temperature and pressure have the same kinetic energy, but different gases diffuse at different rates.

• The lighter the molar mass of an element or compound the faster it will spread.

• Small molecules effuse faster than large ones

• Example: Which of the following gases effuses faster, NH3 or CO2?

Avogadro’s Principle

• Equal volumes of gases at the same temperature and pressure contain equal numbers of particles

• Remember 1 mole = 6.02 x 1023 particles

• At STP (standard temperature & pressure)

1 mole = 22.4 liters

• This is called the molar volume

Ideal Gas Law

PV = nRTP – Pressure (atm)

V – Volume (liters)

n – number of moles

R – Gas Constant 0.0821 L atm/ mol K

T – Temperature (Kelvin)

Practice: If I have 4.0 moles of a gas at a

pressure of 5.6 atm and a volume

of 12 liters, what is the

temperature?

 n = 4.0 moles

P = 5.6 atm

V = 12 liters

T = ?

R = 0.0821 L atm/ mol K

T = PV / nR

T = 205 Kelvin

 

Gas Stoichiometry

• At STP, use stoichiometry and the molar volume (1 mol = 22.4 liters)

• If the gases are NOT at STP, you must use stoichiometry and the ideal gas formula.

At STP!

Practice: How many liters of CO2 are produced when 35.4 grams of C3H8 are combusted at STP?

 

C3H8 + O2 CO2 + H2O

Balance the equation first

  

Next, Convert grams to moles, moles to moles, then moles to liters. Use the molar volume 1 mole = 22.4 at STP.

 

NOT at STP!

Practice: If 5.0 Liters of nitrogen reacts completely by this reaction at 3.00 atm and 298 K, how many grams of ammonia are produced?

 

N2 + 3H2 2NH3