Chapter 14-Gases

Dr. Walker

State of Matter

• Gases are one of the four states of matter along with solids, liquids, and plasma

Conversion to Gases

• From liquids → Evaporation

– Example: Boiling water

• From solids → Sublimation

– Example: Dry Ice (CO2)

How Are Gases Different?

• Gases are considered Fluids

– Gas particles “flow” because they are far apart and move past each other easily.

How Are Gases Different?

• Low Density

– In a solid, particles are locked in place.

– In a liquid, particles are free to move around, but the particles are still fairly close together.

– In a gas, particles are MUCH farther apart. As a result, gases are mostly empty space, and therefore have a lower density.

How Are Gases Different?

• Gases fill their container

– A solid has a definitive shape and volume.

– A liquid has a definitive volume, but takes the shape of its container.

– A gas takes the volume and shape of its container.

Filling A Container

• Gases fill their containers because they have fewer attractive forces keeping them together.

– No surface tension or London dispersion forces.

• As a result, gases expand until they hit some barrier, i. e., the sides of its container.

• Gases

– Lower intermolecular forces

– More entropy (freedom of movement) http://archivedemo.cnx.org/resources/99c7f7d4b6b2e63894a1a13d4f04329990d6c8ed/CNX_Chem_10_01_KMTPhases1.jpg

How Are Gases Different?

• Gases Are Compressible

– Since gas molecules are far apart, the distance between them can be manipulated.

– Applying pressure to a gas will force the molecules closer together.

You’ve Got Me Under Pressure

• Force is acceleration of a mass

– Force is measured in Newtons (N)

– 1 N = 1 kg x m/s2

• Pressure is force exerted over a specific area

• The SI unit for pressure is the Pascal (Pa)

– 1 Pa = 1 N/m2

Different Units of Pressure

Unit Abbreviation # of Pascals

Atmosphere atm 101,325 Pa

Bar bar 100,025 Pa

Mm Hg Mm Hg 133.322 Pa

Pounds per

square inch

psi 6893 Pa

Kinetic-Molecular Theory

• Predicts Gas Behavior.

• Gas particles are in constant, random motion.

• Gas particles are fluid and move past each other easily.

• Gas particles create pressure by colliding with the sides of its container.

Temperature

• With molecules in random motion, they have kinetic energy.

• Not all molecules move at the same speed.

• As a result, temperature is a measure of the AVERAGE kinetic energy of gas molecules.

Measurable Properties

• For a gas, we can measure:

– Temperature (T)

– Pressure (P)

– Total Volume (V)

– Number of moles (n)

Problem Solving

• Usually when we solve problems, you are given all but one piece of information, which you are required to solve.

• The problems in this unit will be no different.

Boyle’s Law

• Boyle found that as pressure on a gas increases in a closed container at constant temperature, the volume decreases.

• Another way to state this: volume and pressure are inversely proportional.

A Representation of Boyle’s Law

Benson, Tom. “Boyle’s Law” <www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html >

Temperature-Volume Relationship

• Heating a gas will make it expand. Cooling a gas will make it contract.

• Have you ever left a balloon in your car overnight to see it smaller the next day?

• The balloon contracted with the colder temperature, illustrating this relationship.

Charles’s Law

• Charles’s Law states temperature and volume are proportional to each other at constant pressure.

Charles’s Law

• A hot air balloon demonstrates Charles’s Law. The air in balloons must be constantly heated. Otherwise, the air in the balloon will cool, the volume of the balloon will decrease, and the balloon will fall. http://z.about.com/d/inventors/1/0/1/U/hydrogen_balloon.jpg

Combining Boyle and Charles

• The Combined Gas Law!!

• P1V1 = P2V2

T1 T2

• How do we solve these problems?

– Plug in what you have

– Ignore what you don’t

– Find your unknown

An Example of Boyle’s Law

• A given sample of gas occupies 523 mL at 1.00 atm at constant temperature. If the pressure is increased to 1.97 atm, what is the new volume of the gas?

How Do We Solve?

• Organize your information

– P1 = 1.00 atm

– V1 = 523 mL

– P2 = 1.97 atm

– V2 = ???

– No temperature is given – ignore it!

How Do We Solve?

• Plan Work

– P1V1 = P2V2

– (1.00 atm)(523 mL) = (1.97 atm)(V2)

• Solve for Unknown

– V2 = (1.00 atm)(523 mL)/(1.97 atm)

– V2 = 265 mL

An Example of Charles’s Law

• A balloon is inflated to 665 mL volume at 27 C. It is immersed in a dry ice bath at -78.5 C. What is the new volume, assuming constant pressure??

An Example of Charles’s Law

• A balloon is inflated to 665 mL volume at 27 C. It is immersed in a dry ice bath at -78.5 C. What is the new volume, assuming constant pressure??

– Note: Anything with temperature must use the Kelvin scale. If the temperature is not in Kelvin, you must convert it!

– K = C + 273

– C = K - 273

How Do We Solve?

• Organize Information

– T1 = 300 K

– V1 = 665 mL

– T2 = 194.5 K

– V2 = ???

– Pressure isn’t given – ignore it!

How Do We Solve?

• Plan Work

– V1/T1 = V2/T2

– 665 mL/300 K = V2/194.5 K

• Solve for Unknown

– V2 = (665 mL)(194.5 K)/300 K

– V2 = 431 mL

Temperature – Pressure Relationship

• Temperature = Average kinetic energy of gas molecules.

• Pressure results from collisions of particles with walls of container.

• If the temperature is raised, the particles collide with the container with more force, creating more pressure (Gay-Lussac’s Law).

Volume-Molar Relationships

• Amedeo Avogadro proposed equal volumes of all gases under the same conditions have the same number of particles.

Write all

Avogadro’s Law

• Gas volume is directly proportional to number of moles of a gas at the same pressure and temperature.

• Covered this material during mole conversions

• V = k n

Avogadro’s Law

• Gas volume varies with temperature and pressure, so a standard set of conditions must be defined.

• The volume of any gas is 22.4 L at 0oC (273 K) and 1 atm. These conditions are known as standard temperature and pressure (STP).

Ideal Gases vs. Real Gases

• Ideal Gases

– “Point mass” – assumes almost no mass and no volume

– Collisions are elastic – no attractive or repulsive forces take place

• Real Gases

– The above points don’t work in real gases – they are assumptions used to model gas behavior

The Ideal Gas Law

• Relates four separate gas laws:

– Boyle (Pressure/Volume)

– Charles (Temperature/Volume)

– Guy-Lussac (Temperature/Pressure)

– Avogadro (Volume/Moles)

The Ideal Gas Law

• The Ideal Gas Law combines all of these equations into one relationship:

• PV = nRT

• R is a proportionality constant and depends on units used for pressure and volume.

• The exact value of R depends on the units used. It will ALWAYS be given! This is a big hint that you need to use the Ideal Gas Law

An example

• How many moles of gas are contained in 22.4 L at 101.325 kPa and 0o C? (R = 8.314 LkPa/moleK)

How do we solve?

• Organize Information

– V = 22.4 L

– P = 101.325 kPa

– T = 0o C + 273 = 273 K (must be in Kelvin)

– R = 8.314 LkPa/moleK

– n = ????

How do we solve?

• Plan Work

– PV = nRT

– (101.325 kPa)(22.4 L) = n(8.314)(273K)

• Solve for unknown

– n = 1.00 mole

Diffusion

• Diffusion: movement of particles from regions of high density to regions of low density

Effusion • Effusion: passage of gas under

pressure through a tiny opening

– Rate inversely proportional to square root of gas’s density

– Kinetic Energy = 1/2 mv2

– If two different gases have the same kinetic energy (temperature):

• Different mass – different velocity

• If the mass term is smaller, the velocity term is larger

– Translation – smallest gases travel the fastest!!

Dalton’s Law of Partial Pressure

• In 1805, John Dalton showed that each gas in a mixture of gases exerts a certain pressure as if it were alone.

• For example, if you bottled air in a jar, the different gases (O2, CO2, N2, etc.) would each exert a certain pressure on the walls of the jar.

Dalton’s Law of Partial Pressure

• Ptotal = PA + PB + Pc.....

• Ptotal is the total pressure exerted by the gas.

• PA, PB, and PC are the partial pressures of each gas individually.

Dalton’s Law of Partial Pressure

• A mixture of H2 and O2 gas exerts a total pressure of 3.0 atm. If the partial pressure of O2 is 2.8 atm, what is the partial pressure of H2?

Dalton’s Law of Partial Pressure

• A mixture of H2 and O2 gas exerts a total pressure of 3.0 atm. If the partial pressure of O2 is 2.8 atm, what is the partial pressure of H2?

3.0 atm = 2.8 atm + PH2 PH2= 0.2 atm

Dalton’s Law of Partial Pressure

• A mixture of Ar and He gases has a total pressure of 50 atm. What is the partial pressure of Ar if it is 20% of the mixture?

Dalton’s Law of Partial Pressure

• A mixture of Ar and He gases has a total pressure of 50 atm. What is the partial pressure of Ar if it is 20% of the mixture?

• Divide percentage by 100

• 50 atm x 0.2 = 10 atm for Ar

The Highlights

• Gases are fluids, have low density, and are compressible.

• Gases expand to fill their entire container and exert pressure and all directions.

• The average kinetic energy of a gas is proportional to its temperature.

The Highlights

• The pressure and volume of a gas at constant temperature are inversely proportional (Boyle)

• The volume of a gas at constant pressure is proportional to the absolute temperature (Charles)

• The pressure of a gas at constant volume is proportional to the absolute temperature (Gay-Lussac)

• Equal volumes of gas under the same conditions contain an equal number of moles of gas (Avogadro)

The Highlights

• The ideal gas law is the complete statement of the relations between P, V, T, and n in a quantity of a gas.

• Each gas in a mixture produces a pressure as if it were alone in a container (Dalton’s Law of Partial Pressures).