topic 12 topic 12 topic 12: kinetic theory table of contents topic 12 topic 12 basic concepts...

Topic 12Topic 12

Topic 12: Kinetic Theory

Table of ContentsTable of ContentsTopic 12Topic 12

Basic Concepts

Additional Concepts

• In the late 1800s, two scientists, Ludwig Boltzmann and James Maxwell, independently proposed a model to explain the properties of gases in terms of particles in motion. This model is now known as the kinetic-molecular theory.

Gases

Kinetic Theory: Basic ConceptsKinetic Theory: Basic ConceptsKinetic Theory: Basic ConceptsKinetic Theory: Basic Concepts

• The model makes the following assumptions about the size, motion, and energy of gas particles.

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• The particles in a gas are separated from one another by empty space.

Particle size

• The volume of the empty space is much greater than the volume of the gas particles themselves.

• Because gas particles are far apart, there are no significant attractive or repulsive forces among them.

Kinetic Theory: Basic ConceptsKinetic Theory: Basic ConceptsKinetic Theory: Basic ConceptsKinetic Theory: Basic ConceptsTopic 12Topic 12

• Gas particles are in constant, random motion. Until they bump into something (another particle or the side of a container), particles move in a straight line.

Particle motion

• When gas particles do collide with something, the collision is said to be elastic.

• An elastic collision is one in which no kinetic energy is lost.


Particle energy

• Mass and velocity determine the kinetic energy of a particle, as represented in the equation below.

KE = kinetic energym= mass of the particlev = velocity of the particle


Particle energy

• The velocity of a particle includes both its speed and its direction.

• Each particle in a sample containing only one gas will have the same mass but not the same velocity.

• Thus, all the particles in a sample of gas do not have the same kinetic energy.


Particle energy

• Temperature is a measure of the average kinetic energy of the particles in a sample of matter.

• At a given temperature, all gases have the same average kinetic energy.


Explaining the behavior of gases

• The kinetic-molecular theory explains the following behavior of gases.

• Low Density Density is a measure of mass per unit volume. The difference between the high density of a solid and the low density of a gas is due mainly to the large amount of space between the particles in the gas. There are fewer particles in a gas than in a solid of the same volume.



• Compression and expansion A gas will expand to fill its container. Thus, the density of a sample of gas will change with the volume of the container it is placed in. The gas will become more dense as it is compressed into a smaller container. The gas will become less dense as it expands in a larger container.


• Diffusion refers to the movement of one material through another, such as when onegas flows into a space already occupied by another gas.


• Diffusion Gas particles flow past each other easily because there are no significant forces of attraction between them.


• Effusion If you have ever seen a tire deflate from a puncture, you are familiar with effusion. Effusion is the escape of a gas through a small opening in its container.



Gas pressure

• When gas particles collide with the walls of their container, they exert pressure on the walls.

• Pressure is force per unit area.

• The pressure exerted by the particles in the atmosphere that surrounds Earth is called atmospheric pressure, or air pressure.

• Air pressure varies at different locations on Earth.


Gas pressure

• Air pressure at higher altitudes, such as on a mountaintop, is slightly lower than air pressure at sea level.


• At Earth’s surface, air pressure is approximately equal to the pressure exerted bya 1-kilogram mass on a square centimeter.

Gas pressure

• Air pressure is measured using a barometer.

• A barometer consists of a thin tube closed on one end and filled with mercury.


Gas pressure

• The tube is placed so that the level of the mercury is determined by air pressure.

• The mercury rises when the air pressure increases and falls when the air pressure decreases.


Forces of Attraction

• The attractive forces that hold particles together in ionic, covalent, and metallic bonds are called intramolecular forces.

• Intermolecular forces, which are weaker than intramolecular forces, also can hold particles together.

• Three types of intermolecular forces are described below: dispersion forces, dipole–dipole forces, and hydrogen bonds.


Dispersion forces

• Weak forces that result from temporary shifts in the density of electrons in electron clouds are called dispersion forces, or London forces.

• When two nonpolar molecules are in close contact, the electron cloud of one molecule repels the electron cloud of the other molecule.


Dispersion forces

• As a result, the electron density in each electron cloud is greater in one region of the cloud.

• Two temporary dipoles form.


Dispersion forces

• Weak dispersion forces exist between oppositely charged regions of the dipoles.

• Dispersion forces, which are the weakest intermolecular forces, are important only when no stronger forces are acting on the particles.

• Dispersion forces are noticeable between identical nonpolar molecules as the number of electrons involved increases.


Dipole–dipole forces

• Attractions between oppositely charged regions of polar molecules are called dipole–dipole forces.

• Polar molecules have a permanent dipole and orient themselves so that oppositely charged regions match up.

• Dipole–dipole forces are stronger than dispersion forces as long as the molecules being compared are similar in mass.


Hydrogen bonds

• A hydrogen bond is a dipole–dipole attraction that occurs between molecules containing a hydrogen atom bonded to a small, highly electronegative atom with at least one lone electron pair.


Hydrogen bonds

• The hydrogen must be bonded to a fluorine, an oxygen, or a nitrogen atom.

• Hydrogen bonds explain why water is a liquid at room temperature, while compounds of comparable mass are gases.


Liquids and Solids

• The kinetic-molecular theory also explains the behavior of liquids and solids.

• However, the forces of attraction between particles in liquids and solids must be considered as well as their energy of motion.


Liquids

• Liquids conform to the shape of their container but have a fixed volume.

• The particles in a liquid maintain a fixed volume because the forces of attraction between them limit their range of motion.


Density and compression

• The density of a liquid is much greater than that of its vapor at the same conditions.

• The higher density is due to intermolecular forces, which hold the particles together.


Fluidity

• Fluidity is the ability to flow.

• Liquids are less fluid than gases.


Viscosity

• A measure of the resistance of a liquid to flow is called viscosity.

• The stronger the intermolecular forces, the higher is the viscosity.

• Viscosity also increases with the mass of a liquid’s particles and the length of molecule chains.


Surface tension

• The energy required to increase the surface area of a liquid by a given amount is called surface tension.

• Surface tension is a measure of the inward pull by particles in the interior of the liquid.


Capillary action • The movement of a liquid up a narrow glass

tube is called capillary action, or capillarity. • Capillary action occurs when adhesive

forces are greater than cohesive forces. • Adhesion is the force of attraction between

molecules that are different, such as water molecules and the molecules of silicon dioxide in glass.

• Cohesion is the force of attraction between identical molecules, such as water molecules.


Solids

• Strong attractive forces between the particles in a solid limit the movement of the particles to vibrations around fixed locations.

• Thus, solids have a definite shape and volume.

• Because solids are so dense, ordinary amounts of pressure will not compress them into a smaller volume.


• A solid whose atoms, ions, or molecules are arranged in an orderly, geometric, three-dimensional structure (lattice) is called a crystalline solid.

Crystalline solids


Crystalline solids • The individual pieces of a crystalline solid

are called crystals. • Crystalline solids are divided into five

categories based on the types of particles they contain: • atomic solids • molecular solids • covalent network solids • ionic solids • metallic solids


Crystalline solids

• Noble gases are atomic solids whose properties reflect the weak dispersion forces between the atoms.

• Molecular solids are held together by dispersion forces, dipole–dipole forces, or hydrogen bonds.

• Elements that are able to form multiple covalent bonds, such as carbon and silicon, are able to form covalent network solids.


• Metallic solids consist of positive metal ions surrounded by a sea of mobile electrons.

Crystalline solids

• The type of ions and the ratio of ions determine the structure of the lattice and the shape of the crystal in an ionic solid.


Crystalline solids • Not all solids are crystalline. • The particles in an amorphous solid are not

arranged in a regular, repeating pattern and do not form crystals.


Crystalline solids

• Examples of amorphous solids include glass, rubber, and many plastics.


Phase Changes

• Most substances can exist in three states— solid, liquid, and gas—depending on the temperature and pressure.


Phase Changes• States of substances are called phases when

they coexist as physically distinct parts of a mixture, such as ice water.

• When energy is added to or taken away from a system, one phase can change into another.


temperature at which the forces holding the crystal lattice together are broken and the solid becomes a liquid.

• The melting point of a crystalline solid is the

Phase changes that require energy

• The amount of energy required to melt one mole of a solid depends on the strength of the forces keeping the particles together.



• If a substance is usually a liquid at room temperature (as water is), the gas phase is called a vapor.

• Vaporization is the process by which a liquid changes into a gas or vapor.

• When vaporization occurs only at the surface of a liquid, the process is called evaporation.



• Vapor pressure is the pressure exerted by a vapor over a liquid.

• As temperature increases, water molecules gain kinetic energy and vapor pressure increases.



• When the vapor pressure of a liquid equals atmospheric pressure, the liquid has reached its boiling point, which is 100°C for water at sea level.

• At this point, molecules throughout the liquid have the energy to enter the gas or vapor phase.



• The process by which a solid changes directly into a gas without first becoming a liquid is called sublimation.

• Solid air fresheners and dry ice are examples of solids that sublime.



• At very low temperatures, ice will sublime in a short amount of time.

• This property of ice is used to preserve freeze-dried foods.


Phase changes that release energy • Some phase changes release energy into their

surroundings. • For example, when a vapor

loses energy, it may change into a liquid.

• Condensation is the process by which a gas or vapor becomes a liquid. It is the reverse of vaporization.


Phase changes that release energy

• Water vapor undergoes condensation when its molecules lose energy, their velocity decreases, and hydrogen bonds begin to form between them.

• When hydrogen bonds form, energy is released.



• When water is placed in a freezer, heat is removed from the water.

• When enough energy has been removed, the hydrogen bonds keep the molecules frozen in set positions.

• The freezing point is the temperature at which a liquid becomes a crystalline solid.



• When a substance changes from a gas or vapor directly into a solid without first becoming a liquid, the process is called deposition.


Phase diagrams

• Temperature and pressure control the phase of a substance.

• A phase diagram is a graph of pressure versus temperature that shows in which phase a substance exists under different conditions of temperature and pressure.

• A phase diagram typically has three regions, each representing a different phase and three curves that separate each phase.


Phase diagrams

• The points on the curves indicate conditions under which two phases coexist.

• The phase diagram for each substance is different because the normal boiling and freezing points of substances are different.


Phase diagrams • The triple point is the point on a phase

diagram that represents the temperature and pressure at which three phases of a substance can coexist.

• All six phase changes can occur at the triple point: freezing and melting, evaporation and condensation, sublimation and deposition.

• The critical point indicates the critical pressure and the critical temperature above which a substance cannot exist as a liquid.


Basic Assessment QuestionsBasic Assessment Questions

Question 1

Classify each crystalline solid as molecular, ionic, covalent network, or metallic.

A. NaCl

B. SiO2

C. Fe

D. H2O

Topic 12Topic 12

Basic Assessment QuestionsBasic Assessment Questions

Answers

A. NaCl

B. SiO2

C. Fe

ionic

covalent network

metallic

D. H2O molecular

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Classify each of the following phase changes.

Question 2

Basic Assessment QuestionsBasic Assessment QuestionsTopic 12Topic 12

dry ice (solid carbon dioxide) to carbon dioxide gas

sublimation

Answer 2a

Question 2a


ice to liquid water

melting

Answer 2b

Question 2b


liquid bromine to bromine vapor

vaporization

Answer 2c

Question 2c


moth balls giving off a pungent odor

sublimation

Answer 2d

Question 2d


liquid water to ice

freezing

Answer 2e

Question 2e


water vapor to liquid water

condensation

Answer 2f

Question 2f


Kinetic Theory: Additional ConceptsKinetic Theory: Additional Concepts Kinetic Theory: Additional ConceptsKinetic Theory: Additional Concepts Topic 12Topic 12

Additional Concepts

Kinetic Theory: Additional ConceptsKinetic Theory: Additional Concepts Kinetic Theory: Additional ConceptsKinetic Theory: Additional Concepts

Diffusion

• The motions of particles of a gas cause them to spread out to fill the container uniformly.

• Diffusion is the process by which particles of matter fill a space because of random motion.

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Diffusion

• If you have seen dye such as food coloring spreading through a liquid, you have watched diffusion.

• Your sense of smell depends on diffusion and air currents for you to detect molecules of a gas that waft by your nose.


Diffusion• Diffusion is slow, but in your lungs,

oxygen reaches your blood rapidly enough by diffusion.

• Oxygen diffuses across the walls of tiny blood vessels called capillaries from the air sacs of your lungs that fill with air each time you inhale.

• The rate of diffusion of a gas depends upon its kinetic energy, that is, on the mass and speed of its molecules.


Diffusion

• The rate of diffusion depends mostly on the mass of the particles.

• Lighter particles diffuse more quickly than heavier particles.

• Because lighter particles have the same average kinetic energy as do heavier particles at the same temperature, lighter particles must have, on average, a greater velocity.


Effusion

• Graham’s law of effusion states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass.


Effusion

• Using Graham’s law, you can also compare the rates of diffusion for two gases.


Finding the Ratio of Diffusion Rates

• The molar mass of helium is 4.00 g/mol; the molar mass of air is 29.0 g/mol.

• What is the ratio of their diffusion rates? Which gas diffuses faster?


Finding the Ratio of Diffusion Rates

• The ratio of the diffusion rates is 2.69. Helium diffuses about 2.7 times faster than air does.


Gas pressure

• The pascal (Pa) is the SI unit of pressure. One pascal is equal to a force of one newton per square meter.

• Some scientists use other units of pressure. • For example, engineers use pounds per

square inch. • Barometers and manometers measure

pressure in millimeters of mercury (mm Hg).

• A unit called the torr is equal to 1 mm Hg.


Gas pressure

• Air pressure is often reported in a unit called an atmosphere (atm).

• One atmosphere is equal to 760 mm Hg, 760 torr, or 101.3 kilopascals (kPa).

• These are all defined units; therefore, they have as many significant figures as needed when used in calculations.


Dalton’s law of partial pressures

• Dalton found that each gas in a mixture exerts pressure independently of the other gases.

• Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture, as shown below.


Dalton’s law of partial pressures

• The portion of the total pressure (Ptotal) exerted by one of the gases is called its partial pressure (Pn).

• The partial pressure of a gas depends on the number of moles of the gas, the size of the container, and the temperature of the mixture.

• The partial pressure of one mole of any gas is the same at a given temperature and pressure.


Finding the Partial Pressure of a Gas

• Air is made up of four main gases: N2, O2, Ar, and CO2.

• Air pressure at sea level is approximately 760 mm Hg.

• Calculate the partial pressure of oxygen, given the following partial pressures: N2, 594 mm Hg; Ar, 7.10 mm Hg; and CO2, 0.27 mm Hg.



• Use Dalton’s law of partial pressures to solve the problem.



• The partial pressure of oxygen is about 159 mm Hg.


Additional Assessment QuestionsAdditional Assessment Questions

Calculate the ratio of diffusion rates for neon and helium. Which gas diffuses faster? About how much faster?

Question 1 Topic 12Topic 12

He; about 2.25 times faster

Answer

Additional Assessment QuestionsAdditional Assessment QuestionsTopic 12Topic 12

Calculate the ratio of diffusion rates for ammonia (NH3) and carbon dioxide (CO2). Which gas diffuses more rapidly?

Question 2


1.61; NH3

Answer


What is the partial pressure of oxygen gas in a mixture of nitrogen gas and oxygen gas with a total pressure of 0.48 atm if the partial pressure of nitrogen gas is 0.24 atm?

Question 3


0.24 atm

Answer


Find the total pressure of a mixture that contains three gases with the following partial pressures: 6.6 kPa, 3.2 kPa, and 1.2 kPa.

Question 4


11.0 kPa

Answer


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