UNIT VIII – STATES OF MATTER AND

THE GAS LAWS

The Kinetic Molecular Theory

Ideal Gas

• A gas whose molecules have mass but no volume • The molecules exert no mutual attraction

Five Postulates

1. The volume occupied by gas molecules is negligibly small 2. All collisions between gas molecules are elastic 3. A gas consists of molecules in constant random motion 4. There are no forces of attraction or repulsion between gas particles 5. The average kinetic energy of gas particles depends on the temperature

Ideal Gases do not exist. Many real gases behave nearly ideally if pressure is not too high and the temperature is not too low.

Real Gases are gases that do not behave completely according to the assumptions of the kinetic molecular theory.

The KMT describes the behavior of gases in terms of particles in motion.

Assumptions of the KMT:

1. Gases consist of small particles that are separated from one another by empty space. The volume of the particles is infinitesimally small compared to the volume of the empty space. There are no significant forces of attraction or repulsion between the particles.

2. Gas particles are in constant, random motion. Collision between particles are elastic (i.e., no loss of kinetic energy). KE can be transferred but not lost.

3. KE = 1/2 mv2 Temperature is a measure of the average kinetic energy of the particles in a sample of matter.

Behavior of Gases

Characteristics of Gases

• Expansion • Fluidity • Low density • Compressibility • Diffusion and Effusion

The volume of a gas changes significantly with changes in temperature or pressure

Gas molecules can be considered to be point masses. That is, the volume of the molecule is infinitesimally small relative to the distance between them.

Effusion and Diffusion

Diffusion - the gradual mixing of two gases due to their spontaneous random motion

Effusion - the process whereby gas molecules confined in a container randomly pass through a tiny opening in the container.

Graham's Law of Effusion

V1/V2 = (m2/m1)½

Diffusion

• The rate of diffusion is proportional to the velocity • Two substances at the same temperature must have the same average kinetic energy

Know the difference between diffusion and effusion

Four Variables of Gases that depend on one another:

1. Pressure 2. Volume 3. Temperature 4. Number of particles in a gas sample

Measuring Pressure

Manometer - a device used to measure the pressure of a gas (2 types)

1. Open manometer

• open to the atmosphere • Pgas = Patm ± h

2. Closed manometer

• closed to the atmosphere • Pgas = h

Standard Temperature and Pressure

Standard Temperature = 0oC, 273 K

Standard Pressure = 1 atm = 760 mm Hg = 760 torr = 101.325 kPa

Pressure of a gas depends on three factors:

1. Number of Molecules (n) 2. Volume of the Molecules (V) 3. Average Kinetic Energy of the Molecules

KE = ½mv2

[The average KE of the gas depends only on the temperature of the gas]

Changing any one factor (n, V, or T) will change the pressure (P) of the gas

Dalton's Law of Partial Pressure

Used for gases collected by water displacement (i.e., collected over water). See below.

Gas Collection by Water Displacement

Forces of Attraction

Intermolecular Forces; Polarity

The forces of attraction between molecules. As the forces between particles increases, their boiling points increase. Thus, the boiling points of ionic and metallic compounds are much higher than those of molecular compounds. (see Table 6-7, p. 190)

Molecular Polarity and dipole-dipole forces

No two elements have exactly the same electronegativity. Therefore, in a covalent bond of two different elements, one of the atoms will attract the electrons more strongly than the other. This difference in electronegativity leads to polar covalent bonds and creates a dipole.

Dipole - the entity formed when two or more atoms that have differing electronegativities combine.

Dipole Moment, µ

a measure of the strength of the dipole

results from the asymmetrical charge distribution on a polar molecule.

µ = Qd

Q = partial charge (coulombs)

d = distance (meters) between the charges

Dipole-dipole forces - the force of attraction between polar molecules

Hydrogen Bonding

When hydrogen is covalently bonded to a highly electronegative atom, a strong partial positive charge results:

O-H water, alcohols N-H ammonia, amines (RNH2) F-H hydrogen fluoride

The bonded hydrogen is slightly positively charged, and is attracted to the negative portion of other molecules - this force of attraction between hydrogen and the negative portion of another molecule constitutes a hydrogen bond.

London Dispersion Forces

Weak forces of attraction resulting from the constant motion of electrons and the creation of instantaneous dipoles

LIQUIDS

Fluid - a substance that can flow and take the shape of its container (liquid or gas)

Properties of Liquids

1. Relative high density 2. Relative incompressibility 3. Ability to diffuse 4. Surface tension 5. Capillary action 6. Evaporation and Boiling 7. Formation of Solids / freezing

Melting

According to the Kinetic Theory the velocity of particles increases as the temperature increases. Also, particles collide with each other more often and with more force. Therefore, they move farther apart (expand). For a solid, the particles move far enough apart for some particles to "slip" over each other. The rigid arrangement of particles starts to break down. We call this "melting."

Freezing

As a liquid is cooled, it will reach a temperature at which the particles move so slowly they can no longer slip over each other. Particles settle into an ordered arrangement and form a solid. This is called "freezing."

for pure substances: m.p. = f.p.

Vapor Equilibrium

The average kinetic energy (KE) of particles in a gas is a constant for all substances at a given temperature.

We saw this relationship when we studied gases. This is also true for liquids and solids. A particle could gain enough kinetic energy through collisions to "escape" the liquid or solid. These escaping particles form a vapor (gaseous phase).

Gas - gaseous state for substances that are gaseous at room temperature.

Vapor - gaseous state for substances that are liquid or solid at room temperature.

The escaping particles could collide with the surface of the liquid or solid again, and recombine with it. This is very unlikely in an open container. However, in a closed container, the probability of a molecule returning to the condensed phase is increased.

Equilibrium exists when the number of particles escaping from the surface of the condensed phase equals the number of particles return to the condensed phase. That is,

# particles escaping = # particles returning

When there is no net change, we are at equilibrium. We call this Dynamic Equilibrium because particles are moving both ways.

Saturated Vapor - exists when a substance is in equilibrium with its vapor. A gaseous phase that is saturated holds all the vapor it can at that temperature and pressure.

X(l) → X(g)

X(l) ← X(g)

X(l) ↔ X(g)

Le Chatelier's Principle

If stress is applied to a system at equilibrium, the system will tend to readjust so that the stress is reduced.

Types of stress include temperature, pressure and concentration changes.

Solids Changing State

Freezing

Melting Point - the temperature at which the vapor pressure of the solid equals the vapor pressure of the liquid.

VPsolid = VPliquid

Solid ↔ Liquid

In a closed container, the solid and liquid have the same vapor pressure.

Boiling

Sublimation - some solids have a high enough vapor pressure at room temperature to vaporize rapidly [ solid ---> gas ] without going through the liquid state.

e.g., dry ice (CO2); moth balls (naphthalene); iodine (I2)

Boiling Point - Evaporation - molecules of a liquid exposed to air can escape (not likely to return). As temperature of a liquid is increased, the vapor pressure of the liquid increases as a result of the increase in kinetic energy of the molecules.

Eventually, the KE of the molecules becomes large enough to overcome the internal pressure of the liquid. This pressure is caused by the pressure of the atmosphere on the liquid surface. When this pressure is overcome, the molecules are colliding violently enough to push each other apart. They are pushed far enough apart to form bubbles of gas within the liquid.

VPliquid = VPvapor

Liquid ↔ Vapor

Normal Boiling Point - The temperature at which the vapor pressure of the liquid is equal to the standard pressure (101.325 kPa; 1 atm, 760 mm Hg, 760 torr). Therefore, boiling point is a function of pressure.

Volatile - a liquid that boils at a low temperature and evaporates at room temperature (alcohol, ether, etc.). These substances have high vapor pressures.

Nonvolatile - A liquid that boils at a high temperature and evaporates slowly at room temperature. (molasses, glycerol). These substances have a low vapor pressure.

Liquefaction of Gases - Condensation of substances that are normally gases at room temperature. To effect liquefaction, you must reduce the temperature and increase pressure to allow van der Waals forces to take effect.

Critical Temperature, Tc - The temperature above which no amount of pressure will liquefy the gas. Also, the maximum temperature at which a liquid can exist.

Critical Pressure - The pressure needed to liquefy a gas at the critical temperature.

Heat of Fusion, Hfus, Enthalpy of Fusion - the energy required to melt 1 gram of a substance at it melting point.

Heat of Vaporization, Hvap, Enthalpy of Vaporization - the energy required to vaporize 1 gram of a substance at its boiling point.

At constant pressure, enthalpy equals the heat transferred

Hydrogen Bonding

When hydrogen is covalently bonded to a highly electronegative atom, a strong partial positive charge results:

O-H water, alcohols N-H ammonia, amines (RNH2) F-H hydrogen fluoride

The bonded hydrogen is slightly positively charged, and is attracted to the negative portion of other molecules - forming a hydrogen bond.

Freezing - The structure of ice occupies a lot of space. As ice melts, and many bonds are broken, molecules move closer together. As water is heated above 0oC, additional H-bonds are broken and molecules continue to move closer. At 3.98oC most H-bonds have been broken. As water is heated above 3.98oC, it expands with increased temperature.

Surface Tension - Results from the particles on the surface being subject to unbalanced forces. Surface particles experience a net force directed perpendicular to the surface (inward). This net force accounts for surface tension and the formation of raindrops (spheres).

Capillary Action - Due to the attractive forces between the liquid and the solid wall of a capillary tube. Water (or any liquid) will continue to rise in a capillary tube until the following forces are balanced:

• attraction between glass and water • attraction between the water molecules • force of gravity on the water column

SOLIDS Properties of Solids

• Definite Shape and Volume • Definite melting point • High Density • Incompressibility • Low rate of diffusion

Crystalline Solids

Binding Forces in Crystals

1. Ionic crystals - very strong binding forces between the positively and negatively charged particles

2. Covalent network crystals - each atom in the crystal is covalently bonded to its nearest neighbor

3. Metallic crystals- crystal structure consists of metal atoms surrounded by a sea of electrons.

4. Covalent molecular crystals - covalently bonded molecular crystals held together by intermolecular forces: London dispersion forces, dipole-dipole forces, or even hydrogen bonding (low m.p.)

Crystal Structure

The study of the solid state is the study of crystals. All true solid substances are crystalline

Crystals - consist of the repetition of identical units in three dimensions

definition - a rigid body in which the particles are arranged in units which form a repeating pattern. These units can repeat in either one, two or three dimensions.

There is a direct relationship between the shape of the repeating units and the external shape of the crystal.

Classification of crystals

• cubic • tetragonal • hexagonal • rhombohedral • orthorhombic • monoclinic • triclinic

Unit cell - the simplest repeating unit

Simplest cubic

simple cubic

body centered

face centered(NaCl)

Space lattice - the three-dimensional arrangement of unit cells repeated over and over in a definite geometric arrangements.

Sodium chloride is face-centered cubic

the particular crystal structure is determined by the ratio of the radii of the ions.

Simple salts are those formed by Groups IA and VIIA elements

always have face-centered cubic lattice, except for the cesium salts

Closest Packing

• hexagonal closest packing - metals at room temperature • cubic closest packing

Elementary Crystals

Almost all metals are packed in one of the three kinds of units

• body-centered cubic, • face-centered cubic, • hexagonal closest packed.

The packing changes as the temperature increases.

Allotropes - different crystalline forms of the same element. For example, CARBON

• diamond - carbon is covalently bonded to 4 other carbon atoms (3 dimensional) • graphite - carbon is covalently bonded to 3 other carbon atoms - hexagonal arrangement

in layers (2 dimensional)

· face-centered cubic lattice - a single molecule

Network Crystal (macromolecule) - one giant molecule

Most molecular solids melt by the breaking down of weak van der Waals forces. In network crystals, atoms are covalently bonded and much more energy is required to break the bonds for these substances to melt.

Characteristics of Crystals

Crystal Type Bonding Melting Points Examples Ionic Electrostatic Force 300 to 1000oC NaCl, LiCl Metallic Delocalized Electrons 100 to 3500oC Na, W Macromolecular Covalent 2000 to 4000oC C, Si Molecular van der Waals Forces -260 to 400oC CH4, C6H6

Some definitions:

Isomorphous - crystals of different solids with the same structure and shape

Polymorphous - one substance with two or more different crystalline structures

e.g., Calcium Carbonate: 1) Calcite - rhombohedral and 2) aragonite - orthorhombic

Hydrated crystals - crystals that contain water of hydration [CuSO4 · 5 H2O]

Anhydrous - without water; [CuSO4]

Hygroscopic - crystals that can pick up water from the air and hold on to it [Na2CO3]

Deliquescent - a substance that is so hygroscopic that it takes up enough water to form a liquid.

Amorphous - not crystalline

Viscosity - resistance of a liquid to flow

Equilibrium

Equilibrium is a dynamic condition in which two opposing changes occur at the same rates in a closed system. e.g., evaporation and condensation.

At equilibrium:

liquid ↔ vapor

Le Chatelier's Principle - when a system at equilibrium is disturbed by a stress, it reestablishes a new equilibrium so as to minimize that added stress.

Effect of Temperature

Our equilibrium can be written as:

liquid + heat ↔ vapor

If the temperature of our system is increased, then the forward reaction rate increases since it is endothermic. The forward reaction proceeds at a higher rate until a new equilibrium is established.

Effect of Concentration

For the equilibrium A + B ↔ C + D

If the concentration of one of the reactants (A or B) is increased, then the rate of the forward reaction is increased until a new equilibrium is established. The forward reaction rate increases since an increase in A means that the likelihood of a collision between A and B is now greater. Now the concentrations of C and D are increasing. Therefore, the likelihood of a reaction between C and D now increases. This continues until the forward rate again equals the reverse rate.

Volatile Liquids - liquids that readily evaporate at room conditions (25 oC and 760 mm Hg).

Nonvolatile Liquids - those liquids that do not readily evaporate at room conditions.

Boiling - occurs when the equilibrium vapor pressure of the liquid equal atmospheric pressure

Phase Diagrams These diagrams show how the states of matter are affected by changes in pressure and temperature.

Phase Diagram for Water

See your textbook for examples of various phase diagrams and the location of the critical points.

You must be able to identify the areas of solid, liquid, gas, normal m.p., normal b.p., triple point, critical point, critical temperature and critical pressure. Remember, to find the normal m.p., and the normal b.p., you simply have to locate the line of standard pressure (1 atm., 760 torr, etc.) and draw a line across the diagram to find the point at which that line intersects with the curves.

Water

1. Structure

• Hydrogen Bonding

2. Physical Properties

Ice

The Gas Laws The Kinetic Molecular Theory

Ideal Gas

• A gas whose molecules have mass but no volume • The molecules exert no mutual attraction

Five Postulates

1. The volume occupied by gas molecules is negligibly small 2. All collisions between gas molecules are elastic 3. A gas consists of molecules in constant random motion 4. There are no forces of attraction or repulsion between gas particles 5. The average kinetic energy of gas particles depends on the temperature

Ideal Gases do not exist. Many real gases behave nearly ideally if pressure is not too high and temperature is not too low.

Real Gases are gases that do not behave completely according to the assumptions of the kinetic molecular theory.

The KMT describes the behavior of gases in terms of particles in motion.

Assumptions of the KMT:

1. Gases consist of small particles that are separated from one another by empty space. The volume of the particles is infinitesimally small compared to the volume of the empty space. There are no significant forces of attraction or repulsion between the particles.

2. Gas particles are in constant, random motion. Collision between particles are elastic (i.e., no loss of kinetic energy). KE can be transferred but not lost.

3. KE = 1/2 mv2 Temperature is a measure of the average kinetic energy of the particles in a sample of matter.

Behavior of Gases

Characteristics of Gases

1. Expansion 2. Fluidity 3. Low density 4. Compressibility 5. Diffusion and Effusion

The volume of a gas changes significantly with changes in temperature or pressure

Gas molecules can be considered to be point masses. That is, the volume of the molecule is infinitesimally small relative to the distance between them.

Standard Temperature and Pressure, STP

Standard Temperature:

1. 0o Celsius

2. 273 Kelvin

3. Kelvin = oC + 273

Absolute Zero:

1. The temperature at which all molecular motion ceases

2. 0 Kelvin

3. -273.15 oC

Standard Pressure

1. 1 atmosphere = 1 atm.

2. 101.325 kPa

3. 760 mm Hg

4. 760 torr

Molar Volume of Gases

therefore, one mole of any gas at STP will occupy the same volume as any other gas at STP.

e.g., one mole O2, 32.0 g; at STP occupies 1000 cm3 and has a mass of 1.43 g

therefore,

32.0 g/mole x 1000 cm3/1.43 g x 1 L/1000 cm3 = 22.4 L/mole

one mole H2, 2.016 g/mole; 1000 cm3 has a mass of 0.0899 g.

2.016 g/mole x 1000 cm3/0.0899 g x 1 L/1000 cm3 = 22.4 L/mole

Molar Volume = 22.4 dm3 = 22.4 L

THE GAS LAWS

Ideal Gas Law - describes a sample of gas under a specific set (static) of conditions

PV = nRT

Boyle's, Charles', Gay-Lussac's and the Combined Gas Laws all describe a change of conditions for a sample of gas.

Boyle's Law -

PV = k

P1V1 = P2V2

Charles' Law

V = k'T

V1/T1 = V2/T2

Gay-Lussac's Law

P = kT

P1/T1 = P2/T2

Combined Gas Law

P1V1/T1 = P2V2/T2

Avogadro's Law

States that at equal temperatures and equal pressures, equal volumes of gases contain the same number of molecules.

where n = number of moles, and V = volume

if V1 = V2 then n1 = n2

Ideal Gas Equation

Charles' Law: V is proportional to T

Boyle's Law: V is inversely proportional to P

Combining: V = k"(T/P) or PV = k"T

k" depends on the number of molecules present

k" = nR

where n = number of moles and R = constant

therefore,

PV = nRT

[Ideal Gas Equation]

R = PV/nT = (101.325 kPa x 22.4 L)/(1 mol x 273 K)

= 8.31 L kPa/mol K

Ideal Gas Law

Shows the relationship between pressure P, volume V, temperature T and the number of moles (n) of a gas

PV = nRT

where R = universal gas constant, 0.08206 L atm/mol K

Molecular Mass Determination

(using PV = nRT)

n = m/M

PV = nRT = mRT/M

or, M = mRT/PV

Density (of a gas) Determination

MP/RT = m/V = D = Density

Gas Stoichiometry

Four Steps

1. Balance the Equation

2. Find number of moles of the given substance

3. Use ratio of moles of given substance to moles of required substance to find moles of gas.

4. Express moles of gas as a volume

e.g., What volume of hydrogen (H2) at STP can be produced when 6.54 g Zn reacts with HCl?

2 HCl + Zn → H2 + ZnCl2

6.54 g Zn x 1 mol/65.4 g Zn x 1 mol H2/1 mol Zn x 22.4 L/mol H2 = 2.24 L

g → m → m → volume

The types of problems you must be able to solve include:

mass to volume volume to mass mole to volume volume to mole volume to volume

These problems are no more difficult than the mass related problems we did in Ch. 9. In fact they are simpler. Just remember, the molar volume for all gases is 22.4 L/mole

Effusion and Diffusion

Diffusion - the gradual mixing of two gases due to their spontaneous random motion

Effusion - the process whereby gas molecules confined in a container randomly pass through a tiny opening in the container.

Graham's Law of Effusion

V1/V2 = (m2/m1)½

Diffusion

· The rate of diffusion is proportional to the velocity

· Two substances at the same temperature must have the same average kinetic energy

Know the difference between diffusion and effusion