Unit 2Structure and properties of matter

Solids Solids can exist as either

crystalline solids, where the atoms, ions, or molecules are ordered in well-defined arrangements.

These solids usually have flat well defined surfaces

Solids can also exist as amorphous solids.

These solids lack well defined shapes and faces

Particles in a sample of liquid are still very close to one another, but are free to move and collide with one another.

The solid and liquid phases for a particular substance generally have small differences in molar volume (The amount of space that one mole of the substance takes up).

Many of the properties of liquids are dependant on the attractive forces between the molecules.

Liquids

Viscosity Viscosity is the resistance of a liquid to flow. A liquid with high viscosity indicates that the

particles are tightly packed together and are attracted strongly to one another.

Surface tension Surface tension is defined as the energy required

to increase the surface are of a liquid by a unit amount.

Liquids that have strong attractive forces between the molecules have high surface tension.

Properties of Liquids

Heating Curves Heating curves are a way

to graphically show the energy involved in phase changes.

During a phase change there are sloped periods and plateaus

The sloped periods represent the heating of a sample.

The plateau periods represent a phase change.

Working With a Heating Curve If we are looking at a heating

curve for water… The first sloped period (A-B)

represents the heating of solid ice.

The first plateau represents the melting of ice into liquid water.

The second slope represents the heating of liquid water.

The second plateau represents the conversion of liquid water into water vapor.

The last slope represents heating water vapor.

By knowing some information about the substance we are studying we can calculate how much energy is required to heat it, and change it’s phase.

For the sloped sections where we are heating a sample we need to know the specific heat of the substance in that state of matter.

For the plateau sections we need to know the energy associated with each of the phase changes for the substance.

Gases

Gases do not have a definite shape or volume.

The attractive forces between particles in a sample of gas are minimal.

Because of this gases can be thought of as a sample of particles moving independently of one another.

This is called an ideal gas.

Properties of Gases

Ideal gases exhibit a specific mathematical relationship between the number of particles present, the temperature, the pressure, and the volume.

PV = nRT R is the ideal gas constant R has a few different values based on the unit of

pressure used. 1 atm = 760 torr = 101.3 kPa R = 0.082 L-atm/mol-K R = 8.314 L-kPa/mol-K R = 62.4 L-torr/mol-K

The Ideal Gas Law

Boyle’s Law: P1V1 = P2V2

Charles’s Law V1/T1 = V2/T2

Gay-Lussacs Law P1/T1 = P2/T2

Other Gas Laws

Gas Densities and Molar Mass The Ideal Gas Law allows us to calculate the

density of a gas using its molar mass, its pressure, and its temperature.

Remember that density = mass/volume

Example: What is the density of CCl4(g) at 714 torr

and 125o C.

Other Applications Of The Gas Laws

A series of measurements are made to determine the molar mass of an unknown gas. First a large flask is evacuated and found to weigh 134.567 g. It is then filled with the gas to a pressure of 735 torr at 31o C and reweighed. It’s mass is now 137.456 g. Finally, the flask filled with water at 31o C and found to weigh 1067.9 g (the density of water at this temperature is 0.997 g/mL). Assume that the ideal gas equation applies, and calculate the molar mass of the gas.

When a mixture of different gases all occupy the same container they all share the same volume, and temperature.

But they might not be present in the same number.

This leads to each individual gas contributing a certain amount of pressure to the total pressure of the sample.

The total pressure of a mixture of gases, Pt, is equal to the sum of the pressure of the individual components.

Partial Pressure

A gaseous mixture made from 6.00 g of O2 and 9.00 g of CH4 is placed in a 15.0 L vessel at 0 oC. what is the partial pressure of the two gases and what is the total pressure?

Example

Often times we collect a gas over water. By doing this we can determine the volume and

temperature of the gas easily. The pressure is more difficult to determine

Pt = Pgas + PH2O

We need to use the vapor pressure of water and subtract it out of the total pressure in the container to determine the pressure of our gas sample.

Collecting Gas Over Water

A sample of KClO3 is partially decomposed, producing O2gas that is collected over water. The volume of gas collected is 0.250 L at 26o C and 756 torr total pressure.

a) How many moles of O2 are collected?

b) How many grams of KClO3 were decomposed?

The kinetic molecular theory states that… Gases consist of large number so of molecules that are in

continuous, random motion. The combined volume of all the molecules of the gas is

negligible relative to the total volume in which the gas is contained.

Attractive and repulsive force between gas molecules are negligible.

Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change, as long as the temperature remains constant.

The average kinetic energy of the molecules is proportional to the absolute temperature.

Pressure is proportional to the number of molecules that collide with the wall of the container.

The Kinetic Molecular Theory

rms (u) is defined as the speed of a molecule possessing average kinetic energy.

Eave = 1/2mu2

Where Eave = average kinetic energy of the sample, and m is the mass of one molecule.

This is slightly different than average speed.

Root-Mean-Square Speed (rms)

We see the kinetic molecular theory at work in gases in two ways…

1. Effect of a volume increase or decrease at constant temperature

◦ A constant temperature means that the average kinetic energy of the molecules in also constant

◦ However If the size of the container is increased the molecules have to move a greater distance to strike the wall of the container.

◦ If the size of the container decreases the molecules will have less distance to cover from wall to wall.

KMT and Gases

2. Effect of a temperature increase at constant volume.

◦ At constant volume the distance the molecules have to travel to strike the wall of the container remains constant.

◦ The only way to increase or decrease the pressure is by changing the temperature.

◦ A higher temperature will result in faster moving molecules and more collisions with the wall of the container.

◦ A lower temperature will result in slower moving molecules and fewer collisions.

A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on…

a) The average kinetic energy of the O2 molecules.

b) The average speed of the O2 molecules.

c) The number of collisions with the container wall per unit time.

d) The total pressure of the container.

Applying KMT

The kinetic molecular theory states that the average kinetic energy of any collection of gas molecules has a specific value at a given temperature.

Example: A sample of light weight He and a sample of Xe, which is much heavier, will have the same average kinetic energy at the same temperature.

Which must mean… The particles of He are moving much faster.

Molecular Effusion and Diffusion

Because the molecules of Xe are moving slower their root-mean-square speed (rms) must be lower too.

Calclate the rms speed of an N2 molecule at 25o C.

The dependence of molecular speed on mass has interesting consequences.

The first is effusion. effusion is the escape of gas molecules

through a tiny hole into an evacuated space.

In 1846 Thomas Graham discovered that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Graham’s Law of Effusion

An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only 0.355 times that of O2 at the same temperature. Calculate the molar mass of the unknown and identify it.

Diffusion is the spreading of one substance throughout a pace or throughout a second substance.

We would expect faster moving molecules to diffuse faster.

So which would diffuse faster Xe at 25o C or He at 25o C?

Diffusion

Although the ideal-gas law is a very useful way to describe gases all gases fail to obey the relationship to some degree.

If we rearrange the equation to solve for n…

For one mole of gas n = 1, PV/RT must equal 1. At high pressures gases no longer follow the ideal gas

equation. This is due to the fact that the molecules are closer to one

another and begin to interact with each other. Gases also deviate from ideal behavior at low temperature. These deviations become significant near the temperature

at which the gas is converted to liquid.

Real Gases

Engineers and scientists who work with gases at high pressures cannot use the ideal gas law.

In this equation a and b are called van der waals constants.

a is a measure of how strongly the gas molecules are attracted to eachother

b is a measure of the small but finite volume occupied by the gas molecules themselves.

The Van der Waals Equation

If 1.000 mol of an ideal gas were confined to 22.41 L at 0.0 o C, it would exert a pressure of 1.000 atm. Use the van der waals equation to estimate the pressure exerted by 1.000 mol of Cl2(g) in 22.41 L at 0.0o C.

Example

Chemical Bonding

Ionic bonds are generally formed between a metal and nonmetal (or polyatomic ion)…or between two polyatomic ions.

NaCl NaNO2

NH4NO3

According to the octet rule all elements prefer to have eight valance (Highest energy level) electrons.

We can use this idea to predict the charge of many elements when they form ionic compounds.

Ionic Bonds

Naming ionic compounds is trickier than naming covalent compounds.

This is because the charges of the ions that make up the compound must cancel each other out to result in a zero charge.

Na+ + Cl- NaCl Just like covalent compounds the name of

the first element is kept the same and the second element gets the ending –ide

Sodium Chloride

Naming Ionic Compounds

We have seen that some combinations of elements can combine in different ratios.

CuCl CuCl2

We know that Chlorine always forms a -1 charge (Because of the octet rule).

Which means that in CuCl copper has a charge of +1 And in CuCl2 copper has a charge of +2 Copper and many other transition elements are able to form

a variety of charges in ionic compounds. When naming these types of compounds we must indicate

the charge of the transition element to differentiate between the two copper chloride compounds.

The Law of Multiple Proportions and Naming

Different ionic compounds have different strengths.

Meaning some ionic compounds are held together tighter than others.

This is all based on Coulomb’s Law

In general the strength of ionic bonds increases as the absolute value of the charges increases and as the ionic radii decrease.

Ionic Bond Strength

In covalent bonds electrons are shared between the nuclei of two atoms to form a molecule or polyatomic ion.

Covalent bonds are generally formed between two nonmetal elements.

These electrons are not always shared equally. The relative electronegativities of the atoms

involved account for the polarity of bonds. If the electronegativities of the atoms involved in

the bond are the same, or very close to the same, the result will be an equal sharing of electrons and a nonpolar bond.

Covalent Bonds

We can use electronegativity data to determine if a bond is polar or nonpolar.

Consider the compound F2. Fluorine is a very electronegative element (4) But it’s the DIFERENCE in electronegativity that

determines if a bond is polar or not. So F2 is nonpolar. The molecule HF however is polar F – 4.0 H – 2.1 The difference in electronegativity is 1.9 If the difference in electronegativity is very large an

ionic bond forms, more on this later.

Polar Covalent Bonds

The unequal sharing of electrons in a polar covalent bond causes a build up of electrons on the more electronegative atom.

This creates an area of partial negative charge and an area of partial positive charge.

Larger differences in electronegativity between the bonded atoms leads to greater partial charges and an molecule that is over all more polar that some others.

Partial positive and negative charges

Covalent compounds are named using a very simple system.

The name of the first element in the formula is kept the same.

The name of the second element is given the ending –ide

The number of each element is also indicated by using a prefix.

Example: N2O2 – Dinitrogen Dioxide

Naming Covalent Compounds

Lewis structures can help us understand the bonding in many covalent compounds.

Steps to drawing Lewis structures1. Sum up the valence electrons from all atoms. 2. Write the symbols for the atoms to show which atoms

are attached to which, and connect them with single bonds.

3. Use remaining electrons to complete the octets around all of the surrounding atoms.

4. Place any leftover electrons on the central atom.5. If there are not enough electrons to give the central

atom a full octet a double (or triple) bond must be made.

Lewis Structures

Draw the Lewis structure for phosphorus trichloride.

Draw the Lewis structure for CH2Cl2

Draw the Lewis structure for HCN

Draw the Lewis structure for BrO3-

Examples

The formal charge of any atom in a covalent molecule is the charge the atom would have if all of the atoms in the molecule had the same electronegativity and shared the electrons equally.

To calculate formal charge…1. All unshared (nonbonding) electrons are

assigned to the atom on which they are found.2. For any bond (single, double, or triple) half of

the bonding electrons are assigned to each atom in the bond.

Formal Charge

Calculate the formal charge on each atom in the molecule CN-

Example

Draw the Lewis structure for CO2

We see that CO2 has two possible Lewis structures. Which one is better?

Calculate the formal charges for each Lewis structure.

We generally choose the Lewis structure in which the atoms bear formal charges closest to zero

We generally choose the Lewis structure in which any negative charges reside on the more electronegative atoms.

How To Use Formal Charge

Use formal charge to determine the preferred Lewis structure of NCS-

Use formal charge to determine the preferred Lewis structure of NCO-

Examples

Consider one molecule of ozone (O3) When drawing its Lewis structure we find

two possibilities. These two possibilities are equivalent to one

another. They are referred to as resonance

structures.

Resonance

Draw all possible resonance structures for NO3

-

Which is predicted to have shorter sulfur-oxygen bonds, SO3 or SO3

2-?

Example

The octet rule fails in many situations involving covalent bonding.

There are three main types of exceptions1. Molecules and polyatomic ions containing

an odd number of electrons.2. Molecules and polyatomic ions in which an

atom has fewer than an octet of valence electrons.

3. Molecules and polyatomic ions in which an atom has more than an octet of valence electrons.

Exceptions To The Octet Rule

ClO2

NO

NO2

O2-

Odd Number of Electrons

BF3

Less than an Octet

PCl5

ICl4-

SF4

More than an Octet

Once we can draw the Lewis structure of a molecule we can determine the actual shape of the molecule.

All electron containing regions around the central atom are called electron domains.

This includes bonding and non-bonding electrons.

The first thing we need to do is determine the shape of the electron domains.

Molecular Shapes

The shape of the electron domains around the central atom are base on the Valence-shell electron-pair repulsion (VSEPR) model.

This theory states that two electron domains will repel each other and will be positioned as far away from each other as possible.

VSEPR Model

Number of Electron Domains

Electron Domain Geometry

Bond Angles

2 Linear 180o

3 Trigonal Planar 120o

4 Tetrahedral 109.5o

5Trigonal bipyramidal 120o

90o

6 Octahedral 90o

Electron Domain Geometries

Linear

Trigonal Planar

Tetrahedral

Trigonal Bipyramid

Octahedral

If all of the electron domains are bonds then the molecular geometry will match the electron domain geometry.

If any of the electron domains are non-bonding electrons the molecular geometry will be different than the electron domain geometry.

Molecular Geometries

A working theory is that when atoms bond the electrons around the central atom actually form “hybrid orbitals”.

These orbitals can the thought of as the mixing of two electron orbitals (s,p,d,f)

Since this is just a theory we do not need to know about it in depth.

For us the hybridization of the central atom follows a patter and matches up with the electron domain geometry.

Hybridization

Number of Electron Domains

Hybridization of Central

Atom

Geometry Examples

2 sp Linear BeF2, HgCl2

3 sp2 Trigonal Planar BF3, SO3

4 sp3 Tetrahedral CH4, NH3, H2O, NH4

+

Hybrid Orbitals

Intermolecular ForcesIMF’s

London Dispersion Forces (LDF) are forces that all molecules and atoms experience.

These forces happen between two molecules or atoms and can be thought of as magnetic forces, either attractive or repulsive.

The strength of these forces can have a large impact on the macroscopic properties of a substance (Ex: Boiling point, hardness, vapor pressure, ect.)

London Dispersion Forces

Two understand LDF’s we must first understand that the electrons in an atom or molecule are not stuck in rigid positions.

Electrons are free to move around the atom or molecule. When the majority of the electrons in an atom or

molecule are located in one area it creates an area of negative charge.

This temporary state is called a temporary dipole. Dipole is a word used to describe molecules that have a

negative and positive end. Molecules that have been temporary polarized then

interact like magnets. Remember Coulombs law

Causes of LDF

LDF’s are generally weak forces. Some molecules experience stronger LDF’s

than others. This is all due to the polarizability of the

atoms or molecules in question. Polarizability refers to the ease with which the

electrons can be localized to one area of the atom or molecule.

Molecules that are more polarizable experience longer lasting temporary dipoles and therefore stronger LDF’s.

Strength of LDF

In general larger molecules and atoms have greater polarizability.

This is because they have more electrons, and the electrons are further from the nucleus.

So in general LDF’s get stronger as atoms or molecules increase in atomic mass.

What about molecules that have similar or exactly the same atomic mass?

Then polarizability is primarily determined by the shape of the molecule.

Polarizability

Dipole-Dipole forces are stronger than London Dispersion Forces.

These forces are only present between two polar molecules.

A polar molecule is one where there is a permanent dipole.

This is due to a difference in electronegativity between different atoms in the molecule.

Dipole-Dipole interactions occur when two polar molecules are attracted to one another according to coulombs law.

Dipole-Dipole Forces

These are interactions between a polar molecule and a nonpolar molecule.

In these cases the polar molecule polarizes the nonpolar molecule creating a temporary dipole.

The strength of these forces increases with the polarity of the polar molecule and the polarizability of the nonpolar molecule.

Dipole-Induced Dipole Interactions

Hydrogen bonds are a special type of dipole-dipole interaction.

These interactions occur between the a hydrogen atom in a polar bond and a nonbonding pair of electrons on a near by small electronegative atom. (such as F, N or O).

These are the strongest intermolecular forces.

Hydrogen Bonding

Many macroscopic properties of solids and liquids are determined by the strengths of intermolecular forces.

Boiling Point: The boiling points of liquids are strongly

influenced by intermolecular forces. Liquids that have strong IMF’s have high

boiling points. This is because the molecules are held more

tightly together and require more heat energy to escape as gases.

What Intermolecular Forces Do

Noble Gas Molecular Weight (AMU)

Boiling Point (K)

He 4.0 4.6

Ne 20.2 27.3

Ar 39.9 87.5

Kr 83.8 120.9

Xe 131.3 166.1

Vapor Pressure is related to boiling point. Vapor pressure is a measure of how many molecules

of a liquid can escape to the gas phase. The vapor pressure of any liquid increases as

temperature increases. But two liquids at the same temperature can have

different vapor pressures based on the strength of the IMF’s in the liquid.

Liquids that have strong IMF’s like water (Lots of hydrogen bonds) have lower vapor pressures than liquids with weaker IMF’s like propane.

A liquid will boil when its vapor pressure matches the atmospheric pressure.

Vapor Pressure

Surface tension is a property of liquids that is greatly dependant on IMF’s.

Surface tension is defined as the amount of energy required to increase the surface are of a liquid by one unit amount.

It might help to think about surface tension as “spreadability”.

Water has a high surface tension because of the strong hydrogen bonds between molecules.

Rubbing alcohol has weaker IMF’s and there for a lower surface tension.

Surface Tension

Phase Diagrams

We have already seen that in solids the particles are tightly packed and held together.

We will now be looking at the different types of solids and their properties.

Bonding In Solids

Molecular solids consist of atoms or molecules held together by intermolecular forces.

Because these forces are weak molecular solids are generally soft.

The also have relatively low melting points (usually below 200o C)

Most of these substance would exist as gases or liquids at room temperature.

Examples: Ar, H2O, CO2

Molecular Solids

Covalent network solids consist of atoms held together in large networks or chains of covalent bonds.

Because covalent bonds are much stronger than IMFs these solids are much harder and have higher melting points than molecular solids.

Diamond and graphite (Two allotropes of carbon) are covalent network solids.

Covalent Network Solids

Ionic solids consist of ions held together by ionic bonds.

The strength of ionic bonds depends greatly on the charges of the ions.

In NaCl the ions have charges of +1 and -1 and has a melting point of 801o C.

MgO consists of ions that have charges of +2 and -2 and melts at 2852o C.

Ionic Solids

Metallic Solids Metallic solids, simply called

metals, consist entirely of metal atoms.

Solid metals can be thought of as an array of positive metal ions in a sea of delocalized electrons.

The more valance electrons an element has the stronger the metallic bonds will be.

The delocalization of electrons is the reason why metals are good conductors of electricity.