Bonding, VSEPR, and Intermolecular Forces

Kevin Hu

November 30, 2010

Contents

1 Chemical Bonding: Basic Concepts 2

1.1 Lewis Dot Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Ionic Bonding and Lattice Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Covalent Bonding and Lewis Structures . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Electronegativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Formal Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.7 Exceptions to the Octet Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8 Bond Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Molecular Geometry and Hybridization of Atomic Orbitals 12

2.1 Molecular Geometry and the VSEPR Model . . . . . . . . . . . . . . . . . . . . . 12

2.2 Polar Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Valence Bond Theory and Hybrid Orbitals . . . . . . . . . . . . . . . . . . . . . . 16

3 Intermolecular Forces, and Liquids and Solids 18

3.1 Kinetic Molecular Theory of Liquids and Solids . . . . . . . . . . . . . . . . . . . 18

3.2 Intermolecular Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Properties of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Phase Changes and Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 21

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Chapter 1

Chemical Bonding: Basic Concepts

1.1 Lewis Dot Diagrams

Definition 1. A Lewis dot diagram of an element consists of the chemical symbol with dots placedaround it. Each dot represents a valence electron.

Lewis dots can be above, below, to the right, and to the left of the symbol. There can be at mosttwo dots in each of these directions; this corresponds to the Pauli exclusion principle, which saysthat no two electrons can have the same four quantum numbers (i.e. no two electrons in the sameorbital can have the same spin).

Furthermore, when drawing dots in a Lewis diagram, there should be at least one dot in eachdirection before a second dot in any direction is placed. This corresponds to Hund’s rule, whichstates that if there are several orbitals available, electrons will occupy the orbitals singly beforethey do so in pairs.

Representative metals form cations by losing all of their valence electrons. For example:

On the other hand, nonmetals form anions by gaining electrons until they are isoelectronic with(have the same number of electrons as) a noble gas. For example:

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1.1.1 Exercises

1. Write the Lewis symbol for Calcium.

2. Write the Lewis symbol for Oxygen.

3. Write the Lewis symbol for Sulfur.

4. Write the Lewis symbol for Selenium.

5. Write the Lewis symbol for Magnesium.

6. Write the Lewis symbol for Aluminum.

7. Write the Lewis symbol for Bromine.

8. Write the Lewis symbol for Xenon.

9. Write the Lewis symbol for a Calcium, 2+ ion.

10. Write the Lewis symbol for a Selenium, 2− ion.

11. Write the Lewis symbol for a Potassium, + ion.

12. Write the Lewis symbol for a Sulfur, 2− ion.

13. Write the Lewis symbol for a Nitrogen, 3− ion.

14. Write the Lewis symbol for an Iodine, 1− ion.

15. Write the Lewis symbol for a Strontium, 2+ ion.

1.2 Ionic Bonding and Lattice Energy

1.2.1 Coulomb’s Law

Theorem 1. Coulomb’s Law states that

E = kQ+Q−

r

whereE is the Potential Energy of interaction,Q+ is the charge of the positive ion,Q− is the chargeof the negative ion, r is the distance between the ions, and k is a constant of proportionality.

When dealing with a positive ion and a negative ion, the value of E will be negative since Q− < 0and Q+ > 0. This makes sense because the ions will be attracted to each other, and attractiveforces have negative direction while repulsive forces have positive direction.

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Notice that if we are dealing with a positive ion and a negative ion, as r decreases, E decreases. Alow potential energy E means that the pair of ions is stable.

We can calculate the distance between ionic centers by summing their ionic radii:

r = r+ + r−.

1.2.2 Lattice Energy

Definition 2. The lattice energy is the energy needed to break the ions in 1 mole of a solid ioniccompound apart into gaseous ions. When ions are gaseous, they are so far apart that their inter-action is negligible.

An example: the lattice energy of NaF is 908 kJ/mol. This means that 908 kJ are needed to vaporizeone mole of NaF (s) into one mole of Na+ (g) ions and one mole of F− (g) ions.

A big lattice energy implies that the ionic solid is stable; why? If it takes a lot of energy to breakapart a solid, it’s a stable solid.

What does this sound like? When an ionic solid melts, the ions have enough energy to overcomepotential energy of attraction and move far away from each other. So if an ionic solid has a highmelting point, it takes a lot of energy to break these ions apart. We conclude that ionic solids withhigh melting points have high lattice energies.

By Coulomb’s Law, a greater separation between ions implies that the energy holding the ionsapart is not very high, so the lattice energy is low since it’s easy to break the ionic solid apart.

The following table summarizes these trends:

r (pm) Lattice Energy (kJ/mol) Melting Point (◦C)NaF 231 908 1012NaCl 276 788 801NaBr 290 736 747NaI 314 686 660CaO 239 3540 2580

1.2.3 Forming Ionic Bonds

Ionic bonds tend to form between two elements if one element has a low ionization energy and theother has high electron affinity; in other words, when the first element easily loses electrons andthe second element easily accepts electrons.

Also, if the lattice energy of an ionic solid is high, the gaseous ionic components will tend to formionic bonds. This makes sense if you think backward: the lattice energy of the ionic solid is high,so it takes a lot of energy to break the solid apart. Thus, a lot of energy is released when the gaseousions are reacted and “put together” into a solid.

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1.2.4 The Born-Haber Cycle

The Born-Haber Cycle relies on Hess’s Law: the heat of reaction is equal to the difference betweenthe heat of formation of the products and the heat of formation of the reactants, or:

∆H◦reaction =

∑∆H◦

f, products −∑

∆H◦f, reactants

The lattice energy of an ionic solid is essentially the heat of formation of the solid from the ionicgaseous components. Therefore, to calculate the lattice energy of an ionic solid, first find the heatof formation of the gaseous ions. Then, find the heat of formation of the ionic solid. Take thedifference, and you’ve found the lattice energy.

When calculating lattice energy, remember to consider enthalpy changes due to phase changes,breaking and forming bonds, ionization, and electron affinity.

1.2.5 Exercises

1. What factors does the energy of attraction between two ions depend on?

2. Which will have the higher melting point: NaCl or CaO?

3. Which will have the higher lattice energy: NaCl or CaO?

4. Which will have the higher melting point: NaCl or NaI?

5. Which will have the higher lattice energy: KI or KCl?

6. Which will have the higher melting point: KCl or CaCl2?

7. Which will have the higher melting point: RbI or NaI?

8. What is the chemical equation for the process corresponding to the lattice energy of MgO?

9. Calculate the lattice energy of potassium chloride, given the following:

Enthalpy of sublimation of potassium: 90.0 kJ

Bond energy between two chlorine atoms: 242.7 kJ

Ionization energy of potassium: 419 kJ

Electron affinity of chlorine: 349 kJ

Heat of formation of potassium chloride: −435.9 kJ

10. Calculate the lattice energy of sodium bromide, given the following:

Enthalpy of sublimation of sodium: 109 kJ

Bond energy between two bromine atoms: 192 kJ

Ionization energy of sodium: 496 kJ

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Electron affinity of bromine: 324 kJ

Heat of formation of sodium bromide: -359 kJ

1.3 Covalent Bonding and Lewis Structures

Definition 3. The Octet Rule states that atoms gain or lose electrons until they have the samenumber (eight) of valence electrons as noble gas atoms.

Covalent bonds are formed when two atoms in a molecule share a pair of electrons. This differsfrom ionic bonds, in which one atom actually takes the electrons from the other atom.

Hydrogen does not follow the Octet Rule. It only needs two electrons to become isoelectronic withhelium.

The formation of a covalent bond in hydrogen chloride can be modeled with Lewis structures:

Electron pairs that are not used in bonding are called lone pairs. The below diagrams show that, incovalent bonding, each atom (except hydrogen) has an octet of valence electrons, through sharingof electron pairs:

Sometimes, two or three pairs of electrons are shared by two atoms in order to reach an octet.These are multiple bonds. Atoms with double bonds are closer together than atoms with singlebonds, and atoms with triple bonds are even closer.

1.3.1 Exercises

1. Draw the Lewis structure for N2H4. How many lone pairs are there on the N atom?

2. How many lone pairs are there on the P atom in PH3?

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3. How many lone pairs are there on the S atom in SCl2?

4. How many lone pairs are there on the O atom in H2CO?

5. Write the Lewis structure for NH+7 .

6. Write the Lewis structure for NCl3.

7. Write the Lewis structure for CF2Cl2.

1.4 Electronegativity

Definition 4. The electronegativity of an atom is its ability to attract a shared electron pair towarditself.

No bonds are completely polar or completely ionic; they exhibit characteristics of both. In chemi-cal bonds, the electron pairs are not always shared equally. The more electronegative element pullsthe electrons more.

If the electronegativity difference between two atoms is equal to zero (e.g. H—H, N—N), the bondbetween the atoms is a nonpolar covalent bond or a pure covalent bond.

If the electronegativity difference between two atoms is less than two (e.g. C—Cl, S—H), thebond between the atoms is a polar covalent bond. Polar, because there are more electrons at one“pole” of the atom and fewer electrons at the other. Covalent, because the atoms are still prettymuch sharing electron pairs.

If the electronegativity difference between two atoms is at least two (e.g. Na—Cl, K—Br), thebond between the atoms is mostly ionic because the more electronegative atom has pretty muchpulled the electrons off of the less electronegative atom. Ionic bonds are always polar.

1.4.1 Trends

Elements lower in the periodic table tend to have lower electronegativity because they already haveso many electrons that it’s hard to pull more electrons.

Elements to the right of the periodic table tend to have higher electronegativity because they wantto complete their octet.

1.4.2 Exercises

1. Arrange the bonds in order of increasing ionic character: C—O, C—H, and O—H.

2. Arrange the bonds in order of increasing ionic character: N—O, Na—O, O—O, and S—O.

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3. Which is the most electronegative element, given the trend of electronegativity: arsenic,selenium, or sulfur?

4. Which atom is the most electronegative: lithium, cesium, phosphorus, arsenic, or germa-nium?

5. What kind of bond forms between rubidium and bromine?

6. What kind of bond forms between sulfur and sulfur?

7. What kind of bond forms between carbon and nitrogen?

8. What kind of bond forms between selenium and chlorine?

9. What kind of bond forms between aluminium and chlorine?

10. What kind of bond forms between potassium and fluorine?

11. What kind of bond forms between chlorine and chlorine?

12. What kind of bond is between the oxygen and hydrogen atoms in CH3OH?

13. Which of the following is/are nonpolar covalent bonds? H—Cl, Li—Br, Se—Br, and Br—Br

1.5 Formal Charge

The formal charge is a property of a structural formula, not of a chemical. It is not the actual chargeof a molecule or any atoms in the molecule.

FC = nv − nN −1

2nB

where FC is the formal charge, nv is the number of valence electrons, nN is the number of non-bonding electrons, and nB is the number of bonding electrons.

If you are comparing two possible Lewis structures for a molecule, the structure with no formalcharges is preferred. For example, of the below two possible structures for BF3, the first structureis preferred.

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In structure 1, the boron atom has 3 − 0 − 12(6) = 0 formal charge, and the fluorine atoms have

7− 6− 12(2) = 0 formal charge.

In structure 2, the boron atom has 3 − 0 − 12(8) = −1 formal charge; the double-bonded fluorine

atom has 7 − 4 − 12(4) = 1 formal charge; and the other fluorine atoms have 7 − 6 − 1

2(2) = 0

formal charge.

In neutral molecules, the sum of formal charges is equal to zero. In polyatomic ions, the sum offormal charges is equal to the charge of the ion.

1.5.1 Exercises

1. In the following molecule, the formal charge of carbon is...? The formal charge of oxygenis...?

2. In the following molecule, the formal charge of sulfur is...? The formal charge of double-bonded oxygen is...? The formal charge of single-bonded oxygen is...?

1.6 Resonance

Sometimes, it’s impossible to draw an accurate electron dot structure. For example, in the nitriteion, NO2, by the Lewis dot structure, one of the oxygen atoms would be double-bonded to thenitrogen atom, and the other oxygen atom would be single-bonded to the nitrogen atom. But thisis not the case if you observe the nitrite ion; both bonds are of the same length.

How can you draw a resonance structure? Draw the different possible dot structures, and draw adouble-sided arrow (↔) to denote resonance. For example, the resonance structure of the nitriteion is:

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1.6.1 Exercises

1. Draw three resonance structures for N2O. The skeletal structure is N—N—O.

2. Draw resonance structures for nitric acid, HNO3.

1.7 Exceptions to the Octet Rule

Sometimes, bad molecules will break the rules.

Boron halides, BX3, will have an incomplete octet.

Also, NO and NO2 have an odd number of electrons, so they can’t possibly have an octet.

Hydroxyl radical and hydroperoxyl radical do not follow the octet rule.

Some molecules have an expanded octet: more than eight valence electrons. Nonmetal atoms fromthe third period or below can form expanded octets. Examples include SF4, SF6, ClF5, BrF5, IF7,and PCl5:

1.7.1 Exercises

1. Draw the Lewis structure for GaI3.

2. Draw the Lewis structure for NO2.

3. Draw the Lewis structure for ClF3.

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1.8 Bond Energies

You can find the average bond energy of a chemical bond by using given enthalpies of reaction. Forexample, if you know the enthalpy of reaction of the decomposition of methane into carbon andhydrogen is 1664 kJ, since this decomposition is equivalent to the breaking of four C—H bonds,you can determine that the average bond energy of a C—H bond is 1664÷ 4 = 416 kJ/mol.

Enthalpies of reaction in the gas phase can be estimated using average bond energies. A chemicalreaction can be viewed as follows: First, the bonds between atoms in the reactants are broken;then, the atoms are rearranged; and finally, new bonds are formed between atoms. Breaking bondstakes energy; forming bonds releases it. But keep in mind that this only works for reactions in thegas phase, and that the enthalpy of reaction that is calculated is only an estimate.

1.8.1 Exercises

1. Estimate the heat of reaction of Cl2 (g) + I2 (g)→ 2ICl (g), using bond energies from a datatable, and given that the bond energy of I—Cl is 210 kJ/mol.

2. Use a data table to find the triple-bond energy between nitrogen atoms and the H—H bondenergy. Given that the reaction 1

2N2 (g) + 3

2H2 (g)→ NH3 (g) has an enthalpy of reaction

of -46.3 kJ/mol, calculate the average N—H bond energy in ammonia.

3. Given bond energies from a data table, find the enthalpy of formation for ammonia. 12

N2 (g)+ 3

2H2 (g)→ NH3.

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Chapter 2

Molecular Geometry and Hybridization ofAtomic Orbitals

2.1 Molecular Geometry and the VSEPR Model

The Valence-Shell Electron-Pair Repulsion theory relies on the fact that electron pairs repel eachother (since they are all negatively charged). Thus, electron pairs will arrange themselves as faraway from each other as possible.

So when there are two electron pairs around the central atom, the farthest they can be is diametri-cally opposite. The shape is then linear and the bond angles are 180 degrees.

When there are three electron pairs, the farthest they can be is in a trigonal planar, or a flat triangle.The bond angles are 120 degrees.

When there are four electron pairs, the farthest they can be is in a tetrahedron. The bond angles are109.5 degrees.

When there are five electron pairs, the farthest they can be is in a trigonal bipyramid, or a flattriangle along with two poles. The “flat triangle” pairs are called equatorial and the “pole” pairsare called polar. The bond angles between the equatorial pairs are 120 degrees, and the bond anglesbetween an equatorial pair and a polar pare is 90 degrees.

When there are six electron pairs, the farthest they can be is in an octahedron. Each bond angle is90 degrees.

2.1.1 Lone Pairs

Lone pairs of electrons take up more room, so they distort the geometry of a molecule. For exam-ple, if a central atom has three bound electron pairs around it, its shape will be a trigonal planar.But if it has two bound electron pairs and one unbound electron pair (lone pair), it will be bent,with bond angle of 119 degrees.

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2.1.2 The Shapes

Memorize this table. Yellow atoms do not really exist; they are simply placeholders.

Total Pairs Bound Pairs Lone Pairs Shape Bond Angle Example Picture

2 2 0 linear 180 CO2

3 3 0 trigonal planar 120 BF3

3 2 1 bent 119 SO2

4 4 0 tetrahedral 109.5 CH4

4 3 1 trigonal pyramid 107.5 NH3

4 2 2 bent 104.5 H2O

5 5 0 trigonal bipyramid 90, 120 PCl5

5 4 1 seesaw 173.1, 101.6 SF4

5 3 2 T-shape 87.5, < 180 ClF3

5 2 3 linear 180 XeF2

6 6 0 octahedral 90, 180 SF6

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Total Pairs Bound Pairs Lone Pairs Shape Bond Angle Example Picture

6 5 1 square pyramid 84.8 BrF5

6 4 2 square planar 90, 180 XeF4

7 7 0 pentagonal bipyramid 90, 72 IF7

2.1.3 Bond Angles

Lone pairs repel each other more than they repel bonding pairs of electrons, and lone pairs repelbonding pairs of electrons more than bonding pairs of electrons repel each other, so when there arelone pairs present, bond angles tend to decrease.

2.1.4 Exercises

1. Predict the geometry and bond angles of SnCl4.

2. Predict the geometry and bond angles of O3.

3. Predict the geometry and bond angles of IF5.

4. Predict the geometry and bond angles of XeF2.

5. Predict the geometry and bond angles of BeCl2.

6. Predict the geometry and bond angles of NF3.

7. Predict the geometry and bond angles of SF4.

8. Predict the geometry and bond angles of ClF3.

9. Predict the geometry and bond angles of KrF4.

10. Predict the geometry and bond angles of ClO−2 .

11. Predict the geometry and bond angles of CO2−3 .

12. Predict the geometry and bond angles of ZnCl2−4 .

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2.2 Polar Molecules

Definition 5. A dipole is when the center of positive charge and the center of negative charge arenot the same. A molecule with a dipole is polar and has a dipole moment.

The dipole moment, µ, is a vector with its tail at the positive end and the head at the negative(Memory trick: things tend to move from up to down, like in gravity). The length of the vectorrepresents the magnitude of the dipole moment.

The dipole moment can be calculated with the formula:

µ = Qr

where Q is the magnitude of the charge from either end of the dipole and r is the distance betweenthe centers of positive and negative charge.

Polar molecules have dipole moments, and only polar molecules have dipole moments. In general,homonuclear diatomic molecules are nonpolar while heteronuclear diatomic molecules are polar.

2.2.1 Polyatomic Molecules

For a polyatomic molecule, the dipole moments of each bond are additive. In other words, you canadd the vectors of the dipole moments of each bond to find the dipole moment of the molecule.

Again, a molecule with a dipole moment is polar, and a molecule with no dipole moment isnonpolar.

Sometimes, the vectors can add to zero; for example, in carbon dioxide, the dipole moments cancelout, so the carbon dioxide molecule is nonpolar.

2.2.2 Exercises

1. Is CO polar or nonpolar?

2. Is H2CO polar or nonpolar?

3. Is CCl4 polar or nonpolar?

4. Is BCl3 polar or nonpolar?

5. Is SO3 polar or nonpolar?

6. Is PF3 polar or nonpolar?

7. Is SF6 polar or nonpolar?

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8. Is BeH2 polar or nonpolar?

9. Is CO2 polar or nonpolar?

10. Is SO2 polar or nonpolar?

11. Is NO2 polar or nonpolar?

2.3 Valence Bond Theory and Hybrid Orbitals

Valence Bond Theory is one of the two quantum mechanics descriptions of chemical bonding.

VBT states that a covalent bond forms when orbitals from two atoms overlap. This overlap createsa region where the probability of finding an electron is very high; this tends to attract both atoms.

Sometimes, a phenomenon called hybridization may occur. We illustrate it with the followingexample.

In its ground state, an isolated beryllium atom has ground state configuration 1s22s2. Its orbitaldiagram looks like this:

But what can account for the compound BeCl2? This orbital diagram makes it look like Be won’tform bonds.

The 2s and 2p orbitals actually have similar energy levels, so it doesn’t take much energy to raisean electron from a 2s orbital to a 2p orbital. On the other hand, forming a chemical bond releasesa relatively huge amount of energy, so if an electron is promoted to a higher orbital and then twobonds are formed, the process has a net release of energy.

So maybe when two chlorine atoms are nearby, the orbital diagram for beryllium becomes this:

But through observation, it’s been determined that the two bonds formed between beryllium andthe chlorine atoms are equal in length and strength. So what may occur is hybridization. The 2sorbitals “mix” with a 2p orbital to create hybrid orbitals: the sp orbitals. So, really, the orbitaldiagram for beryllium near two chlorine atoms is:

There are five common types of hybrid orbitals. These types, and their characteristic geometries,are shown in the table below.

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Hybrid Orbital Geometry Bond Angle Examplesp linear 180 BeCl2sp2 planar triangle 120 BF3

sp3 tetrahedral 109.5 CH4, NH+4

sp3d trigonal bipyramid 90, 120 PCl5sp3d2 octahedral 90 SF6, SbCl−6

2.3.1 Different Bonds

Single bonds are called sigma bonds or σ bonds. They are shaped cylindrically between the centersof the two atoms.

Multiple bonds also contain pi bonds or π bonds. They extend above and below the sigma bonds,reaching over and under them. Each π bond has two regions of electron density (above and below),but remember that it’s still just one bond.

2.3.2 Exercises

1. According to Valence Bond Theory, what causes a chemical bond?

2. What’s the hybridization of the central atom in PH3?

3. What’s the hybridization of the central atom in PCl5?

4. What’s the hybridization of the central atom in H2CO? What are the bond angles? Howmany sigma and pi bonds are there in the entire molecule?

5. How many sigma bonds and how many pi bonds are there in a molecule of carbon dioxide?

6. What is the angle between two sp orbitals on the same atom?

7. What is the angle between two sp2 orbitals on the same atom?

8. What is the angle between two sp3 orbitals on the same atom?

9. What hybrid orbital set is used by C in CS2?

10. What hybrid orbital set is used by N in N?

11. What hybrid orbital set is used by B in BF3?

12. What hybrid orbital set is used by Cl in ClF3?

13. What hybrid orbital set is used by S in SF2?

14. What hybrid orbital set is used by S in SF4?

15. What hybrid orbital set is used by Xe in XeF4?

16. What is the geometry of SeCl6, in which the sulfur atom is sp3d2 hybridized?

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Chapter 3

Intermolecular Forces, and Liquids andSolids

3.1 Kinetic Molecular Theory of Liquids and Solids

Gases Liquids SolidsTakes volume/shape of container Definite volume, indefinite shape Definite volume and shape

Fluid (flows) Fluid Not fluidHighly compressible Slightly compressible Virtually incompressible

Low density High density High densityMolecules far apart Molecules close together Molecules close together

3.2 Intermolecular Forces

3.2.1 van der Waals Forces

van der Waals forces keep atoms together.

Dipole-Dipole Forces

When two polar molecules are nearby, the positive end of one molecule will attract the negativeend of the other, and vice versa. A larger dipole moment causes a stronger force of attraction.

Dipole-induced Dipole Forces

A polar molecule can polarize another molecule. This creates, or “induces” a new dipole in thesecond molecule. These dipoles can then interact.

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London Dispersion Forces

The constant motion of electrons means that there might be an imbalance of electrons on differentsides of a molecule at a specific time. Then there will be a temporary dipole moment. Thistemporary dipole moment can induce dipoles in nearby molecules.

The polarizability of a molecule is the tendency for an electron cloud to be distorted by nearbyelectrical charges. As the number of electrons in a molecule increases, the polarizability increasesas well. The number of electrons of a molecule corresponds to the mass of the molecule, so thestrength of dispersion forces increases as molecular mass increases.

3.2.2 Ion-Dipole Forces

There is an electrostatic attraction between an ion and the part of a polar molecule with oppositecharge. For example, water molecules are polar, so when table salt (an ionic compound, NaCl)enters water, the sodium cation will be attracted to the negative part of a water molecule while thechlorine anion will be attracted to the positive part of a water molecule; hence, salt dissolves.

3.2.3 Hydrogen Bonding

Hydrogen bonding is not actually chemical bonding. The hydrogen atom in a polar bond willhave a dipole-dipole interaction with an O, N, or F atom that has a lone pair of electrons availablebecause the hydrogen atom has a partial positive charge that attracts the lone pair of electrons.

3.2.4 Relative Strengths

Hydrogen bonding is the strongest intermolecular force. Dipole-dipole forces are of intermediatestrength. The London Dispersion Forces are weakest.

3.2.5 Exercises

1. The dipole moment of HCl is 1.03 D, and the dipole moment of HCN is 2.99 D. Which oneprobably has a higher boiling point?

2. Which has a higher boiling point: O2 or CO?

3. Which has a higher boiling point: Br2 or ICl?

4. Which has a higher boiling point: H2O or H2S?

5. Which has a higher boiling point: PH3 or AsH3?

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6. Which substance probably has the strongest intermolecular attractive forces? N2, Ar, F2, orCl2?

7. What intermolecular forces are experienced by CCl4 (l)?

8. What intermolecular forces are experienced by HBr (l)?

9. What intermolecular forces are experienced by CH3OH (l)?

10. What intermolecular forces are experienced by PCl3?

11. What intermolecular forces are experienced by CO2?

12. What intermolecular forces are experienced by Cl2?

13. What intermolecular forces are experienced by ICl?

14. Which has the strongest intermolecular forces? CH4, Cl2, CO, or CS2?

15. Which of the following is/are capable of hydrogen bonding? CH3F, HF, CH3CH2OH,CH3NH2, or CH4?

16. Which type(s) of intermolecular forces must be overcome to vaporize water?

17. Which type(s) of intermolecular forces must be overcome to dissociate hydrogen gas intohydrogen atoms?

18. Which type(s) of intermolecular forces must be overcome to boil liquid diatomic oxygen?

3.3 Properties of Liquids

Surface tension is the amount of energy required to increase the surface area of a liquid by a unitarea. Strong intermolecular forces increase surface tension because the molecules don’t want tomove away from each other.

Cohesion is the intermolecular attraction between similar molecules in a drop of liquid. Memorytrick: the prefix “co-” means “mutually,” and cohesion is between the same type of molecule. It’smutual.

Adhesion is the intermolecular attraction between dissimilar molecules; e.g. between water andwax. Memory trick: the prefix “ad-” means “placed near.” Adhesion occurs when you place aliquid near another substance.

Viscosity is a liquid’s resistance to flow. Strong intermolecular forces increase viscosity becausethe molecules don’t want to move away from each other.

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3.3.1 Water

Water has a large surface tension, a high specific heat, a huge heat of vaporization, and a highboiling point. These are due to the strength of hydrogen bonding between water molecules.

Water’s density is a strange animal. As water is cooled from 100◦ C to 4◦ C, its density increases.But if it is cooled below 4◦, the density decreases. Also, unlike almost every other substance, thedensity of solid water (ice) is less than the density of liquid water, so ice floats on water.

3.3.2 Exercises

1. How can a glass be filled slightly above the rim?

2. Water has the formula H2O, and ether has the formula CH3CH2OCH2CH3. Why does etherhave a greater viscosity?

3. Which has a greater viscosity at room temperature? C2H5OH or CH3OCH3?

3.4 Phase Changes and Phase Diagrams

3.4.1 Liquid-Vapor Equilibrium

In a closed container, a liquid and its vapor will eventually reach equilibrium. At equilibrium, therate of vaporization will equal the rate of condensation. This does not mean that vaporization andcondensation stop.

The vapor will exert a pressure called the vapor pressure. At liquid-vapor equilibrium, the vaporpressure is the equilibrium vapor pressure.

As temperature increases, the rate of vaporization increases and the rate of condensation remainsconstant, so the net rate of vaporization increases. This explains high humidity during the summercompared to during the winter.

3.4.2 Boiling

Boiling of a liquid occurs when bubbles form. In order for bubbles to form, the vapor inside thebubble must push outward, against the atmospheric pressure. In other words, the boiling point ofa liquid is where the vapor pressure is equal to the atmospheric pressure. Atmospheric pressurechanges from time to time, so boiling points of liquids change. The normal boiling point is theboiling temperature when the atmospheric pressure is 1 atm.

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3.4.3 Heat of Vaporization

The energy needed to vaporize one mole of a certain liquid is the molar heat of vaporization.Liquids with strong intermolecular forces have high heats of vaporization, low vapor pressures,and high normal boiling points. (Why?)

3.4.4 The Clausius-Clapeyron Equation

lnP = −∆Hvap

RT+ C

ln

(P1

P2

)=

∆Hvap

R

(T1 − T2T1T2

)where ln is the natural logarithm, P is vapor pressure, T is absolute temperature, C is a constant,and R = 8.314 J/(K·mol) is the ideal gas constant.

3.4.5 Critical Temperature and Pressure

The critical temperature of a substance is the highest temperature where the substance can exist asa liquid. The critical pressure of a substance is the lowest pressure that will liquefy a gas at thecritical temperature.

3.4.6 Liquid-Solid Equilibrium

The molar heat of fusion of a substance is the amount of energy needed to melt one mole of asolid. The molar heat of fusion is always smaller than the molar heat of vaporization becausevaporization completely separates molecules from each other, whereas melting only separates themolecules by a small amount.

3.4.7 Heating Curves

A heating curve is a graph of Temperature vs. Heat Absorbed. When absorbed heat is low, thesubstance is a solid. As the absorbed heat increases, the temperature of the substance increasesroughly linearly. Then, at the melting/freezing point, the temperature of the substance remainsconstant as absorbed heat increases. This is because the inputted heat becomes potential energy(changing the state of matter) and not kinetic energy (temperature).

After the substance is completely melted, it is a liquid, and again, the temperature of the substanceincreases roughly linearly with the increase of absorbed heat. Again, at the boiling/condensationpoint, the temperature will remain constant as the state of matter changes to a gas.

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When all of the liquid has vaporized, the substance becomes a gas, and the temperature of thesubstance continues to increase roughly linearly with the increase of absorbed heat.

This can continue, as gas will eventually become plasma; but this is beyond our scope.

Keep in mind that a cooling curve is the opposite of a heating curve; the x-axis becomes “heatlost” instead of “heat absorbed.”

3.4.8 Sublimation and Deposition

Sublimation is the conversion of a solid directly into a gas, while deposition is the conversion of agas directly into a solid. Dry ice and iodine sublime readily, and ice sublimes to an extent.

Just as with liquids vaporizing, a solid that sublimates will have a greater vapor pressure as tem-perature increases.

Hess’s Law gives us:

∆Hsub = ∆Hfus + ∆Hvap

3.4.9 Phase Diagrams

Phase diagrams describe a substance’s state of matter at each pressure and temperature.

The lines in the phase diagram represent equilibriums. For example, the line between the solid andliquid regions indicates where a substance can exist in both solid and liquid form.

All three lines, and all three regions, meet at the triple point, where gas, solid, and liquid forms areall in equilibrium.

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3.4.10 Exercises

1. How do pressure cookers work?

2. How much heat is released when 1 gram of steam condenses at 100◦ C?

3. The heat of fusion of aluminium is 10.7 kJ/mol. How much energy is needed to melt onethousand kilograms of aluminum at the melting point, or 660◦ C?

4. The vapor pressure of water is 55.32 mmHg at 40.0◦ C, and 92.51 mmHg at 50.0◦ C. Calcu-late the molar heat of vaporization of water.

5. The molar heat of vaporization of bromine is 30.04 kJ/mol. What is the heat of vaporizationper gram of bromine?

6. The heat of vaporization of iodine is 41.7 kJ/mol at the boiling point of iodine, or 456 K.How much heat is needed to vaporize 40.0 g of iodine?

7. The molar heats of fusion and vaporization of potassium are, respectively, 2.4 and 79.1kJ/mol. What is the molar heat of sublimation of potassium?

8. The heat of vaporization of ammonia is 23.2 kJ/mol at its boiling point. How many grams ofammonia can be vaporized with 25 kJ of heat?

9. How much heat is needed to convert 1 kg of ice at −10◦ C completely into steam at 120◦ C?

10. Which of the following is/are endothermic? Melting of ice, evaporation of ethanol, conden-sation of steam, freezing of water, and sublimation of iodine?

11. Which substance has the higher vapor pressure at a given temperature: C2H5OH or CH3OH?

12. Which substance has the higher vapor pressure at a given temperature: Cl2 or Br2?

13. Which substance has the higher vapor pressure at a given temperature: CH3Br or CH3Cl?

14. The vapor pressure of liquid potassium is 1.00 mmHg at 341◦ C and 10.0 mmHg at 443◦ C.What is the molar heat of vaporization of potassium?

15. The vapor pressure of ethanol is 100 mmHg at 34.9◦ C, and 400 mmHg at 63.5◦ C. What isthe molar heat of vaporization of ethanol?

16. The vapor pressure of liquid potassium is 10.0 mmHg at 443◦ C. The heat of vaporization is82.5 kJ/mol. What is the boiling point?

17. The vapor pressure of ethanol is 400 mmHg at 63.5◦ C. Its molar heat of vaporization is 41.7kJ/mol. What is the vapor pressure of ethanol at 34.9◦ C?

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