Chem Exam 3 Flashcards

Potential Energy Between Charged Particles E potential

Tro, Chemistry: A Molecular Approach

1  q1 • q2  =   4π ∈0  r 

1

Bonding • a chemical bond forms when the potential energy of the bonded atoms is less than the potential energy of the separate atoms • have to consider following interactions: nucleus-to-nucleus repulsion electron-to-electron repulsion nucleus-to-electron attraction

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Types of Bonds Types of Atoms metals to nonmetals nonmetals to nonmetals metal to metal Tro, Chemistry: A Molecular Approach

Type of Bond Ionic Covalent Metallic

Bond Characteristic electrons transferred electrons shared electrons pooled 3

Ionic Bonds • when metals bond to nonmetals, some electrons from the metal atoms are transferred to the nonmetal atoms metals have low ionization energy, relatively easy to remove an electron from nonmetals have high electron affinities, relatively good to add electrons to

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Covalent Bonds • nonmetals have relatively high ionization energies, so •

it is difficult to remove electrons from them when nonmetals bond together, it is better in terms of potential energy for the atoms to share valence electrons

 potential energy lowest when the electrons are between the nuclei

• shared electrons hold the atoms together by attracting nuclei of both atoms

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Determining the Number of Valence Electrons in an Atom • the column number on the Periodic Table will tell you how many valence electrons a main group atom has  Transition Elements all have 2 valence electrons; Why? 1A

2A

3A

4A

5A

6A

7A

8A

Li

Be

B

C

N

O

F

Ne

1 e-1

2 e-1

3 e-1

4 e-1

5 e-1

6 e-1

7 e-1

8 e-1

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Lewis Symbols of Atoms • aka electron dot symbols • use symbol of element to represent nucleus and •

inner electrons use dots around the symbol to represent valence electrons  pair first two electrons for the s orbital  put one electron on each open side for p electrons  then pair rest of the p electrons •

Li

•

Be

• •

B

• •

• Tro, Chemistry: A Molecular Approach

•

C •

• •

•

N •

• • •

•

O ••

• • •

• •

F ••

•• • •

• •

Ne

• •

•• 7

Lewis Symbols of Ions • Cations have Lewis symbols without valence electrons Lost in the cation formation

• Anions have Lewis symbols with 8 valence electrons Electrons gained in the formation of the anion •

Li•

Li+1

• •

F ••

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• •

 ••  • F • • •   •• 

−1

8

Octet Rule

• when atoms bond, they tend to gain, lose, or share electrons to •

result in 8 valence electrons ns2np6  noble gas configuration

• many exceptions

 H, Li, Be, B attain an electron configuration like He  He = 2 valence electrons  Li loses its one valence electron  H shares or gains one electron  though it commonly loses its one electron to become H+

 Be loses 2 electrons to become Be2+  though it commonly shares its two electrons in covalent bonds, resulting in 4 valence electrons

 B loses 3 electrons to become B3+  though it commonly shares its three electrons in covalent bonds, resulting in 6 valence electrons

 expanded octets for elements in Period 3 or below  using empty valence d orbitals Tro, Chemistry: A Molecular Approach

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Lewis Theory • the basis of Lewis Theory is that there are

certain electron arrangements in the atom that are more stable octet rule

• bonding occurs so atoms attain a more stable electron configuration

more stable = lower potential energy no attempt to quantify the energy as the calculation is extremely complex Tro, Chemistry: A Molecular Approach

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Energetics of Ionic Bond Formation • the ionization energy of the metal is endothermic  Na(s) → Na+(g) + 1 e ─ ∆H° = +603 kJ/mol

• the electron affinity of the nonmetal is exothermic  ½Cl2(g) + 1 e ─ → Cl─(g)

∆H° = ─ 227 kJ/mol

• generally, the ionization energy of the metal is larger

•

than the electron affinity of the nonmetal, therefore the formation of the ionic compound should be endothermic but the heat of formation of most ionic compounds is exothermic and generally large; Why?  Na(s) + ½Cl2(g) → NaCl(s)

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∆H°f = -410 kJ/mol 11

Ionic Bonds • electrostatic attraction is nondirectional!! no direct anion-cation pair

• no ionic molecule chemical formula is an empirical formula, simply giving the ratio of ions based on charge balance

• ions arranged in a pattern called a crystal lattice every cation surrounded by anions; and every anion surrounded by cations maximizes attractions between + and - ions Tro, Chemistry: A Molecular Approach

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Lattice Energy • the lattice energy is the energy released when the

solid crystal forms from separate ions in the gas state  always exothermic  hard to measure directly, but can be calculated from knowledge of other processes

• lattice energy depends directly on size of charges and inversely on distance between ions

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Born-Haber Cycle • method for determining the lattice energy of an ionic substance by using other reactions use Hess’s Law to add up heats of other processes

•

∆H°f(salt) = ∆H°f(metal atoms, g) + ∆H°f(nonmetal atoms, g)

+ ∆H°f(cations, g) + ∆H°f(anions, g) + ∆H°f(crystal lattice)  ∆H°f(crystal lattice) = Lattice Energy  metal atoms (g) → cations (g), ∆H°f = ionization energy don’t forget to add together all the ionization energies to get to the desired cation M2+ = 1st IE + 2nd IE

 nonmetal atoms (g) → anions (g), ∆H°f = electron affinity

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Trends in Lattice Energy Ion Size • the force of attraction between charged particles is inversely proportional to the distance between them • larger ions mean the center of positive charge (nucleus of the cation) is farther away from negative charge (electrons of the anion) larger ion = weaker attraction = smaller lattice energy Tro, Chemistry: A Molecular Approach

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Trends in Lattice Energy Ion Charge • the force of attraction between

•

oppositely charged particles is directly proportional to the product of the charges larger charge means the ions are more strongly attracted

Lattice Energy = -910 kJ/mol

 larger charge = stronger attraction = larger lattice energy

• of the two factors, ion charge generally more important Tro, Chemistry: A Molecular Approach

Lattice Energy = -3414 kJ/mol 16

Ionic Bonding Model vs. Reality • ionic compounds have high melting points and boiling points  MP generally > 300°C  all ionic compounds are solids at room temperature

• because the attractions between ions are strong, breaking down the crystal requires a lot of energy  the stronger the attraction (larger the lattice energy), the higher the melting point

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Ionic Bonding Model vs. Reality

• ionic solids are brittle and hard • the position of the ion in the crystal is critical to establishing maximum attractive forces – displacing the ions from their positions results in like charges close to each other and the repulsive forces take over +

+

-

+

+ +

+

-+ - +- + + +

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-+ -+ +- +- +- + + + + -+ + + + - + - + - + -

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Ionic Bonding Model vs. Reality • ionic compounds conduct electricity in the liquid state • • •

or when dissolved in water, but not in the solid state to conduct electricity, a material must have charged particles that are able to flow through the material in the ionic solid, the charged particles are locked in position and cannot move around to conduct in the liquid state, or when dissolved in water, the ions have the ability to move through the structure and therefore conduct electricity

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Covalent Bonding: Bonding and Lone Pair Electrons • Covalent bonding results when atoms share pairs • •

of electrons to achieve an “octet” Electrons that are shared by atoms are called bonding pairs Electrons that are not shared by atoms but belong to a particular atom are called lone pairs  aka nonbonding pairs Bonding Pairs

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•• •• • •• • •• O •• •• S • O •• •

Lone Pairs 20

Single Covalent Bonds • two atoms share a pair of electrons  2 electrons

• one atom may have more than one single bond

••

••

••

•

F

F

•

•• F ••

••

••

••

• F •• •••

•• H• • O •H •• ••• H O H •• •

F •

••

••

••

F

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Double Covalent Bond • two atoms sharing two pairs of electrons 4 electrons

•

•• •O •• • • •O •• O• •• •• •• •

•• •O ••

·· · ·· O ··O ·

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Triple Covalent Bond • two atoms sharing 3 pairs of electrons 6 electrons

••

••

•• N •• •• N

··N Tro, Chemistry: A Molecular Approach

•• •N •

•

•

•• •N •

N ·· 23

Covalent Bonding Model vs. Reality • molecular compounds have low melting points and boiling points

 MP generally < 300°C  molecular compounds are found in all 3 states at room temperature

• melting and boiling involve breaking the attractions

between the molecules, but not the bonds between the atoms  the covalent bonds are strong  the attractions between the molecules are generally weak  the polarity of the covalent bonds influences the strength of the intermolecular attractions

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Ionic Bonding Model vs. Reality • some molecular solids are brittle and hard, but many are soft and waxy • the kind and strength of the intermolecular attractions varies based on many factors • the covalent bonds are not broken, however, the polarity of the bonds has influence on these attractive forces Tro, Chemistry: A Molecular Approach

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Ionic Bonding Model vs. Reality • molecular compounds do not conduct electricity in the • • •

liquid state molecular acids conduct electricity when dissolved in water, but not in the solid state in molecular solids, there are no charged particles around to allow the material to conduct when dissolved in water, molecular acids are ionized, and have the ability to move through the structure and therefore conduct electricity

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Bond Polarity • covalent bonding between unlike atoms results in unequal sharing of the electrons

one atom pulls the electrons in the bond closer to its side one end of the bond has larger electron density than the other

• the result is a polar covalent bond bond polarity the end with the larger electron density gets a partial negative charge the end that is electron deficient gets a partial positive charge Tro, Chemistry: A Molecular Approach 27

Electronegativity • measure of the pull an atom has on bonding electrons • increases across period (left to right) and • decreases down group (top to bottom)

fluorine is the most electronegative element francium is the least electronegative element

• the larger the difference in

electronegativity, the more polar the bond negative end toward more electronegative atom

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Electronegativity and Bond Polarity • If difference in electronegativity between bonded atoms is 0, the bond is pure covalent  equal sharing

• If difference in electronegativity between bonded atoms • •

0

is 0.1 to 0.4, the bond is nonpolar covalent If difference in electronegativity between bonded atoms 0.5 to 1.9, the bond is polar covalent If difference in electronegativity between bonded atoms larger than or equal to 2.0, the bond is ionic 4%

Percent Ionic Character 51%

“100%”

0.4

2.0 Electronegativity Difference

4.0 29

Bond Dipole Moments

• the dipole moment is a quantitative way of describing the polarity of a bond  a dipole is a material with positively and negatively charged ends  measured

• dipole moment, µ, is a measure of bond polarity  it is directly proportional to the size of the partial charges and directly proportional to the distance between them  µ = (q)(r)  not Coulomb’s Law  measured in Debyes, D

• the percent ionic character is the percentage of a bond’s measured dipole moment to what it would be if full ions Tro, Chemistry: A Molecular Approach

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Lewis Structures • use common bonding patterns  C = 4 bonds & 0 lone pairs, N = 3 bonds & 1 lone pair, O= 2 bonds & 2 lone pairs, H and halogen = 1 bond, Be = 2 bonds & 0 lone pairs, B = 3 bonds & 0 lone pairs  often Lewis structures with line bonds have the lone pairs left off  their presence is assumed from common bonding patterns

• structures which result in bonding patterns different from common have formal charges

B

C

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N

O

F 31

Exceptions to the Octet Rule • expanded octets elements with empty d orbitals can have more than 8 electrons

• odd number electron species e.g., NO will have 1 unpaired electron free-radical very reactive

• incomplete octets B, Al Tro, Chemistry: A Molecular Approach

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Bond Energies • chemical reactions involve breaking bonds in reactant • •

molecules and making new bond to create the products the ∆H°reaction can be calculated by comparing the cost of breaking old bonds to the profit from making new bonds the amount of energy it takes to break one mole of a bond in a compound is called the bond energy  in the gas state  homolytically – each atom gets ½ bonding electrons

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Using Bond Energies to Estimate ∆H°rxn • the actual bond energy depends on the surrounding •

atoms and other factors we often use average bond energies to estimate the ∆ Hrxn  works best when all reactants and products in gas state

• bond breaking is endothermic, ∆H(breaking) = + • bond making is exothermic, ∆H(making) = − ∆Hrxn = ∑ (∆H(bonds broken)) + ∑ (∆H(bonds formed)) Tro, Chemistry: A Molecular Approach

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Bond Lengths • the distance between the nuclei of

bonded atoms is called the bond length • because the actual bond length depends on the other atoms around the bond we often use the average bond length averaged for similar bonds from many compounds Tro, Chemistry: A Molecular Approach

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Trends in Bond Lengths • the more electrons two atoms share, the shorter the covalent bond  C≡C (120 pm) < C=C (134 pm) < C−C (154 pm)  C≡N (116 pm) < C=N (128 pm) < C−N (147 pm)

• decreases from left to right across period  C−C (154 pm) > C−N (147 pm) > C−O (143 pm)

• increases down the column  F−F (144 pm) > Cl−Cl (198 pm) > Br−Br (228 pm)

• in general, as bonds get longer, they also get weaker Tro, Chemistry: A Molecular Approach

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Metallic Bonds

• low ionization energy of metals allows them to

lose electrons easily • the simplest theory of metallic bonding involves the metals atoms releasing their valence electrons to be shared by all to atoms/ions in the metal an organization of metal cation islands in a sea of electrons electrons delocalized throughout the metal structure

• bonding results from attraction of cation for the delocalized electrons

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Metallic Bonding Model vs. Reality • metallic solids conduct electricity • because the free electrons are mobile, it

allows the electrons to move through the metallic crystal and conduct electricity • as temperature increases, electrical conductivity decreases • heating causes the metal ions to vibrate faster, making it harder for electrons to make their way through the crystal Tro, Chemistry: A Molecular Approach

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Metallic Bonding Model vs. Reality • metallic solids conduct heat • the movement of the small, light electrons through the solid can transfer kinetic energy quicker than larger particles • metallic solids reflect light • the mobile electrons on the surface absorb the outside light and then emit it at the same frequency Tro, Chemistry: A Molecular Approach

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Metallic Bonding Model vs. Reality • metallic solids are malleable and ductile • because the free electrons are mobile, the

direction of the attractive force between the metal cation and free electrons is adjustable • this allows the position of the metal cation islands to move around in the sea of electrons without breaking the attractions and the crystal structure Tro, Chemistry: A Molecular Approach

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Metallic Bonding Model vs. Reality • metals generally have high melting points and boiling points

 all but Hg are solids at room temperature

• the attractions of the metal cations for the free electrons • • • •

is strong and hard to overcome melting points generally increase to right across period the charge on the metal cation increases across the period, causing stronger attractions melting points generally decrease down column the cations get larger down the column, resulting in a larger distance from the nucleus to the free electrons

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Structure Determines Properties! • properties of molecular substances depend on

the structure of the molecule • the structure includes many factors, including: the skeletal arrangement of the atoms the kind of bonding between the atoms ionic, polar covalent, or covalent

the shape of the molecule

• bonding theory should allow you to predict the shapes of molecules

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Using Lewis Theory to Predict Molecular Shapes • Lewis theory predicts there are regions of electrons in an atom based on placing shared pairs of valence electrons between bonding nuclei and unshared valence electrons located on single nuclei • this idea can then be extended to predict the shapes of molecules by realizing these regions are all negatively charged and should repel Tro, Chemistry: A Molecular Approach

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VSEPR Theory • electron groups around the central atom will be most stable when they are as far apart as possible – we call this valence shell electron pair repulsion theory

since electrons are negatively charged, they should be most stable when they are separated as much as possible

• the resulting geometric arrangement will allow us to predict the shapes and bond angles in the molecule

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Electron Groups

• the Lewis structure predicts the arrangement of valence • •

electrons around the central atom(s) each lone pair of electrons constitutes one electron group on a central atom each bond constitutes one electron group on a central atom  regardless of whether it is single, double, or triple

•• •O •

•• N

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•• O •• ••

there are 3 electron groups on N 1 lone pair 1 single bond 1 double bond

45

Molecular Geometries • there are 5 basic arrangements of electron groups around a central atom

 based on a maximum of 6 bonding electron groups  though there may be more than 6 on very large atoms, it is very rare

• each of these 5 basic arrangements results in 5 different basic molecular shapes

 in order for the molecular shape and bond angles to be a “perfect” geometric figure, all the electron groups must be bonds and all the bonds must be equivalent

• for molecules that exhibit resonance, it doesn’t matter which resonance form you use – the molecular geometry will be the same

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Linear Geometry

• when there are 2 electron groups around the central • •

atom, they will occupy positions opposite each other around the central atom this results in the molecule taking a linear geometry the bond angle is 180° •• • •

Cl

••

Be

••

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Cl

• •

•• • •

O

••

C

O

• •

••

47

Trigonal Geometry

• when there are 3 electron groups around the central • •

atom, they will occupy positions in the shape of a triangle around the central atom this results in the molecule taking a trigonal planar geometry the bond angle is 120° •• • •

••

F

B

F

••

• •

•• • •

F

• •

•• Tro, Chemistry: A Molecular Approach

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Not Quite Perfect Geometry

Because the bonds are not identical, the observed angles are slightly different from ideal. Tro, Chemistry: A Molecular Approach

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Tetrahedral Geometry

• when there are 4 electron groups around the central • •

atom, they will occupy positions in the shape of a tetrahedron around the central atom this results in the molecule taking a tetrahedral geometry the bond angle is 109.5° •• • •

F

• •

•• • •

••

F

C

F

••

• •

•• • •

F

• •

••

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Trigonal Bipyramidal Geometry • when there are 5 electron groups around the central atom, they

• • • • •

will occupy positions in the shape of a two tetrahedra that are base-to-base with the central atom in the center of the shared bases this results in the molecule taking a trigonal bipyramidal geometry the positions above and below the central atom are called the axial positions the positions in the same base plane as the central atom are called the equatorial positions the bond angle between equatorial positions is 120° the bond angle between axial and equatorial positions is 90°

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Octahedral Geometry • when there are 6 electron groups around the central

•

atom, they will occupy positions in the shape of two square-base pyramids that are base-to-base with the central atom in the center of the shared bases this results in the molecule taking an octahedral geometry  it is called octahedral because the geometric figure has 8 sides

• all positions are equivalent • the bond angle is 90° Tro, Chemistry: A Molecular Approach

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The Effect of Lone Pairs • lone pair groups “occupy more space” on the central atom

because their electron density is exclusively on the central atom rather than shared like bonding electron groups

• relative sizes of repulsive force interactions is: Lone Pair – Lone Pair > Lone Pair – Bonding Pair > Bonding Pair – Bonding Pair

• this effects the bond angles, making them smaller than expected

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Derivative Shapes • the molecule’s shape will be one of basic molecular geometries if all the electron groups are bonds and all the bonds are equivalent • molecules with lone pairs or different kinds of surrounding atoms will have distorted bond angles and different bond lengths, but the shape will be a derivative of one of the basic shapes Tro, Chemistry: A Molecular Approach

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Derivative of Trigonal Geometry • when there are 3 electron groups around the central

• • •

atom, and 1 of them is a lone pair, the resulting shape of the molecule is called a trigonal planar - bent shape the bond angle is < 120°

••

••

••

O

S

O

• •

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• •

••

••

••

O

S

O

• •

• •

••

••

••

O

S

O

• •

55

Derivatives of Tetrahedral Geometry

• when there are 4 electron groups around the central atom, and 1 is a lone pair, the result is called a pyramidal shape

 because it is a triangular-base pyramid with the central atom at the apex

• when there are 4 electron groups around the central atom, and 2 are lone pairs, the result is called a tetrahedral-bent shape

 it is planar  it looks similar to the trigonal planar-bent shape, except the angles are smaller

• for both shapes, the bond angle is < 109.5° Tro, Chemistry: A Molecular Approach

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Derivatives of the Trigonal Bipyramidal Geometry

• when there are 5 electron groups around the central atom, and •

some are lone pairs, they will occupy the equatorial positions because there is more room when there are 5 electron groups around the central atom, and 1 is a lone pair, the result is called see-saw shape  aka distorted tetrahedron

• when there are 5 electron groups around the central atom, and • • •

2 are lone pairs, the result is called T-shaped when there are 5 electron groups around the central atom, and 3 are lone pairs, the result is called a linear shape the bond angles between equatorial positions is < 120° the bond angles between axial and equatorial positions is < 90°

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 linear = 180° axial-to-axial

57

Derivatives of the Octahedral Geometry • when there are 6 electron groups around the central •

atom, and some are lone pairs, each even number lone pair will take a position opposite the previous lone pair when there are 6 electron groups around the central atom, and 1 is a lone pair, the result is called a square pyramid shape  the bond angles between axial and equatorial positions is < 90°

• when there are 6 electron groups around the central atom, and 2 are lone pairs, the result is called a square planar shape  the bond angles between equatorial positions is 90° Tro, Chemistry: A Molecular Approach

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Multiple Central Atoms

• many molecules have larger structures with many • •

interior atoms we can think of them as having multiple central atoms when this occurs, we describe the shape around each central atom in sequence ••

shape around left C is tetrahedral shape around center C is trigonal planar shape around right O is tetrahedral-bent Tro, Chemistry: A Molecular Approach

H O •• | || • • H − C −C −O −H | •• H 61

Polarity of Molecules • in order for a molecule to be polar it must 1) have polar bonds  electronegativity difference - theory  bond dipole moments - measured

2) have an unsymmetrical shape  vector addition

• polarity affects the intermolecular forces of attraction  therefore boiling points and solubilities  like dissolves like

• nonbonding pairs affect molecular polarity, strong pull in its direction Tro, Chemistry: A Molecular Approach

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Valence Bond Theory • Linus Pauling and others applied the principles of quantum mechanics to molecules • they reasoned that bonds between atoms would arise when the orbitals on those atoms interacted to make a bond • the kind of interaction depends on whether the orbitals align along the axis between the nuclei, or outside the axis Tro, Chemistry: A Molecular Approach

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Orbital Interaction • as two atoms approached, the partially filled or empty valence atomic orbitals on the atoms would interact to form molecular orbitals • the molecular orbitals would be more stable than the separate atomic orbitals because they would contain paired electrons shared by both atoms

the interaction energy between atomic orbitals is negative when the interacting atomic orbitals contain a total of 2 electrons Tro, Chemistry: A Molecular Approach

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Valence Bond Theory Main Concepts 1. the valence electrons in an atom reside in

the quantum mechanical atomic orbitals or hybrid orbitals 2. a chemical bond results when these atomic orbitals overlap and there is a total of 2 electrons in the new molecular orbital a) the electrons must be spin paired

3. the shape of the molecule is determined by the geometry of the overlapping orbitals

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Hybridization

• some atoms hybridize their orbitals to maximize bonding hybridizing is mixing different types of orbitals to make a new set of degenerate orbitals sp, sp2, sp3, sp3d, sp3d2 more bonds = more full orbitals = more stability

• better explain observed shapes of molecules • same type of atom can have different hybridization depending on the compound C = sp, sp2, sp3 Tro, Chemistry: A Molecular Approach

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Orbital Diagrams with Hybridization • place electrons into hybrid and unhybridized valence orbitals as if all the orbitals have equal energy • when bonding, σ bonds form between hybrid orbitals and π bonds form between unhybridized orbitals that are parallel

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sp3 Hybridization • atom with 4 areas of electrons tetrahedral geometry 109.5° angles between hybrid orbitals

• atom uses hybrid orbitals for all bonds and lone pairs H H s

sp3 •• sp3 C N H s H H

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Types of Bonds • a sigma (σ) bond results when the bonding atomic orbitals point along the axis connecting the two bonding nuclei  either standard atomic orbitals or hybrids  s-to-s, p-to-p, hybrid-to-hybrid, s-to-hybrid, etc.

• a pi (π) bond results when the bonding atomic

orbitals are parallel to each other and perpendicular to the axis connecting the two bonding nuclei  between unhybridized parallel p orbitals

• the interaction between parallel orbitals is not as

strong as between orbitals that point at each other; therefore σ bonds are stronger than π bonds

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sp2

sp2

• atom with 3 areas of electrons trigonal planar system C = trigonal planar  N = trigonal bent  O = “linear” 

•

H s

•• O •• C sp2

•• O •• 3 sp

H s

120° bond angles flat atom uses hybrid orbitals for σ bonds and lone pairs, uses nonhybridized p orbital for π bond

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sp

• atom with 2 areas of electrons  linear shape 180° bond angle

• atom uses hybrid orbitals for σ bonds or lone

pairs, uses nonhybridized p orbitals for π bonds

H s Tro, Chemistry: A Molecular Approach

C sp

π σ π

N sp 71

sp d 3

• atom with 5 areas of electrons around it

trigonal bipyramid shape See-Saw, T-Shape, Linear 120° & 90° bond angles

•• •• O ••

-1 •• •• F •• • • O• • I •• ••O •• F • • ••

• use empty d orbitals from

valence shell • d orbitals can be used to make π bonds Tro, Chemistry: A Molecular Approach

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sp3d2 • atom with 6 areas of electrons around it octahedral shape Square Pyramid, Square Planar 90° bond angles

• use empty d orbitals from valence shell • d orbitals can be used to make π bonds Tro, Chemistry: A Molecular Approach

••F•• •• ••F •• • •

•• •• F •• Br • •

••F•• ••

•• F • • ••

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Molecular Orbital Theory

• in MO theory, we apply Schrödinger’s wave equation to the molecule to calculate a set of molecular orbitals  in practice, the equation solution is estimated  we start with good guesses from our experience as to what the orbital should look like  then test and tweak the estimate until the energy of the orbital is minimized

• in this treatment, the electrons belong to the whole molecule – so the orbitals belong to the whole molecule  unlike VB Theory where the atomic orbitals still exist in the molecule Tro, Chemistry: A Molecular Approach

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LCAO • the simplest guess starts with the atomic orbitals of the atoms adding together to make molecular orbitals – this is called the Linear Combination of Atomic Orbitals method weighted sum

• because the orbitals are wave functions, the waves can combine either constructively or destructively

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Molecular Orbitals • when the wave functions combine constructively, the resulting molecular orbital has less energy than the original atomic orbitals – it is called a Bonding Molecular Orbital  σ, π  most of the electron density between the nuclei

• when the wave functions combine destructively, the

resulting molecular orbital has more energy than the original atomic orbitals – it is called a Antibonding Molecular Orbital  σ*, π*  most of the electron density outside the nuclei  nodes between nuclei

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Interaction of 1s Orbitals

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Molecular Orbital Theory • Electrons in bonding MOs are stabilizing Lower energy than the atomic orbitals

• Electrons in anti-bonding MOs are destabilizing Higher in energy than atomic orbitals Electron density located outside the internuclear axis Electrons in anti-bonding orbitals cancel stability gained by electrons in bonding orbitals Tro, Chemistry: A Molecular Approach

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MO and Properties • Bond Order = difference between number of electrons in bonding and antibonding orbitals  only need to consider valence electrons  may be a fraction  higher bond order = stronger and shorter bonds  if bond order = 0, then bond is unstable compared to individual atoms - no bond will form.

• A substance will be paramagnetic if its MO diagram has unpaired electrons  if all electrons paired it is diamagnetic

# Bond Elec. - # Antibond Elec. Bond Order = 2

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Heteronuclear Diatomic Molecules

• the more electronegative atom has lower energy orbitals • when the combining atomic orbitals are identical and •

equal energy, the weight of each atomic orbital in the molecular orbital are equal when the combining atomic orbitals are different kinds and energies, the atomic orbital closest in energy to the molecular orbital contributes more to the molecular orbital  lower energy atomic orbitals contribute more to the bonding MO  higher energy atomic orbitals contribute more to the antibonding MO

• nonbonding MOs remain localized on the atom donating its atomic orbitals

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Polyatomic Molecules • when many atoms are combined together, the atomic orbitals of all the atoms are combined to make a set of molecular orbitals which are delocalized over the entire molecule • gives results that better match real molecule properties than either Lewis or Valence Bond theories Tro, Chemistry: A Molecular Approach

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Freedom of Motion • the molecules in a gas have complete freedom of motion

 their kinetic energy overcomes the attractive forces between the molecules

• the molecules in a solid are locked in place, they cannot move around

 though they do vibrate, they don’t have enough kinetic energy to overcome the attractive forces

• the molecules in a liquid have limited freedom – they can move around a little within the structure of the liquid

 they have enough kinetic energy to overcome some of the attractive forces, but not enough to escape each other Tro, Chemistry: A Molecular Approach

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Properties of the 3 Phases of Matter State

Shape

Volume Compressible Flow

Solid

Fixed

Fixed

No

No

Strength of Intermolecular Attractions very strong

Liquid

Indef.

Fixed

No

Yes

moderate

Gas

Indef.

Indef.

Yes

Yes

very weak

•Fixed = keeps shape when placed in a container •Indefinite = takes the shape of the container Tro, Chemistry: A Molecular Approach

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Solids • some solids have their particles arranged in an orderly geometric pattern – we call these crystalline solids  salt and diamonds

• other solids have particles that do not show a regular geometric pattern over a long range – we call these amorphous solids  plastic and glass Tro, Chemistry: A Molecular Approach

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Why are molecules attracted to each other?

• intermolecular attractions are due to attractive forces between opposite charges

 + ion to - ion  + end of polar molecule to - end of polar molecule  H-bonding especially strong

 even nonpolar molecules will have temporary charges

• larger the charge = stronger attraction • longer the distance = weaker attraction • however, these attractive forces are small relative to the bonding forces between atoms

 generally smaller charges  generally over much larger distances Tro, Chemistry: A Molecular Approach

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Trends in the Strength of Intermolecular Attraction? • the stronger the attractions between the atoms or • •

molecules, the more energy it will take to separate them boiling a liquid requires we add enough energy to overcome the attractions between the molecules or atoms the higher the normal boiling point of the liquid, the stronger the intermolecular attractive forces

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Dispersion Forces • fluctuations in the electron distribution in atoms and molecules result in a temporary dipole

 region with excess electron density has partial (─) charge  region with depleted electron density has partial (+) charge

• the attractive forces caused by these temporary dipoles are called dispersion forces  aka London Forces

• all molecules and atoms will have them • as a temporary dipole is established in one molecule, it induces a dipole in all the surrounding molecules

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Size of the Induced Dipole • the magnitude of the induced dipole depends on •

several factors polarizability of the electrons  volume of the electron cloud

•

larger molar mass = more electrons = larger electron cloud = increased polarizability = stronger attractions shape of the molecule more surface-to-surface contact = larger induced dipole = stronger attraction

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Dipole-Dipole Attractions • polar molecules have a permanent dipole  because of bond polarity and shape  dipole moment  as well as the always present induced dipole

• the permanent dipole adds to the attractive forces between the molecules

 raising the boiling and melting points relative to nonpolar molecules of similar size and shape

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Attractive Forces and Solubility

• Solubility depends on the attractive forces of solute and solvent molecules

 Like dissolves Like  miscible liquids will always dissolve in each other

• polar substance dissolve in polar solvents hydrophilic groups = OH, CHO, C=O, COOH, NH2, Cl

• nonpolar molecules dissolve in nonpolar solvents  hydrophobic groups = C-H, C-C

• Many molecules have both hydrophilic and

hydrophobic parts - solubility becomes competition between parts

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Hydrogen Bonding

• When a very electronegative atom is bonded to

hydrogen, it strongly pulls the bonding electrons toward it O-H, N-H, or F-H

• Since hydrogen has no other electrons, when it loses the electrons, the nucleus becomes deshielded exposing the H proton

• The exposed proton acts as a very strong center of positive charge, attracting all the electron clouds from neighboring molecules

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Ion-Dipole Attraction • in a mixture, ions from an ionic compound are

attracted to the dipole of polar molecules • the strength of the ion-dipole attraction is one of the main factors that determines the solubility of ionic compounds in water

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Surface Tension

• surface tension is a property of liquids that results from •

the tendency of liquids to minimize their surface area in order to minimize their surface area, liquids form drops that are spherical  as long as there is no gravity

• the layer of molecules on the surface behave differently than the interior

 because the cohesive forces on the surface molecules have a net pull into the liquid interior

• the surface layer acts like an elastic skin

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Factors Affecting Surface Tension • the stronger the intermolecular attractive forces, the higher the surface tension will be • raising the temperature of a liquid reduces its surface tension raising the temperature of the liquid increases the average kinetic energy of the molecules the increased molecular motion makes it easier to stretch the surface Tro, Chemistry: A Molecular Approach

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Viscosity

• viscosity is the resistance of a liquid to flow  1 poise = 1 P = 1 g/cm∙s  often given in centipoise, cP

• larger intermolecular attractions = larger viscosity • higher temperature = lower viscosity

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Capillary Action • capillary action is the ability of a liquid to flow up a thin tube against the influence of gravity the narrower the tube, the higher the liquid rises

• capillary action is the result of the two forces working in conjunction, the cohesive and adhesive forces cohesive forces attract the molecules together adhesive forces attract the molecules on the edge to the tube’s surface Tro, Chemistry: A Molecular Approach

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Vaporization

• molecules in the liquid are constantly • • •

in motion the average kinetic energy is proportional to the temperature however, some molecules have more kinetic energy than the average if these molecules are at the surface, they may have enough energy to overcome the attractive forces

 therefore – the larger the surface area, the faster the rate of evaporation

• this will allow them to escape the liquid and become a vapor

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Distribution of Thermal Energy

• only a small fraction of the molecules in a liquid have enough • •

energy to escape but, as the temperature increases, the fraction of the molecules with “escape energy” increases the higher the temperature, the faster the rate of evaporation

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Condensation • some molecules of the vapor will lose energy

through molecular collisions • the result will be that some of the molecules will get captured back into the liquid when they collide with it • also some may stick and gather together to form droplets of liquid particularly on surrounding surfaces

• we call this process condensation Tro, Chemistry: A Molecular Approach

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Effect of Intermolecular Attraction on Evaporation and Condensation

• the weaker the attractive forces between molecules, the • • •

less energy they will need to vaporize also, weaker attractive forces means that more energy will need to be removed from the vapor molecules before they can condense the net result will be more molecules in the vapor phase, and a liquid that evaporates faster – the weaker the attractive forces, the faster the rate of evaporation liquids that evaporate easily are said to be volatile  e.g., gasoline, fingernail polish remover  liquids that do not evaporate easily are called nonvolatile  e.g., motor oil

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Energetics of Vaporization • when the high energy molecules are lost from the liquid, it lowers the average kinetic energy • if energy is not drawn back into the liquid, its temperature will decrease – therefore, vaporization is an endothermic process and condensation is an exothermic process

• vaporization requires input of energy to overcome the attractions between molecules Tro, Chemistry: A Molecular Approach

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Heat of Vaporization • the amount of heat energy required to vaporize one mole of the liquid is called the Heat of Vaporization, ∆Hvap  sometimes called the enthalpy of vaporization

• always endothermic, therefore ∆Hvap is + • somewhat temperature dependent •

∆Hcondensation = -∆Hvaporization

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Dynamic Equilibrium • in a closed container, once the rates of vaporization and • •

condensation are equal, the total amount of vapor and liquid will not change evaporation and condensation are still occurring, but because they are opposite processes, there is no net gain or loss or either vapor or liquid when two opposite processes reach the same rate so that there is no gain or loss of material, we call it a dynamic equilibrium  this does not mean there are equal amounts of vapor and liquid – it means that they are changing by equal amounts

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Vapor Pressure • the pressure exerted by the vapor when it is in dynamic equilibrium with its liquid is called the vapor pressure  remember using Dalton’s Law of Partial Pressures to account for the pressure of the water vapor when collecting gases by water displacement?

• the weaker the attractive forces between the molecules, •

the more molecules will be in the vapor therefore, the weaker the attractive forces, the higher the vapor pressure  the higher the vapor pressure, the more volatile the liquid

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Dynamic Equilibrium • a system in dynamic equilibrium can respond to changes in the conditions • when conditions change, the system shifts its position to relieve or reduce the effects of the change

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Vapor Pressure vs. Temperature • increasing the temperature increases the number of molecules able to escape the liquid • the net result is that as the temperature increases, the vapor pressure increases • small changes in temperature can make big changes in vapor pressure • the rate of growth depends on strength of the intermolecular forces Tro, Chemistry: A Molecular Approach

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Boiling Point • when the temperature of a liquid reaches a point where its vapor pressure is the same as the external pressure, vapor bubbles can form anywhere in the liquid not just on the surface

• this phenomenon is what is called boiling and

the temperature required to have the vapor pressure = external pressure is the boiling point

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Boiling Point • the normal boiling point is the temperature at •

which the vapor pressure of the liquid = 1 atm the lower the external pressure, the lower the boiling point of the liquid

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Clausius-Clapeyron Equation 2-Point Form • the equation below can be used with just two measurements of vapor pressure and temperature

 however, it generally gives less accurate results  fewer data points will not give as accurate an average because there is less averaging out of the errors  as with any other sets of measurements

• can also be used to predict the vapor pressure if you know the heat of vaporization and the normal boiling point

 remember: the vapor pressure at the normal boiling point is 760 torr

 P2  − ∆H vap  1 1   −  ln  = R  T2 T1   P1  Tro, Chemistry: A Molecular Approach

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Supercritical Fluid

• as a liquid is heated in a sealed container, more vapor collects causing the pressure inside the container to rise  and the density of the vapor to increase  and the density of the liquid to decrease

• at some temperature, the meniscus between the liquid and vapor •

disappears and the states commingle to form a supercritical fluid supercritical fluid have properties of both gas and liquid states

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The Critical Point • the temperature required to produce a supercritical fluid is called the critical temperature • the pressure at the critical temperature is called the critical pressure • at the critical temperature or higher temperatures, the gas cannot be condensed to a liquid, no matter how high the pressure gets Tro, Chemistry: A Molecular Approach

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Sublimation and Deposition

• molecules in the solid have thermal energy that allows • • •

them to vibrate surface molecules with sufficient energy may break free from the surface and become a gas – this process is called sublimation the capturing of vapor molecules into a solid is called deposition the solid and vapor phases exist in dynamic equilibrium in a closed container  at temperatures below the melting point  therefore, molecular solids have a vapor pressure

solid Tro, Chemistry: A Molecular Approach

sublimation deposition

gas 112

Melting = Fusion • as a solid is heated, its temperature rises and the molecules vibrate more vigorously • once the temperature reaches the melting point, the molecules have sufficient energy to overcome some of the attractions that hold them in position and the solid melts (or fuses) • the opposite of melting is freezing Tro, Chemistry: A Molecular Approach

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Energetics of Melting • when the high energy molecules are lost from the solid, it lowers the average kinetic energy • if energy is not drawn back into the solid its temperature will decrease – therefore, melting is an endothermic process and freezing is an exothermic process

• melting requires input of energy to overcome the attractions between molecules Tro, Chemistry: A Molecular Approach

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Heat of Fusion

• the amount of heat energy required to melt one mole of the solid is called the Heat of Fusion, ∆Hfus

 sometimes called the enthalpy of fusion

• always endothermic, therefore ∆Hfus is + • somewhat temperature dependent • • •

∆Hcrystallization = -∆Hfusion generally much less than ∆Hvap ∆Hsublimation = ∆Hfusion + ∆Hvaporization

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Phase Diagrams • describe the different states and state changes that

occur at various temperature - pressure conditions • areas represent states • lines represent state changes liquid/gas line is vapor pressure curve both states exist simultaneously critical point is the furthest point on the vapor pressure curve

• triple point is the temperature/pressure condition where all three states exist simultaneously • for most substances, freezing point increases as pressure increases Tro, Chemistry: A Molecular Approach

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Water – An Extraordinary Substance • water is a liquid at room temperature  most molecular substances with small molar masses are gases at room temperature  due to H-bonding between molecules

• water is an excellent solvent – dissolving many ionic and polar molecular substances

 because of its large dipole moment  even many small nonpolar molecules have solubility in water  e.g., O2, CO2

• water has a very high specific heat for a molecular substance  moderating effect on coastal climates

• water expands when it freezes  at a pressure of 1 atm

 about 9%  making ice less dense than liquid water Tro, Chemistry: A Molecular Approach

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Determining Crystal Structure • crystalline solids have a very regular geometric • • •

arrangement of their particles the arrangement of the particles and distances between them is determined by x-ray diffraction in this technique, a crystal is struck by beams of x-rays, which then are reflected the wavelength is adjusted to result in an interference pattern – at which point the wavelength is an integral multiple of the distances between the particles

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Bragg’s Law

• when the interference between x-rays is constructive,

• •

the distance between the two paths (a) is an integral multiple of the wavelength nλ =2a the angle of reflection is therefore related to the distance (d) between two layers of particles sinθ = a/d combining equations and rearranging we get an equation called Bragg’s Law

n•λ d= 2 • sin θ

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Crystal Lattice • when allowed to cool slowly, the particles in a liquid will arrange themselves to give the maximum attractive forces therefore minimize the energy

• the result will generally be a crystalline solid • the arrangement of the particles in a crystalline solid is called the crystal lattice • the smallest unit that shows the pattern of arrangement for all the particles is called the unit cell Tro, Chemistry: A Molecular Approach

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Unit Cells

• unit cells are 3-dimensional,

 usually containing 2 or 3 layers of particles

• unit cells are repeated over and over to give the macroscopic • • •

crystal structure of the solid starting anywhere within the crystal results in the same unit cell each particle in the unit cell is called a lattice point lattice planes are planes connecting equivalent points in unit cells throughout the lattice

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Unit Cells • the number of other particles each particle is in contact with is called its coordination number

 for ions, it is the number of oppositely charged ions an ion is in contact with

• higher coordination number means more interaction, •

therefore stronger attractive forces holding the crystal together the packing efficiency is the percentage of volume in the unit cell occupied by particles  the higher the coordination number, the more efficiently the particles are packing together

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Cubic Unit Cells • all 90° angles between corners of the unit cell • the length of all the edges are equal • if the unit cell is made of spherical particles ⅛ of each corner particle is within the cube ½ of each particle on a face is within the cube ¼ of each particle on an edge is within the cube • Volume of a Cube = ( edge length )

3

4 3 • Volume of a Sphere = π r 3 Tro, Chemistry: A Molecular Approach

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Cubic Unit Cells Simple Cubic

• 8 particles, one at each corner •

• •

of a cube 1/8th of each particle lies in the unit cell each particle part of 8 cells 1 particle in each unit cell 8 corners x 1/8 edge of unit cell = twice the radius coordination number of 6

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2r

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Cubic Unit Cells Body-Centered Cubic • 9 particles, one at each corner of •

• •

a cube + one in center 1/8th of each corner particle lies in the unit cell 2 particles in each unit cell 8 corners x 1/8 + 1 center edge of unit cell = (4/√ 3) times the radius of the particle coordination number of 8

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Cubic Unit Cells Face-Centered Cubic • 14 particles, one at each corner of a •

• •

cube + one in center of each face 1/8th of each corner particle + 1/2 of face particle lies in the unit cell 4 particles in each unit cell 2r 8 corners x 1/8 + 6 faces x 1/2 edge of unit cell = 2√ 2 times the radius of the particle coordination number of 12

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126

Classifying Crystalline Solids • classified by the kinds of units found • sub-classified by the kinds of attractive forces holding • • •

the units together molecular solids are solids whose composite units are molecules ionic solids are solids whose composite units are ions atomic solids are solids whose composite units are atoms  nonbonding atomic solids are held together by dispersion forces  metallic atomic solids are held together by metallic bonds  network covalent atomic solids are held together by covalent bonds

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Molecular Solids • the lattice site are occupied by molecules • the molecules are held together by intermolecular attractive forces dispersion forces, dipole attractions, and H-bonds

• because the attractive forces are weak, they tend to have low melting point generally < 300°C Tro, Chemistry: A Molecular Approach

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Ionic Solids Attractive Forces • held together by attractions between opposite charges  nondirectional  therefore every cation attracts all anions around it, and vice versa

• the coordination number represents the number of close cation•

anion interactions in the crystal the higher the coordination number, the more stable the solid  lowers the potential energy of the solid

• the coordination number depends on the relative sizes of the cations and anions

 generally, anions are larger than cations  the number of anions that can surround the cation limited by the size of the cation  the closer in size the ions are, the higher the coordination number is Tro, Chemistry: A Molecular Approach

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Nonbonding Atomic Solids • noble gases in solid form • solid held together by weak dispersion forces very low melting

• tend to arrange atoms in closest-packed structure either hexagonal cp or cubic cp maximizes attractive forces and minimizes energy Tro, Chemistry: A Molecular Approach

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Metallic Atomic Solids • solid held together by metallic bonds strength varies with sizes and charges of cations coulombic attractions

• melting point varies • mostly closest packed arrangements of the lattice points cations Tro, Chemistry: A Molecular Approach

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Network Covalent Solids • atoms attached to its nearest neighbors by covalent • •

bonds because of the directionality of the covalent bonds, these do not tend to form closest-packed arrangements in the crystal because of the strength of the covalent bonds, these have very high melting points  generally > 1000°C

• dimensionality of the network affects other physical properties

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The Diamond Structure: a 3-Dimensional Network • the carbon atoms in a diamond each have 4 covalent bonds to surrounding atoms sp3 tetrahedral geometry

• this effectively makes each crystal one giant molecule held together by covalent bonds you can follow a path of covalent bonds from any atom to every other atom Tro, Chemistry: A Molecular Approach

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The Graphite Structure: a 2-Dimensional Network • in graphite, the carbon atoms in a sheet are covalently bonded together

 forming 6-member flat rings fused together  similar to benzene  bond length = 142 pm

 sp2  each C has 3 sigma and 1 pi bond

 trigonal-planar geometry  each sheet a giant molecule

• the sheets are then stacked and held together by dispersion forces

 sheets are 341 pm apart Tro, Chemistry: A Molecular Approach

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Band Theory • the structures of metals and covalent network solids result in every atom’s orbitals being shared by the entire structure • for large numbers of atoms, this results in a large number of molecular orbitals that have approximately the same energy, we call this an energy band Tro, Chemistry: A Molecular Approach

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Band Theory

• when 2 atomic orbitals combine they produce

both a bonding and an antibonding molecular orbital • when many atomic orbitals combine they produce a band of bonding molecular orbitals and a band of antibonding molecular orbitals • the band of bonding molecular orbitals is called the valence band • the band of antibonding molecular orbitals is called the conduction band Tro, Chemistry: A Molecular Approach

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Band Gap • at absolute zero, all the electrons will occupy the valence band • as the temperature rises, some of the electrons may acquire enough energy to jump to the conduction band • the difference in energy between the valence band and conduction band is called the band gap the larger the band gap, the fewer electrons there are with enough energy to make the jump Tro, Chemistry: A Molecular Approach

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Band Gap and Conductivity • the more electrons at any one time that a substance has in the •

conduction band, the better conductor of electricity it is if the band gap is ~0, then the electrons will be almost as likely to be in the conduction band as the valence band and the material will be a conductor  metals  the conductivity of a metal decreases with temperature

• if the band gap is small, then a significant number of the

electrons will be in the conduction band at normal temperatures and the material will be a semiconductor  graphite  the conductivity of a semiconductor increases with temperature

• if the band gap is large, then effectively no electrons will be in the conduction band at normal temperatures and the material will be an insulator

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Doping Semiconductors • doping is adding impurities to the semiconductor’s • • •

crystal to increase its conductivity goal is to increase the number of electrons in the conduction band n-type semiconductors do not have enough electrons themselves to add to the conduction band, so they are doped by adding electron rich impurities p-type semiconductors are doped with an electron deficient impurity, resulting in electron “holes” in the valence band. Electrons can jump between these holes in the valence band, allowing conduction of electricity

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Diodes • when a p-type semiconductor adjoins an n-type semiconductor, the result is an p-n junction • electricity can flow across the p-n junction in only one direction – this is called a diode • this also allows the accumulation of electrical energy – called an amplifier

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Solubility • when one substance (solute) dissolves in another

•

(solvent) it is said to be soluble salt is soluble in water bromine is soluble in methylene chloride when one substance does not dissolve in another it is said to be insoluble oil is insoluble in water

• the solubility of one substance in another

depends on two factors – nature’s tendency towards mixing, and the types of intermolecular attractive forces Tro, Chemistry: A Molecular Approach

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Solubility • there is usually a limit to the solubility of one substance in another gases are always soluble in each other two liquids that are mutually soluble are said to be miscible alcohol and water are miscible oil and water are immiscible

• the maximum amount of solute that can be dissolved •

in a given amount of solvent is called the solubility the solubility of one substance in another varies with temperature and pressure

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Mixing and the Solution Process Entropy • formation of a solution does not necessarily lower the potential energy of the system

 the difference in attractive forces between atoms of two separate ideal gases vs. two mixed ideal gases is negligible  yet the gases mix spontaneously

• the gases mix because the energy of the • •

system is lowered through the release of entropy entropy is the measure of energy dispersal throughout the system energy has a spontaneous drive to spread out over as large a volume as it is allowed

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Relative Interactions and Solution Formation Solute-to-Solvent

Solute-to-Solute + > Solution Forms Solvent-to-Solvent

Solute-to-Solvent

Solute-to-Solute + = Solution Forms Solvent-to-Solvent

Solute-to-Solvent

Solute-to-Solute + Solution May or < Solvent-to-Solvent May Not Form

• when the solute-to-solvent attractions are weaker than the sum of the solute-to-solute and solvent-to-solvent attractions, the solution will only form if the energy difference is small enough to be overcome by the entropy

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Will It Dissolve? • Chemist’s Rule of Thumb – Like Dissolves Like • a chemical will dissolve in a solvent if it has a similar •

structure to the solvent when the solvent and solute structures are similar, the solvent molecules will attract the solute particles at least as well as the solute particles to each other

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Heats of Hydration • for aqueous ionic solutions, the energy added to overcome the attractions between water molecules and the energy released in forming attractions between the water molecules and ions is combined into a term called the heat of hydration  attractive forces in water = H-bonds  attractive forces between ion and water = ion-dipole  ∆Hhydration = heat released when 1 mole of gaseous ions dissolves in water Tro, Chemistry: A Molecular Approach

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Solution Equilibrium • the dissolution of a solute in a solvent is an equilibrium • • •

process initially, when there is no dissolved solute, the only process possible is dissolution shortly, solute particles can start to recombine to reform solute molecules – but the rate of dissolution >> rate of deposition and the solute continues to dissolve eventually, the rate of dissolution = the rate of deposition – the solution is saturated with solute and no more solute will dissolve

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Solubility Limit • a solution that has the maximum amount of solute dissolved in it is said to be saturated  depends on the amount of solvent  depends on the temperature  and pressure of gases

• a solution that has less solute than saturation is said to •

be unsaturated a solution that has more solute than saturation is said to be supersaturated

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Temperature Dependence of Solubility of Solids in Water • solubility is generally given in grams of solute that will •

dissolve in 100 g of water for most solids, the solubility of the solid increases as the temperature increases  when ∆Hsolution is endothermic

• solubility curves can be used to predict whether a solution with a particular amount of solute dissolved in water is saturated (on the line), unsaturated (below the line), or supersaturated (above the line) Tro, Chemistry: A Molecular Approach

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Temperature Dependence of Solubility of Gases in Water • solubility is generally given in moles of solute

that will dissolve in 1 Liter of solution • generally lower solubility than ionic or polar covalent solids because most are nonpolar molecules • for all gases, the solubility of the gas decreases as the temperature increases the ∆Hsolution is exothermic because you do not need to overcome solute-solute attractions Tro, Chemistry: A Molecular Approach

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Pressure Dependence of Solubility of Gases in Water • the larger the partial pressure of a gas in contact with a liquid, the more soluble the gas is in the liquid

151

Henry’s Law • the solubility of a gas (Sgas) is directly proportional to its partial pressure, (Pgas) Sgas = kHPgas

• kH is called Henry’s Law Constant Tro, Chemistry: A Molecular Approach

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Concentrations • solutions have variable composition • to describe a solution, need to describe components • •

and relative amounts the terms dilute and concentrated can be used as qualitative descriptions of the amount of solute in solution concentration = amount of solute in a given amount of solution  occasionally amount of solvent

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Solution Concentration Molarity • moles of solute per 1 liter of solution • used because it describes how many molecules of solute in each liter of solution • if a sugar solution concentration is 2.0 M, 1 liter of solution contains 2.0 moles of sugar, 2 liters = 4.0 moles sugar, 0.5 liters = 1.0 mole sugar moles of solute molarity = liters of solution Tro, Chemistry: A Molecular Approach

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Solution Concentration Molality, m • moles of solute per 1 kilogram of solvent defined in terms of amount of solvent, not solution like the others

• does not vary with temperature because based on masses, not volumes

moles of solute molality, m = kg of solvent Tro, Chemistry: A Molecular Approach

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Percent

• parts of solute in every 100 parts solution • mass percent = mass of solute in 100 parts solution by mass

if a solution is 0.9% by mass, then there are 0.9 grams of solute in every 100 grams of solution or 0.9 kg solute in every 100 kg solution

Mass of Solute, g Mass Percent = ×100% Mass of Solution, g Mass of Solute + Mass of Solvent = Mass of Solution Tro, Chemistry: A Molecular Approach

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Percent Concentration Part (solute) Percent = ×100% Whole (solution) Mass of Solute, g Mass Percent = ×100% Mass of Solution, g Mass of Solute + Mass of Solvent = Mass of Solution Mass of Solute, g × 100% Volume of Solution, mL Mass of Solute + Volume of Solvent ≠ Volume of Solution Percent Mass/Volume =

Volume of Solute, mL × 100% Volume of Solution, mL Volume of Solute + Volume of Solvent ≠ Volume of Solution Volume Percent =

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Using Concentrations as Conversion Factors • concentrations show the relationship between the amount of solute and the amount of solvent  12%(m/m) sugar(aq) means 12 g sugar ≡ 100 g solution  or 12 kg sugar ≡ 100 kg solution; or 12 lbs. ≡ 100 lbs. solution

 5.5%(m/v) Ag in Hg means 5.5 g Ag ≡ 100 mL solution  22%(v/v) alcohol(aq) means 22 mL EtOH ≡ 100 mL solution

• The concentration can then be used to convert the amount of solute into the amount of solution, or vice versa Tro, Chemistry: A Molecular Approach

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Preparing a Solution • need to know amount of solution and concentration of solution • calculate the mass of solute needed

start with amount of solution use concentration as a conversion factor 5% by mass ⇒ 5 g solute ≡ 100 g solution

“Dissolve the grams of solute in enough solvent to total the total amount of solution.”

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Solution Concentration PPM • grams of solute per 1,000,000 g of solution • mg of solute per 1 kg of solution • 1 liter of water = 1 kg of water for water solutions we often approximate the kg of the solution as the kg or L of water

grams solute x 106 grams solution mg solute mg solute kg solution L solution

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Solution Concentrations Mole Fraction, XA

• the mole fraction is the fraction of the moles of one • • •

component in the total moles of all the components of the solution total of all the mole fractions in a solution = 1 unitless the mole percentage is the percentage of the moles of one component in the total moles of all the components of the solution  = mole fraction x 100%

mole fraction of A = XA = Tro, Chemistry: A Molecular Approach

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Converting Concentration Units

• assume a convenient amount of solution

 given %(m/m), assume 100 g solution  given %(m/v), assume 100 mL solution  given ppm, assume 1,000,000 g solution  given M, assume 1 liter of solution  given m, assume 1 kg of solvent  given X, assume you have a total of 1 mole of solutes in the solution

• determine amount of solution in non-given unit(s)  if assume amount of solution in grams, use density to convert to mL and then to L  if assume amount of solution in L or mL, use density to convert to grams

• determine the amount of solute in this amount of solution, in

grams and moles • determine the amount of solvent in this amount of solution, in grams and moles • use definitions to calculate other units Tro, Chemistry: A Molecular Approach

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Thirsty Solutions • a concentrated solution will draw solvent molecules toward it due to the natural drive for materials in nature to mix • similarly, a concentrated solution will draw pure solvent vapor into it due to this tendency to mix • the result is reduction in vapor pressure

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Raoult’s Law • the vapor pressure of a volatile solvent above a solution is equal to its mole fraction of its normal vapor pressure, P° Psolvent in solution = χsolvent∙P° since the mole fraction is always less than 1, the vapor pressure of the solvent in solution will always be less than the vapor pressure of the pure solvent Tro, Chemistry: A Molecular Approach

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Ionic Solutes and Vapor Pressure • according to Raoult’s Law, the effect of solute on • •

the vapor pressure simply depends on the number of solute particles when ionic compounds dissolve in water, they dissociate – so the number of solute particles is a multiple of the number of moles of formula units the effect of ionic compounds on the vapor pressure of water is magnified by the dissociation  since NaCl dissociates into 2 ions, Na+ and Cl−, one mole of NaCl lowers the vapor pressure of water twice as much as 1 mole of C12H22O11 molecules would

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Raoult’s Law for Volatile Solute • when both the solvent and the solute can evaporate, •

both molecules will be found in the vapor phase the total vapor pressure above the solution will be the sum of the vapor pressures of the solute and solvent  for an ideal solution

Ptotal = Psolute + Psolvent

• the solvent decreases the solute vapor pressure in the same way the solute decreased the solvent’s Psolute = χsolute∙P°solute and Psolvent = χsolvent∙P°solvent Tro, Chemistry: A Molecular Approach

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Ideal vs. Nonideal Solution • in ideal solutions, the made solute-solvent interactions are equal to the sum of the broken solute-solute and solvent-solvent interactions ideal solutions follow Raoult’s Law

• effectively, the solute is diluting the solvent • if the solute-solvent interactions are stronger or weaker than the broken interactions the solution is nonideal Tro, Chemistry: A Molecular Approach

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Vapor Pressure of a Nonideal Solution

• when the solute-solvent interactions are stronger than the solute-solute + solvent-solvent, the total vapor pressure of the solution will be less than predicted by Raoult’s Law  because the vapor pressures of the solute and solvent are lower than ideal

• when the solute-solvent interactions are weaker than the solute-solute + solvent-solvent, the total vapor pressure of the solution will be larger than predicted by Raoult’s Law Tro, Chemistry: A Molecular Approach

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Freezing Point Depression

• the freezing point of a solution is lower than the freezing point of the pure solvent  for a nonvolatile solute  therefore the melting point of the solid solution is lower

• the difference between the freezing point of the solution and freezing point of the pure solvent is directly proportional to the molal concentration of solute particles

(FPsolvent – FPsolution) = ∆Tf = m∙Kf

• the proportionality constant is called the Freezing Point Depression Constant, Kf  the value of Kf depends on the solvent  the units of Kf are °C/m Tro, Chemistry: A Molecular Approach

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Boiling Point Elevation

• the boiling point of a solution is higher than the boiling point of the pure solvent  for a nonvolatile solute

• the difference between the boiling point of the solution

•

and boiling point of the pure solvent is directly proportional to the molal concentration of solute particles (BPsolution – BPsolvent) = ∆Tb = m∙Kb the proportionality constant is called the Boiling Point Elevation Constant, Kb

 the value of Kb depends on the solvent  the units of Kb are °C/m Tro, Chemistry: A Molecular Approach

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Osmosis • osmosis is the flow of solvent through a semipermeable membrane from solution of low concentration to solution of high concentration • the amount of pressure needed to keep osmotic flow from taking place is called the osmotic pressure • the osmotic pressure, Π, is directly proportional to the molarity of the solute particles R = 0.08206 (atm∙L)/(mol∙K) Tro, Chemistry: A Molecular Approach

Π = MRT

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Colligative Properties • colligative properties are properties whose value depends only on the number of solute particles, and not on what they are  Vapor Pressure Depression, Freezing Point Depression, Boiling Point Elevation, Osmotic Pressure

• the van’t Hoff factor, i, is the ratio of moles of solute •

particles to moles of formula units dissolved measured van’t Hoff factors are often lower than you might expect due to ion pairing in solution

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Colloids • a colloidal suspension is a heterogeneous mixture in which one substance is dispersed through another most colloids are made of finely divided particles suspended in a medium

• the difference between colloids and regular suspensions is generally particle size – colloidal particles are from 1 to 100 nm in size Tro, Chemistry: A Molecular Approach

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Properties of Colloids • the particles in a colloid exhibit Brownian motion • colloids exhibit the Tyndall Effect scattering of light as it passes through a suspension colloids scatter short wavelength (blue) light more effectively than long wavelength (red) light

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