Properties of Substances and Mixtures

3.1

Intermolecular and Interparticle Forces

Syllabus

Learning Objective	Essential Knowledge
3.1.A Explain the relationship between the chemical structures of molecules and the relative strength of their intermolecular forces when: i. The molecules are of the same chemical species. ii. The molecules are of two different chemical species.	3.1.A.1 London dispersion forces are a result of the Coulombic interactions between temporary, fluctuating dipoles. London dispersion forces are often the strongest net intermolecular force between large molecules. i. Dispersion forces increase with increasing contact area between molecules and with increasing polarizability of the molecules. ii. The polarizability of a molecule increases with an increasing number of electrons in the molecule and the size of the electron cloud. It is enhanced by the presence of pi bonding. iii. The term "London dispersion forces" should not be used synonymously with the term "van der Waals forces." 3.1.A.2 The dipole moment of a polar molecule leads to additional interactions with other chemical species. i. Dipole-induced dipole interactions are present between a polar and nonpolar molecule. These forces are always attractive. The strength of these forces increases with the magnitude of the dipole of the polar molecule and with the polarizability of the nonpolar molecule. ii. Dipole-dipole interactions are present between polar molecules. The interaction strength depends on the magnitudes of the dipoles and their relative orientation. Interactions between polar molecules are typically greater than those between nonpolar molecules of comparable size because these interactions act in addition to London dispersion forces. iii. Ion-dipole forces of attraction are present between ions and polar molecules. These tend to be stronger than dipole-dipole forces. 3.1.A.3 The relative strength and orientation dependence of dipole-dipole and ion-dipole forces can be understood qualitatively by considering the sign of the partial charges responsible for the molecular dipole moment, and how these partial charges interact with an ion or with an adjacent dipole. 3.1.A.4 Hydrogen bonding is a strong type of intermolecular interaction that exists when hydrogen atoms covalently bonded to the highly electronegative atoms (N, O, and F) are attracted to the negative end of a dipole formed by the electronegative atom (N, O, and F) in a different molecule, or a different part of the same molecule. 3.1.A.5 In large biomolecules, noncovalent interactions may occur between different molecules or between different regions of the same large biomolecule.

Learning Objective

Essential Knowledge

3.1.A
Explain the relationship between the chemical structures of molecules and the relative strength of their intermolecular forces when:
i. The molecules are of the same chemical species.
ii. The molecules are of two different chemical species.

3.1.A.1 London dispersion forces are a result of the Coulombic interactions between temporary, fluctuating dipoles. London dispersion forces are often the strongest net intermolecular force between large molecules.
- i. Dispersion forces increase with increasing contact area between molecules and with increasing polarizability of the molecules.
- ii. The polarizability of a molecule increases with an increasing number of electrons in the molecule and the size of the electron cloud. It is enhanced by the presence of pi bonding.
- iii. The term "London dispersion forces" should not be used synonymously with the term "van der Waals forces."
3.1.A.2 The dipole moment of a polar molecule leads to additional interactions with other chemical species.
- i. Dipole-induced dipole interactions are present between a polar and nonpolar molecule. These forces are always attractive. The strength of these forces increases with the magnitude of the dipole of the polar molecule and with the polarizability of the nonpolar molecule.
- ii. Dipole-dipole interactions are present between polar molecules. The interaction strength depends on the magnitudes of the dipoles and their relative orientation. Interactions between polar molecules are typically greater than those between nonpolar molecules of comparable size because these interactions act in addition to London dispersion forces.
- iii. Ion-dipole forces of attraction are present between ions and polar molecules. These tend to be stronger than dipole-dipole forces.
3.1.A.3 The relative strength and orientation dependence of dipole-dipole and ion-dipole forces can be understood qualitatively by considering the sign of the partial charges responsible for the molecular dipole moment, and how these partial charges interact with an ion or with an adjacent dipole.
3.1.A.4 Hydrogen bonding is a strong type of intermolecular interaction that exists when hydrogen atoms covalently bonded to the highly electronegative atoms (N, O, and F) are attracted to the negative end of a dipole formed by the electronegative atom (N, O, and F) in a different molecule, or a different part of the same molecule.
3.1.A.5 In large biomolecules, noncovalent interactions may occur between different molecules or between different regions of the same large biomolecule.

Source: College Board AP Course and Exam Description

Intermolecular forces 分子间作用力 (IMFs) are attractions between molecules – much weaker than bonds, but they set melting/boiling points. From weakest to strongest:

London dispersion: an instantaneous dipole induces a dipole in a neighbour

Hydrogen bonding: an H on N/O/F is attracted to a lone pair on another molecule

London dispersion forces 伦敦色散力: present in all molecules; they arise from Coulombic attraction between temporary, fluctuating dipoles, and are stronger for larger, more polarizable electron clouds - often the strongest net force between large molecules.
Dipole–dipole 偶极-偶极: between polar molecules. Their strength depends on the size of the dipoles and their relative orientation - a $\delta+$ end lining up with a neighbour's $\delta-$ end attracts, so these act in addition to dispersion and make polar molecules stickier than nonpolar ones of similar size.
Ion–dipole 离子-偶极: between an ion and a polar molecule (the ion pulls on the oppositely-charged end of the dipole). These are stronger than dipole-dipole forces, and are exactly what lets water dissolve an ionic solid - each $\text{Na}^+$ is surrounded by the $\delta-$ oxygen ends of water molecules.
Hydrogen bonding 氢键: a strong dipole force when H is bonded to N, O, or F.

The whole ladder is understood qualitatively by looking at the sign of the partial charges: a larger or better-aligned partial charge, or a full ionic charge, gives a stronger attraction. Stronger IMFs mean higher boiling points and lower vapor pressure. This is why water ($18\ \text{g/mol}$, hydrogen-bonded) boils at $100\,{}^{\circ}\text{C}$ while methane ($16\ \text{g/mol}$, dispersion only) boils at $-162\,{}^{\circ}\text{C}$.

Vocabulary Train

English	Chinese	Pinyin
Intermolecular forces	分子间作用力	fèn zǐ jiàn zuò yòng lì
London dispersion forces	伦敦色散力	lún dūn sè sàn lì
Dipole–dipole	偶极-偶极	ǒu jí - ǒu jí
Ion–dipole	离子-偶极	lí zi - ǒu jí
Hydrogen bonding	氢键	qīng jiàn

Exercise sheet

3.2

Properties of Solids

Syllabus

Learning Objective	Essential Knowledge
3.2.A Explain the relationship among the macroscopic properties of a substance, the particulate-level structure of the substance, and the interactions between these particles.	3.2.A.1 Many properties of liquids and solids are determined by the strengths and types of intermolecular forces present. Because intermolecular interactions are overcome completely when a substance vaporizes, the vapor pressure and boiling point are directly related to the strength of those interactions. Melting points also tend to correlate with interaction strength, but because the interactions are only rearranged, in melting, the relations can be more subtle. 3.2.A.2 Particulate-level representations, showing multiple interacting chemical species, are a useful means to communicate or understand how intermolecular interactions help to establish macroscopic properties. 3.2.A.3 Due to strong interactions between ions, ionic solids tend to have low vapor pressures, high melting points, and high boiling points. They tend to be brittle due to the repulsion of like charges caused when one layer slides across another layer. They conduct electricity only when the ions are mobile, as when the ionic solid is melted (i.e., in a molten state) or dissolved in water or another solvent. 3.2.A.4 In covalent network solids, the atoms are covalently bonded together into a three-dimensional network (e.g., diamond) or layers of two-dimensional networks (e.g., graphite). These are only formed from nonmetals and metalloids: elemental (e.g., diamond, graphite) or binary compounds (e.g., silicon dioxide and silicon carbide). Due to the strong covalent interactions, covalent solids have high melting points. Three-dimensional network solids are also rigid and hard, because the covalent bond angles are fixed. However, graphite is soft because adjacent layers can slide past each other relatively easily. 3.2.A.5 Molecular solids are composed of distinct, individual units of covalently-bonded molecules attracted to each other through relatively weak intermolecular forces. Molecular solids generally have a low melting point because of the relatively weak intermolecular forces present between the molecules. They do not conduct electricity because their valence electrons are tightly held within the covalent bonds and the lone pairs of each constituent molecule. Molecular solids are sometimes composed of very large molecules or polymers. 3.2.A.6 Metallic solids are good conductors of electricity and heat, due to the presence of free valence electrons. They also tend to be malleable and ductile, due to the ease with which the metal cores can rearrange their structure. In an interstitial alloy, interstitial atoms tend to make the lattice more rigid, decreasing malleability and ductility. Alloys typically retain a sea of mobile electrons and so remain conducting. 3.2.A.7 In large biomolecules or polymers, noncovalent interactions may occur between different molecules or between different regions of the same large biomolecule. The functionality and properties of such molecules depend strongly on the shape of the molecule, which is largely dictated by noncovalent interactions.

Learning Objective

Essential Knowledge

3.2.A
Explain the relationship among the macroscopic properties of a substance, the particulate-level structure of the substance, and the interactions between these particles.

3.2.A.1 Many properties of liquids and solids are determined by the strengths and types of intermolecular forces present. Because intermolecular interactions are overcome completely when a substance vaporizes, the vapor pressure and boiling point are directly related to the strength of those interactions. Melting points also tend to correlate with interaction strength, but because the interactions are only rearranged, in melting, the relations can be more subtle.
3.2.A.2 Particulate-level representations, showing multiple interacting chemical species, are a useful means to communicate or understand how intermolecular interactions help to establish macroscopic properties.
3.2.A.3 Due to strong interactions between ions, ionic solids tend to have low vapor pressures, high melting points, and high boiling points. They tend to be brittle due to the repulsion of like charges caused when one layer slides across another layer. They conduct electricity only when the ions are mobile, as when the ionic solid is melted (i.e., in a molten state) or dissolved in water or another solvent.
3.2.A.4 In covalent network solids, the atoms are covalently bonded together into a three-dimensional network (e.g., diamond) or layers of two-dimensional networks (e.g., graphite). These are only formed from nonmetals and metalloids: elemental (e.g., diamond, graphite) or binary compounds (e.g., silicon dioxide and silicon carbide). Due to the strong covalent interactions, covalent solids have high melting points. Three-dimensional network solids are also rigid and hard, because the covalent bond angles are fixed. However, graphite is soft because adjacent layers can slide past each other relatively easily.
3.2.A.5 Molecular solids are composed of distinct, individual units of covalently-bonded molecules attracted to each other through relatively weak intermolecular forces. Molecular solids generally have a low melting point because of the relatively weak intermolecular forces present between the molecules. They do not conduct electricity because their valence electrons are tightly held within the covalent bonds and the lone pairs of each constituent molecule. Molecular solids are sometimes composed of very large molecules or polymers.
3.2.A.6 Metallic solids are good conductors of electricity and heat, due to the presence of free valence electrons. They also tend to be malleable and ductile, due to the ease with which the metal cores can rearrange their structure. In an interstitial alloy, interstitial atoms tend to make the lattice more rigid, decreasing malleability and ductility. Alloys typically retain a sea of mobile electrons and so remain conducting.
3.2.A.7 In large biomolecules or polymers, noncovalent interactions may occur between different molecules or between different regions of the same large biomolecule. The functionality and properties of such molecules depend strongly on the shape of the molecule, which is largely dictated by noncovalent interactions.

Source: College Board AP Course and Exam Description

A solid's properties reflect the particles and forces holding it: ionic, covalent-network (like diamond or the layers of graphite, very hard, high-melting), metallic, and molecular solids (held by weak IMFs, soft, low-melting). Matching a solid's properties to its structure is a common exam task.

Metallic solids conduct electricity and heat and are malleable 可锻的 and ductile 可延展的, all because their free valence electrons 自由价电子 move easily and let the metal ions slide past one another without breaking the bonding. Solids are also either crystalline 晶体 (particles in a regular, repeating 3-D arrangement) or amorphous 非晶体 (no long-range order, like glass).

The four solid structures: giant ionic, simple molecular, giant covalent, and metallic

Vocabulary Train

English	Chinese	Pinyin
malleable	可锻的	kě duàn de
ductile	可延展的	kě yán zhǎn de
free valence electrons	自由价电子	zì yóu jià diàn zi
crystalline	晶体	jīng tǐ
amorphous	非晶体	fēi jīng tǐ

Exercise sheet

3.3

Solids, Liquids, and Gases

Syllabus

Learning Objective	Essential Knowledge
3.3.A Represent the differences between solid, liquid, and gas phases using a particulate-level model.	3.3.A.1 Solids can be crystalline, where the particles are arranged in a regular three-dimensional structure, or they can be amorphous, where the particles do not have a regular, orderly arrangement. In both cases, the motion of the individual particles is limited, and the particles do not undergo overall translation with respect to each other. The structure of the solid is influenced by interparticle interactions and the ability of the particles to pack together. 3.3.A.2 The constituent particles in liquids are in close contact with each other, and they are continually moving and colliding. The arrangement and movement of particles are influenced by the nature and strength of the forces (e.g., polarity, hydrogen bonding, and temperature) between the particles. 3.3.A.3 The solid and liquid phases for a particular substance typically have similar molar volume because, in both phases, the constituent particles are in close contact at all times. 3.3.A.4 In the gas phase, the particles are in constant motion. Their frequencies of collision and the average spacing between them are dependent on temperature, pressure, and volume. Because of this constant motion, and minimal effects of forces between particles, a gas has neither a definite volume nor a definite shape. Exclusion Statement: Understanding/interpreting phase diagrams will not be assessed on the AP Exam.

Learning Objective

Essential Knowledge

3.3.A
Represent the differences between solid, liquid, and gas phases using a particulate-level model.

3.3.A.1 Solids can be crystalline, where the particles are arranged in a regular three-dimensional structure, or they can be amorphous, where the particles do not have a regular, orderly arrangement. In both cases, the motion of the individual particles is limited, and the particles do not undergo overall translation with respect to each other. The structure of the solid is influenced by interparticle interactions and the ability of the particles to pack together.
3.3.A.2 The constituent particles in liquids are in close contact with each other, and they are continually moving and colliding. The arrangement and movement of particles are influenced by the nature and strength of the forces (e.g., polarity, hydrogen bonding, and temperature) between the particles.
3.3.A.3 The solid and liquid phases for a particular substance typically have similar molar volume because, in both phases, the constituent particles are in close contact at all times.
3.3.A.4 In the gas phase, the particles are in constant motion. Their frequencies of collision and the average spacing between them are dependent on temperature, pressure, and volume. Because of this constant motion, and minimal effects of forces between particles, a gas has neither a definite volume nor a definite shape.
- Exclusion Statement: Understanding/interpreting phase diagrams will not be assessed on the AP Exam.

Source: College Board AP Course and Exam Description

The three states differ in how tightly particles are held. Rising temperature raises average kinetic energy; when it overcomes the attractions, the substance melts or boils. Gases are mostly empty space, so they are compressible and fill their container.

Particles are packed in a solid, close but mobile in a liquid, and far apart in a gas

Explore

Melt and boil by adding heat

Temperature sets the average kinetic energy of the particles. Warm a solid and the particles break their fixed pattern (melt), then spread right out (boil).

Exercise sheet

3.4

The Ideal Gas Law

Syllabus

Learning Objective	Essential Knowledge
3.4.A Explain the relationship between the macroscopic properties of a sample of gas or mixture of gases using the ideal gas law.	3.4.A.1 The macroscopic properties of ideal gases are related through the ideal gas law: EQN: $PV = nRT$. 3.4.A.2 In a sample containing a mixture of ideal gases, the pressure exerted by each component (the partial pressure) is independent of the other components. Therefore, the partial pressure of a gas within the mixture is proportional to its mole fraction ($X$), and the total pressure of the sample is the sum of the partial pressures. EQN: $P_{A} = P_{total} \times X_{A}$, where $X_{A} =$ moles A/total moles; EQN: $P_{total} = P_{A} + P_{B} + P_{C} + \ldots$ 3.4.A.3 Graphical representations of the relationships between $P$, $V$, $T$, and $n$ are useful to describe gas behavior.

Learning Objective

Essential Knowledge

3.4.A
Explain the relationship between the macroscopic properties of a sample of gas or mixture of gases using the ideal gas law.

3.4.A.1 The macroscopic properties of ideal gases are related through the ideal gas law:
- EQN: $PV = nRT$.
3.4.A.2 In a sample containing a mixture of ideal gases, the pressure exerted by each component (the partial pressure) is independent of the other components. Therefore, the partial pressure of a gas within the mixture is proportional to its mole fraction ($X$), and the total pressure of the sample is the sum of the partial pressures.
- EQN: $P_{A} = P_{total} \times X_{A}$, where $X_{A} =$ moles A/total moles;
- EQN: $P_{total} = P_{A} + P_{B} + P_{C} + \ldots$
3.4.A.3 Graphical representations of the relationships between $P$, $V$, $T$, and $n$ are useful to describe gas behavior.

Source: College Board AP Course and Exam Description

An ideal gas obeys

$$PV=nRT,$$

linking pressure, volume, moles, and absolute temperature. Use it to find any one quantity from the others, or (holding some constant) to predict how a gas responds to a change.

An ideal gas is a model of point particles with no forces between them

Worked example. How many moles of gas fill a $2.0\ \text{L}$ container at $300\ \text{K}$ and $1.5\ \text{atm}$? Using $R=0.0821\ \text{L atm/(mol K)}$,

$$n=\frac{PV}{RT}=\frac{1.5\times2.0}{0.0821\times300}=0.12\ \text{mol}.$$

Always use kelvin for $T$ and match the units of $R$ to your pressure and volume.

Explore

Compress a gas and watch the pressure

$PV = nRT$. At fixed temperature, squeezing the gas into a smaller volume packs the molecules closer, so they hit the walls more often and the pressure rises.

Exercise sheet

3.5

Kinetic Molecular Theory

Syllabus

Learning Objective	Essential Knowledge
3.5.A Explain the relationship between the motion of particles and the macroscopic properties of gases with: i. The kinetic molecular theory (KMT). ii. A particulate model. iii. A graphical representation.	3.5.A.1 The kinetic molecular theory (KMT) relates the macroscopic properties of gases to motions of the particles in the gas. The Maxwell-Boltzmann distribution describes the distribution of the kinetic energies of particles at a given temperature. 3.5.A.2 All the particles in a sample of matter are in continuous, random motion. The average kinetic energy of a particle is related to its average velocity by the equation: EQN: $KE = \frac{1}{2}\,mv^{2}$. 3.5.A.3 The Kelvin temperature of a sample of matter is proportional to the average kinetic energy of the particles in the sample. 3.5.A.4 The Maxwell-Boltzmann distribution provides a graphical representation of the energies/velocities of particles at a given temperature.

Learning Objective

Essential Knowledge

3.5.A
Explain the relationship between the motion of particles and the macroscopic properties of gases with:
i. The kinetic molecular theory (KMT).
ii. A particulate model.
iii. A graphical representation.

3.5.A.1 The kinetic molecular theory (KMT) relates the macroscopic properties of gases to motions of the particles in the gas. The Maxwell-Boltzmann distribution describes the distribution of the kinetic energies of particles at a given temperature.
3.5.A.2 All the particles in a sample of matter are in continuous, random motion. The average kinetic energy of a particle is related to its average velocity by the equation:
- EQN: $KE = \frac{1}{2}\,mv^{2}$.
3.5.A.3 The Kelvin temperature of a sample of matter is proportional to the average kinetic energy of the particles in the sample.
3.5.A.4 The Maxwell-Boltzmann distribution provides a graphical representation of the energies/velocities of particles at a given temperature.

Source: College Board AP Course and Exam Description

Kinetic theory: gas pressure

Kinetic molecular theory 分子运动论 explains gas behavior: particles are tiny, in constant random motion, with negligible volume and no attractions, and collisions are elastic. Temperature is proportional to average kinetic energy, so at a given temperature lighter molecules move faster (Graham's law of effusion).

The Maxwell-Boltzmann distribution of molecular speeds shifts right when heated

Explore

Heat a gas and watch the speed spread

Gas molecules have a range of speeds. Raising the temperature shifts the whole distribution to higher speeds and flattens it, so more molecules move fast.

Vocabulary Train

English	Chinese	Pinyin
Kinetic molecular theory	分子运动论	fēn zǐ yùn dòng lùn

Exercise sheet

3.6

Deviation from the Ideal Gas Law

Syllabus

Learning Objective	Essential Knowledge
3.6.A Explain the relationship among non-ideal behaviors of gases, interparticle forces, and/or volumes.	3.6.A.1 The ideal gas law does not explain the actual behavior of real gases. Deviations from the ideal gas law may result from interparticle attractions among gas molecules, particularly at conditions that are close to those resulting in condensation. Deviations may also arise from particle volumes, particularly at extremely high pressures.

Source: College Board AP Course and Exam Description

Real gases deviate from ideal behavior at high pressure and low temperature, where molecules are close enough that their real volume and their attractions matter. Attractions lower the pressure below ideal; molecular volume raises it.

Exercise sheet

3.7

Solutions and Mixtures

Syllabus

Learning Objective	Essential Knowledge
3.7.A Calculate the number of solute particles, volume, or molarity of solutions.	3.7.A.1 Solutions, also sometimes called homogeneous mixtures, can be solids, liquids, or gases. In a solution, the macroscopic properties do not vary throughout the sample. In a heterogeneous mixture, the macroscopic properties depend on location in the mixture. 3.7.A.2 Solution composition can be expressed in a variety of ways; molarity is the most common method used in the laboratory. EQN: $M = n_{solute}/L_{solution}$

Learning Objective

Essential Knowledge

3.7.A
Calculate the number of solute particles, volume, or molarity of solutions.

3.7.A.1 Solutions, also sometimes called homogeneous mixtures, can be solids, liquids, or gases. In a solution, the macroscopic properties do not vary throughout the sample. In a heterogeneous mixture, the macroscopic properties depend on location in the mixture.
3.7.A.2 Solution composition can be expressed in a variety of ways; molarity is the most common method used in the laboratory.
- EQN: $M = n_{solute}/L_{solution}$

Source: College Board AP Course and Exam Description

A solution 溶液 is a homogeneous mixture of a solute 溶质 dissolved in a solvent 溶剂. Concentration is usually molarity 摩尔浓度:

$$M=\frac{\text{moles of solute}}{\text{liters of solution}}.$$

Dilution conserves moles: $M_1V_1=M_2V_2$.

Worked example. What volume of water must you add to $50\ \text{mL}$ of $6.0\ \text{M}$ HCl to make it $2.0\ \text{M}$? The moles of HCl are unchanged, so $M_1V_1=M_2V_2$ gives the final volume $V_2=\dfrac{M_1V_1}{M_2}=\dfrac{6.0\times50}{2.0}=150\ \text{mL}$. You therefore add $150-50=100\ \text{mL}$ of water.

Vocabulary Train

English	Chinese	Pinyin
solution	溶液	róng yè
solute	溶质	róng zhì
solvent	溶剂	róng jì
molarity	摩尔浓度	mó ěr nóng dù

Exercise sheet

3.8

Representations of Solutions

Syllabus

Learning Objective	Essential Knowledge
3.8.A Using particulate models for mixtures: i. Represent interactions between components. ii. Represent concentrations of components.	3.8.A.1 Particulate representations of solutions communicate the structure and properties of solutions, by illustration of the relative concentrations of the components in the solution and/or drawings that show interactions among the components. Exclusion Statement: Colligative properties will not be assessed on the AP Exam. Exclusion Statement: Calculations of molality, percent by mass, and percent by volume for solutions will not be assessed on the AP Exam.

Learning Objective

Essential Knowledge

3.8.A
Using particulate models for mixtures:
i. Represent interactions between components.
ii. Represent concentrations of components.

3.8.A.1 Particulate representations of solutions communicate the structure and properties of solutions, by illustration of the relative concentrations of the components in the solution and/or drawings that show interactions among the components.
- Exclusion Statement: Colligative properties will not be assessed on the AP Exam.
- Exclusion Statement: Calculations of molality, percent by mass, and percent by volume for solutions will not be assessed on the AP Exam.

Source: College Board AP Course and Exam Description

A particulate diagram shows the solute and solvent particles. For an ionic solute, show it fully dissociated into separate ions surrounded by solvent; count particles to reason about concentration and conductivity.

Exercise sheet

3.9

Separation of Solutions and Mixtures

Syllabus

Learning Objective	Essential Knowledge
3.9.A Explain the results of a separation experiment based on intermolecular interactions.	3.9.A.1 The components of a liquid solution cannot be separated by filtration. They can, however, be separated using processes that take advantage of differences in the intermolecular interactions of the components. i. Chromatography (paper, thin-layer, and column) separates chemical species by taking advantage of the differential strength of intermolecular interactions between and among the components of the solution (the mobile phase) and with the surface components of the stationary phase. The resulting chromatogram can be used to infer the relative polarities of components in a mixture. ii. Distillation separates chemical species by taking advantage of the differential strength of intermolecular interactions between and among the components and the effects these interactions have on the vapor pressures of the components in the mixture.

Learning Objective

Essential Knowledge

3.9.A
Explain the results of a separation experiment based on intermolecular interactions.

3.9.A.1 The components of a liquid solution cannot be separated by filtration. They can, however, be separated using processes that take advantage of differences in the intermolecular interactions of the components.
- i. Chromatography (paper, thin-layer, and column) separates chemical species by taking advantage of the differential strength of intermolecular interactions between and among the components of the solution (the mobile phase) and with the surface components of the stationary phase. The resulting chromatogram can be used to infer the relative polarities of components in a mixture.
- ii. Distillation separates chemical species by taking advantage of the differential strength of intermolecular interactions between and among the components and the effects these interactions have on the vapor pressures of the components in the mixture.

Source: College Board AP Course and Exam Description

Because a mixture's components keep their properties, physical methods separate them: filtration (by particle size), distillation (by boiling point), and chromatography 色谱法 (by how strongly each component sticks to a stationary phase versus moving with a solvent).

Paper chromatography separates a mixture as the solvent rises up the paper

Vocabulary Train

English	Chinese	Pinyin
chromatography	色谱法	sè pǔ fǎ

Exercise sheet

3.10

Solubility

Syllabus

Learning Objective	Essential Knowledge
3.10.A Explain the relationship between the solubility of ionic and molecular compounds in aqueous and nonaqueous solvents, and the intermolecular interactions between particles.	3.10.A.1 Substances with similar intermolecular interactions tend to be miscible or soluble in one another.

Source: College Board AP Course and Exam Description

Solubility 溶解度 is how much solute dissolves. "Like dissolves like": polar (and ionic) solutes dissolve in polar solvents; nonpolar in nonpolar. Dissolving happens when solute–solvent attractions are comparable to the attractions being broken.

A cluster of large, glassy, bright blue crystals of copper sulfate Blue copper(II) sulfate crystals grown from solution: a saturated solution left to evaporate deposits its dissolved solid back out as regular crystals

Vocabulary Train

English	Chinese	Pinyin
Solubility	溶解度	róng jiě dù

Exercise sheet

3.11

Spectroscopy and the Electromagnetic Spectrum

Syllabus

Learning Objective	Essential Knowledge
3.11.A Explain the relationship between a region of the electromagnetic spectrum and the types of molecular or electronic transitions associated with that region.	3.11.A.1 Differences in absorption or emission of photons in different spectral regions are related to the different types of molecular motion or electronic transition: i. Microwave radiation is associated with transitions in molecular rotational levels. ii. Infrared radiation is associated with transitions in molecular vibrational levels. iii. Ultraviolet/visible radiation is associated with transitions in electronic energy levels.

Learning Objective

Essential Knowledge

3.11.A
Explain the relationship between a region of the electromagnetic spectrum and the types of molecular or electronic transitions associated with that region.

3.11.A.1 Differences in absorption or emission of photons in different spectral regions are related to the different types of molecular motion or electronic transition:
- i. Microwave radiation is associated with transitions in molecular rotational levels.
- ii. Infrared radiation is associated with transitions in molecular vibrational levels.
- iii. Ultraviolet/visible radiation is associated with transitions in electronic energy levels.

Source: College Board AP Course and Exam Description

Spectroscopy 光谱学 studies how matter absorbs or emits light. Different regions of the electromagnetic spectrum probe different changes: microwaves (rotation), infrared (bond vibrations), ultraviolet–visible (electron transitions). The light absorbed reveals structure.

Explore

Scan across the electromagnetic spectrum

Light is a wave with a range of wavelengths. Shorter wavelength means higher frequency and more energy per photon, from radio waves up to gamma rays.

Vocabulary Train

English	Chinese	Pinyin
Spectroscopy	光谱学	guāng pǔ xué

Exercise sheet

3.12

Properties of Photons

Syllabus

Learning Objective	Essential Knowledge
3.12.A Explain the properties of an absorbed or emitted photon in relationship to an electronic transition in an atom or molecule.	3.12.A.1 When a photon is absorbed (or emitted) by an atom or molecule, the energy of the species is increased (or decreased) by an amount equal to the energy of the photon. 3.12.A.2 The wavelength of the electromagnetic wave is related to its frequency and the speed of light by the equation: EQN: $c = \lambda\nu$. The energy of a photon is related to the frequency of the electromagnetic wave through Planck's equation: EQN: $E = h\nu$.

Learning Objective

Essential Knowledge

3.12.A
Explain the properties of an absorbed or emitted photon in relationship to an electronic transition in an atom or molecule.

3.12.A.1 When a photon is absorbed (or emitted) by an atom or molecule, the energy of the species is increased (or decreased) by an amount equal to the energy of the photon.
3.12.A.2 The wavelength of the electromagnetic wave is related to its frequency and the speed of light by the equation:
- EQN: $c = \lambda\nu$.
The energy of a photon is related to the frequency of the electromagnetic wave through Planck's equation:
- EQN: $E = h\nu$.

Source: College Board AP Course and Exam Description

Light is carried by photons 光子, each with energy $E=h\nu=\dfrac{hc}{\lambda}$. Higher frequency (shorter wavelength) means higher energy. A molecule absorbs a photon only when its energy matches an allowed energy gap.

Vocabulary Train

English	Chinese	Pinyin
photons	光子	guāng zi

Exercise sheet

3.13

The Beer-Lambert Law

Syllabus

Learning Objective	Essential Knowledge
3.13.A Explain the amount of light absorbed by a solution of molecules or ions in relationship to the concentration, path length, and molar absorptivity.	3.13.A.1 The Beer-Lambert law relates the absorption of light by a solution to three variables according to the equation: EQN: $A = \varepsilon bc$. The molar absorptivity, $\varepsilon$, describes how intensely a chemical species absorbs light of a specific wavelength. The path length, $b$, and concentration, $c$, are proportional to the number of light-absorbing particles in the light path. 3.13.A.2 In most experiments the path length and wavelength of light are held constant. In such cases, the absorbance is proportional only to the concentration of absorbing molecules or ions. The spectrophotometer is typically set to the wavelength of maximum absorbance (optimum wavelength) for the species being analyzed to ensure the maximum sensitivity of measurement.

Learning Objective

Essential Knowledge

3.13.A
Explain the amount of light absorbed by a solution of molecules or ions in relationship to the concentration, path length, and molar absorptivity.

3.13.A.1 The Beer-Lambert law relates the absorption of light by a solution to three variables according to the equation:
- EQN: $A = \varepsilon bc$.
The molar absorptivity, $\varepsilon$, describes how intensely a chemical species absorbs light of a specific wavelength. The path length, $b$, and concentration, $c$, are proportional to the number of light-absorbing particles in the light path.
3.13.A.2 In most experiments the path length and wavelength of light are held constant. In such cases, the absorbance is proportional only to the concentration of absorbing molecules or ions. The spectrophotometer is typically set to the wavelength of maximum absorbance (optimum wavelength) for the species being analyzed to ensure the maximum sensitivity of measurement.

Source: College Board AP Course and Exam Description

The Beer–Lambert law 比尔-朗伯定律 relates how much light a solution absorbs to its concentration:

$$A=\varepsilon\,b\,c,$$

where $A$ is absorbance, $\varepsilon$ the molar absorptivity, $b$ the path length, and $c$ the concentration. Since $A$ is proportional to $c$, measuring absorbance is a fast way to find an unknown concentration.

Worked example. A dye has molar absorptivity $\varepsilon=2000\ \text{L/(mol cm)}$; in a $1.0\ \text{cm}$ cell a sample reads absorbance $A=0.40$. Its concentration is $c=\dfrac{A}{\varepsilon b}=\dfrac{0.40}{2000\times1.0}=2.0\times10^{-4}\ \text{M}$. Because $A\propto c$, a solution twice as concentrated would read $A=0.80$ – the basis of a calibration curve.

Explore

Link absorbance to concentration

The Beer-Lambert law says absorbance $A = \varepsilon b c$: absorbance is proportional to concentration, so a calibration line lets you read an unknown concentration.

Vocabulary Train

English	Chinese	Pinyin
Beer–Lambert law	比尔-朗伯定律	bǐ ěr - lǎng bó dìng lǜ

Exercise sheet

3.13

Exam tips

Intermolecular forces (dispersion < dipole–dipole < hydrogen bonding) set boiling points — they are much weaker than the bonds inside a molecule.
Boiling breaks the forces between molecules, not the covalent bonds within them.
Use $PV=nRT$ with temperature in kelvin and $R$ matched to your pressure/volume units.
For solutions use molarity $M=\text{mol}/\text{L}$; dilution conserves moles, so $M_1V_1=M_2V_2$.
"Like dissolves like" — polar/ionic solutes dissolve in polar solvents, non-polar in non-polar.

Intermolecular and Interparticle Forces

Properties of Solids

Solids, Liquids, and Gases

Melt and boil by adding heat

The Ideal Gas Law

Compress a gas and watch the pressure

Kinetic Molecular Theory

Heat a gas and watch the speed spread

Deviation from the Ideal Gas Law

Solutions and Mixtures

Representations of Solutions

Separation of Solutions and Mixtures

Solubility

Spectroscopy and the Electromagnetic Spectrum

Scan across the electromagnetic spectrum

Properties of Photons

The Beer-Lambert Law

Link absorbance to concentration

Exam tips

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