AP Chemistry Notes

Atomic Structure + Properties (7-9% of Exam Score)

Moles Conversion Chart

  • Molar Mass:

    • Grams/mol

  • Avogadro's Number:

    • 6.02 Imes 10^{23} particles/mol

Molar Conversions

  • Mass (in grams) to Moles: divide by molar mass (g/mol).

  • Moles to Number of Particles: multiply by Avogadro's number (particles/mol).

Practice Problems: Moles and Hydrates

  • Example 1: Determining moles of H2O in 1 mole of MgCl2 Imes nH_2O.

    • Heat the hydrate to drive off water.

    • Calculate the change in mass after each heating.

    • No significant change between the second and third heating indicates the hydrate is fully dehydrated.

    • Determine 'n' (moles of water per mole of MgCl_2).

    • In this example, the formula is MgCl2 Imes 6H2O.

  • Example 2: Determining the value of 'x' in an unknown hydrate of sodium sulfate (Na2SO4 Imes xH_2O).

    1. Determine moles of water:

      • Mass of water removed = Mass of hydrate - Mass of anhydrous sodium sulfate.

      • 3.22 \,g - 1.42 \,g = 1.80 \,g \,H_2O removed

      • Convert grams of water to moles: \frac{1.80 \,g}{18 \,g/mol} = 0.10 \,mol \,H_2O

    2. Determine moles of anhydrous Na2SO4.

      • \frac{1.42 \,g \,anhydrate}{142 \,g/mol} = 0.010 \,mol \,anhydrous \,Na2SO4

    3. Find the ratio of water to anhydrate.

      • \frac{0.10 \,mol \,H2O}{0.010 \,mol \,anhydrous \,Na2SO_4} = 10

      • Therefore, x = 10.

Practice Problems: Empirical Formula

  • Example: Determining the empirical formula of a compound containing C, H, and N.

    1. Determine moles of C from CO_2 product.

      • Molar mass of CO_2 = 44.0 \,g/mol.

      • \frac{44.0 \,g}{44.0 \,g/mol} = 1.0 \,mol \,CO_2

      • 1C : 1CO_2 ratio → 1.0 mol C in the compound.

    2. Determine moles of H from moles of H_2O product.

      • Molar mass of H_2O = 18.0 \,g/mol.

      • \frac{45.0 \,g}{18.0 \,g/mol} = 2.5 \,mol \,H_2O

      • 2H : 1H_2O ratio → 5.0 mol H in the compound.

    3. Find the ratio of moles H to moles C.

      • 5H : 1C, so the compound's empirical formula is CH_5N.

Practice: Mixture Analysis

  • Spectrophotometry: Analyzing a mixture containing cobalt (Co) using nitric acid (HNO_3) to convert all Co to Co^{2+}(aq).

    • The Co^{2+} solution is diluted to a volume of 50.00 mL and spectrophotometrically analyzed at a wavelength of 510 nm to determine its concentration.

    1. Determine the concentration of the Co^{2+} solution using a calibration curve.

      • From the graph, an absorbance of 0.74 corresponds to a concentration of 0.0131M

    2. Calculate the number of moles of Co^{2+} in the 50.00 mL solution.

      • Molarity (M) = moles of solute / Liters of solution.

      • 50.00 \,mL * \frac{1 \,L}{1000 \,mL} = 0.05000 \,L

      • 0.05000 \,L * \frac{0.0131 \,mol}{L} = 6.55 * 10^{-4} \,mol \,Co^{2+}

    3. Determine the percent cobalt in the mixture.

      • 6.55 * 10^{-4} \,mol \,Co^{2+} * \frac{58.93 \,g}{1 \,mol} = 0.0386 \,g \,Co

      • (\frac{0.0386 \,g \,Co}{0.630 \,g \,mixture}) * 100\% = 6.13\% \,Co

Mass Spectrometry

  • Process:

    • A sample enters the mass spectrometer and is vaporized by a heater.

    • An electron beam source ionizes the sample.

    • Ions are accelerated through a magnetic field.

    • The magnetic field deflects lighter ions more than heavier ions.

    • A detector records the abundance of each ion.

  • Analysis:

    • Mass spectra show relative abundance vs. mass-to-charge ratio.

    • Isotopes are identified by their mass-to-charge ratio.

Average Atomic Mass Calculation

  • Example: Chlorine

    1. Identify isotopes' masses and percent abundances from the mass spectrum graph.

      • 35 u -- 75%

      • 37 u -- 25%

    2. Multiply each isotope's mass by its relative abundance (NOT percent abundance!).

      • 35 \,u * 0.75 = 26.25 \,u

      • 37 \,u * 0.25 = 9.25 \,u

    3. Add the results.

      • 26.25 \,u + 9.25 \,u = 35.5 \,u

      • The approximate average atomic mass of Chlorine is 35.5 u (rounded to 36 u to report 2 sig figs).

Coulomb's Law

  • F = k \frac{q1 q2}{r^2}

    • F = Force of attraction.

    • k = Coulomb's constant.

    • q1 and q2 = magnitudes of the charges.

    • r = distance between the charges.

*Significance: Describes the electrostatic force between charged particles. Used to understand electron interactions within atoms.

Photoelectron Spectroscopy (PES)

  • Principle:

    • PES measures the energy required to remove electrons from different subshells within an atom.

    • Position of a peak is related to the energy required to remove the electron from the corresponding subshell: Higher binding energy means the electron is closer to the nucleus.

    • Height of a peak is proportional to the number of electrons in that subshell.

Practice - PES

  • (a) The peak at 100 MJ/mol represents the electron closest to the nucleus. According to Coulomb's law, the attraction between charged particles increases as the distance between them decreases. Since the 100 MJ/mol peak has the highest binding energy, these electrons must be closest to the nucleus.

  • (b) Based on the spectrum, the complete electron configuration of the element is 1s^22s^22p^63s^1

  • (c) On the graph, the peak(s) corresponding to the valence electrons of the element that has one more proton in its nucleus than the unknown element has peak on the left of the peak at 0.80 MJ/mol and twice as tall.

Molecular/Ionic Compounds (7-9% of Exam Score)

Electronegativity

  • Definition: The ability of an atom in a molecule to attract shared electrons to itself.

  • Trends:

    • Increases across a period (left to right).

    • Decreases down a group (top to bottom).

    • Electronegativity values will not be given on the AP exam, memorize the trends!

Chemical Bonds

  • Definition: Attraction between the nucleus of one atom and the electron of another.

  • Types:

    • Ionic bonds: Transferring electrons (usually metal + nonmetal).

    • Covalent bonds: Sharing electrons (usually 2 nonmetals).

      • Nonpolar - electrons shared equally.

      • Polar - electrons shared unequally.

    • Metallic bonds: Electrons not associated with a single atom or molecule (delocalized).

Bond Polarity

  • Definition: Difference in electronegativity values of 2 elements.

  • Atoms with high electronegativity develop a negative partial charge.

  • Atoms with low electronegativity develop a positive partial charge.

  • The dipole arrow points toward the more electronegative atom.

Electronegativity + Bond Type

  • Electronegativity difference between bonding atoms and the resulting bond type.

  • Zero: Pure covalent.

  • Intermediate: Polar covalent.

  • Large: Ionic.

Bond Type

Electronegativity Difference

Character

Pure covalent

< 0.4

Covalent character decreases; ionic character increases.

Polar covalent

between 0.4 and 1.8

Ionic

> 1.8

What Happens in a Chemical Bond?

  • Attraction between the nucleus of one atom and the electron of another.

  • Balance between attraction (protons and electrons) and repulsion (proton-proton and electron-electron).

Potential Energy Curves (Covalent Bonds)

  • Description: Shows the potential energy of a system as a function of internuclear distance.

    • Sufficiently far apart to have no interaction.

    • Atoms begin to interact as they move closer together.

    • Optimum distance to achieve lowest overall energy of the system.

    • Unstable vs. Stable region in PE diagrams.

Bond Order, Length, and Strength

Bond Order

Bond Diagram

Strength

Length

Single

X:X

Weakest

Longest

Double

X::X

Middle

Middle

Triple

X:::X

Strongest

Shortest

Ionic Bonds

  • Electrostatic attraction between a cation and anion.

  • Interactions between cations and anions can be explained with Coulomb’s law.

  • Larger ion charge -> larger force of attraction.

  • Greater distance between charges -> smaller force of attraction.

Comparing PE Diagrams

  • Nucleus less attracted to the bonding electrons, Longer bond length, Smaller bond energy for X-Y Blue Curve

  • Nucleus more attracted to the bonding electrons Shorter bond length, Larger bond energy for XY Red Curve

Ionic Compound

  • Ionic bond - electrostatic attraction between a cation and anion

  • In order to conduct electricity, the substance must have:

    1. Charged particles

    2. Particles must be free to move

Metallic Bonds

  • Positive metal ions surrounded by a ‘sea of mobile valence electrons’ (delocalized).

  • Properties:

    • Good conductors of electricity.

    • Malleable - bendable.

    • Ductile - pulled in a wire.

Alloys

  • Definition: Combining two or more metallic elements.

  • Types:

    • Substitutional alloy:

      • Atoms of comparable radii.

      • One atom substitutes for another atom in the lattice.

      • E.g., brass (copper + zinc).

    • Interstitial alloy:

      • Atoms of different radii.

      • Smaller atom fills space between larger atoms.

      • Usually, the alloy is stronger than the base metal.

      • E.g., steel (carbon between iron).

Resonance

  • Definition: Occurs when multiple valid Lewis structures can be drawn for a molecule or ion.

  • The actual molecule is an average of all resonance structures.

Formal Charge

  • Hypothetical charge the atom would have if all atoms had the same EN

  • To calculate: FC = # of valence electrons - # of assigned electrons

Best Lewis Diagram

  • The BEST Lewis diagram has the minimum number of non-zero formal charges.

  • If non-zero formal charges must remain, the negative charge must be assigned to the MOST electronegative atom.

  • The sum of all individual formal charges must add up to the charge of the chemical species.

VSEPR (Valence Shell Electron Pair Repulsion)

  • Negative electrons repel each other (Coulombic forces).

  • Bonds and lone pairs of electrons (electron domains) are negative.

  • Bonds and lone pairs arrange themselves as far apart in space as possible to minimize repulsion.

Molecular Geometry

  • Geometry depends on number of electron domains (bonds + lone pairs) around the central atom.

  • # electron domains = steric number.

  • Electron domain counts equally (single, double, triple bonds all count as just 1).

  • MEMORIZE SHAPE + NAME + ANGLES!!

VSEPR Table

  • VSEPR geometries, including bond angles, based on the number of bonding domains and lone pairs.

  • Common geometries include linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral.

Molecular Geometry and Polarity

  • Regardless of shape, molecules with only nonpolar bonds are nonpolar.

  • Molecules where the central atom is symmetrically surrounded by identical atoms are nonpolar, even if bonds are polar.

  • Symmetrical shapes: linear, trigonal planar, tetrahedral, trigonal bipyramidal, square planar, octahedral (memorize!!).

  • Molecules with asymmetrical shapes that contain any polar bonds are polar overall.

Intro to Hybridization

  • Hybridization: Combining atomic orbitals to form new hybrid orbitals for bonding.

Hybridization Table

  • Hybridization, geometry, and angles based on the number of attachments around an atom (Steric number)

Intermolecular Forces (18-22% of Exam Score)

London Dispersion Forces (LDF)

  • ALL molecules have LDF.

  • Strength depends on how easily electrons can disperse. The larger the electron cloud, the more polarizable it is; thus, the greater the strength of the interaction.

  • TIP: On a FRQ, if you are comparing sizes of molecules and their respective LDFs, use the term larger/smaller polarizable electron cloud

Hydrogen “Bonding”

  • Special type of dipole-dipole (very strong).

  • Takes place between an H atom covalently bonded to a highly electronegative atom (F, O, N) and a highly electronegative atom on another molecule.

Ion-Dipole Interaction

  • When ionic compounds dissolve in aqueous solutions, the dipole of the water interacts with the charged ions and cause them to separate.

  • Interactions between ions and water = ion-dipole interactions.

  • EVEN STRONGER than hydrogen bonding!!

Properties of Solids

  • General:

    • Very strong interactions between particles.

    • Have definite shape and volume.

    • Regular, crystalline structure.

    • Fixed arrangement of particles.

    • Vibrational degree of freedom.

  • Types:

    • Ionic (NaCl).

    • Molecular (H_2O).

    • Metallic (Al).

    • Covalent Network (diamond).

Ionic Solids

  • Cation + anion.

  • The formula represents the ratio between ions, not discrete particles.

  • Generally high melting point and boiling point due to strong coulombic attraction between ions.

  • Brittle.

  • Poor conductors in solid-state, but good when liquid/aqueous since ions are free to flow.

Molecular Solids

  • Formed by distinct, individual neutral molecules (form molecular lattice).

  • Exclusively of non-metals, the chemical formula represents the actual number of atoms in each individual molecule.

  • Relatively low melting/boiling point due to weak IMFs.

  • Poor conductors in all states since electrons are held tightly in covalent bonds.

Covalent Network Solids

  • Formed by distinct atoms all bonded together covalently in a 3D network.

  • Formed by carbon and metalloids such as silicon, germanium, boron, etc.

  • Very high melting point and hardness.

  • Poor conductors as electrons are held tightly in covalent bonds.

    • Examples: SiO_2, SiC, GaAs, etc.

Exception: Graphite

  • Carbon in graphite is sp2 hybridized and forms very large sheets of carbon atoms in trigonal planar arrangements

  • Weak IMFs hold sheets together, so graphite is soft as layers can slide past each other

  • Excellent conductor of electricity as delocalized electrons flow around graphite sheets

Metallic Solids

  • Formed by metallic elements.

  • Exhibit metallic bonding where valence electrons are free to flow from atom to atom (sea of electrons).

  • Great conductors of heat and electricity.

  • Malleable and ductile.

Ideal Gas Law

  • PV = nRT

    • P = Pressure

    • V = Volume

    • n = # of moles

    • R = Ideal gas constant

    • T = Temperature(K)

Gas Variable Relationships (PV = nRT)

  • A gas in a rigid container has a pressure of 6.0 atm. The container is opened until the pressure is reduced to 3.0 atm, and then closed again.

  • A balloon is filled with hot air and then taken outside on a cold day. The volume of the balloon is decreased by one-sixth of its original volume.

  • Gas in a movable piston is compressed from an initial volume of 12 L to 6 L, and the temperature is increased from 400 K to 800 K.

Dalton’s Law of Partial Pressures

  • Partial Pressure = (Mole Fraction) x (Total Pressure)

Kinetic Molecular Theory

  • Gases are in constant motion and exhibit perfectly elastic collisions

  • Increasing temperature means that particles will collide with more frequency and force, thus causing pressure and volume to increase.

Chromatography

*Liquid solution components can be separated by processes that account for differences in the intermolecular interactions of the components.
Chromatography accounts for differences in the intermolecular interactions between and among the components of the solution (mobile phase) and the surface components of the stationary phase.

Distillation

*Longer carbon chain = stronger/bigger polarizable electron cloud = stronger LDF forces = higher boiling point

identifying polarity

  • Nonpolar molecules? Ethane/Ethyne because molecules are symmetric and polarities cancel out.
    Why is ethanol soluble in water but ethanethiol is not as soluble? Ethanol can form hydrogen bonds with water whereas ethanethiol cannot. The hydrogen bonds increase the attraction of ethanol to water, making it more soluble.

Spectroscopy + Electromagnetic spectrum

  • Microwave radiation -> transitions in molecular rotational levels

  • Infrared radiation -> transitions in molecular vibrational levels (require more energy than rotations)

  • Ultraviolet/visible radiation -> transitions in electronic energy levels

Electrolytic Cell

c = λv

  • c = the speed of light 3.0 \times 10^8 \frac{m}{s} or 3.0 \times 10^{17} \frac{nm}{s}

  • \lambda = wavelength (m or nm)

  • v = frequency (Hz or s^{-1})
    E= hv

  • E = energy of the photon (J)

  • h = Planck's constant 6.626 \times 10^{-34}(J.s)

  • v = frequency (Hz or s^{-1})

Beer-Lambert Law

  • A = ebc

    • A = absorbance measurement

    • ε = molar absorptivity (describes how intensely a sample absorbs light of a specific wavelength)

    • b = path length

    • c = concentration

Chemical Reactions (7-9% of Exam Score)

Equations

  • Balanced Molecular Equations - shows all species participating in a reaction (mass is converted).

  • Complete Ionic Equations - ions in aqueous solution as separate charged particles (identify spectator ions).

  • Net Ionic Equations - do not include spectator ions (represent species undergoing change).

Stoichiometry

  • Calculations involving mole ratios, limiting reactants, and theoretical yields based on balanced chemical equations.

Titration

  • Definition: Solution of known concentration (standard solution) is combined with a solution of unknown concentration to determine the moles in the unknown.

  • Titrant (known concentration) is in the buret

  • Analyte (unknown concentration) is in the flask

  • Equivalence Point - titration added from the buret has completely reacted with all the analyte in the flask (in stoichiometric ratios)

  • End Point - where the indicator changes color

Oxidation Numbers

  • Rules for assigning oxidation numbers to atoms in compounds.
    *Atoms in elemental form = 0
    *Monatomic ions = their charge
    *Oxygen most often = -2, notable exception is peroxides (i.e. H2O2)
    *Hydrogen = +1 with nonmetal
    *Hydrogen = -1 with metal
    *Fluorine = -1
    *Oxidation numbers in polyatomic ion = charge

Types of chemical reactions

*Acid-base reactions - transfer of one or more protons (H+) between chemical species
*Sets of conjugate acid-base pairs
*Oxidation-reduction (redox) - transfer of one or more electrons (e-) between chemical species
Changing oxidation numbers
*Precipitation reaction - formation of insoluble ionic compound from 2 aqueous solutions
*Remember: all sodium, potassium, ammonium, and nitrate salts are soluble in water!

Kinetics (7-9% of Exam Score)

Introduction to Reaction Rates

*Kinetics of a chemical reaction = rate of change of reactant or product concentrations per unit of time
*Rates of change for concentration are determined by stoichiometry in the balanced chemical equation

Factors Affecting Reaction Rates

Collision theory - rate of a reaction is influenced by anything that influences the number or force of collisions
Reactant concentrations
Temperature
Surface area
Catalysts

  • Two samples of Mg(s) of equal mass were placed in equal amounts of HCl (aq) contained in two separate reaction vessels. Particle representations of the mixing of Mg(s) and HCl (aq) in the two reaction vessels are shown in Figure 1 and Figure 2 above. Water molecules are not included in the particle representations. Which of the reactions will initially proceed faster, and why?

Rate Law

  • Rate Law - expresses the rate of reaction as proportional to the concentration + of each reactant raised to a power

  • Rate can also be defined as the rate of appearance of the products.
    *Power of each reactant = order of reaction with respect to each reactant: Sum of power = overall reaction order

Units of the Rate constant

Overall Reaction Order

General Rate Law

Rate Constant Units

0

Rate = k

mol L-1 s-1 (or Ms-1)

1

Rate = k [A]

S-1

2

Rate = k [A]²

L mol-1 s-1 (or M-1s-1)

3

Rate = k [A]² [B]

L2 mol-2 s-1 (or M-2s-1)

Reaction Orders (Graphs)

  • Zero order - plot of [X] vs time is linear

  • First order - plot of ln[X] vs time is linear

  • Second order - plot of 1/[X] vs time is linear

Half Life First Order

*ln(rate of \, decay)
*k = - m \frac{1}{days} or days^{-1}
*Calculate slope of line to get rate constant k and then plug into half life equation.

Elementary Reactions

  • Process in a chemical reaction that occurs in a single step

  • Overall reaction is one or more elementary steps

  • Rate law for overall reaction has to be determined using experimental data

  • Rate law for elementary reaction can be determined using stoichiometry in the equation.

Elementary Reactions (Continues)

  • If a question asks “why is the overall reaction unlikely to occur in one step”, the answer tends to be because it is unlikely many molecules will come together in the proper orientation to overcome the activation energy barrier.

Collision Model\ Reactions must successfully collide to initiate bond - breaking/making events

  • reactants must successfully collide to initiate bond-breaking/making events.

  • Small fraction of collisions lead to reaction.
    *

  • Successful collisions require sufficient energy to overcome activation energy barriers and orientations

For reaction to occur, reactant particles must

  1. Collide

  2. Have proper orientation

  3. Have sufficient energy

Maxwell Botzmann Distribution

  • Collision Model For reaction to occur: Reactants must successfully collide to initiate bond - breaking/making events Small fraction of collisions lead to reactionSuccessful collisions require sufficient energy to overcome activation energy barriers and orientations

Maxell-Boltzmann

Distribution of particle energiesGain qualitative estimate of fraction of collisions with sufficient energy to lead to a reaction and how that fraction depends on temperature

Multi-step Reaction Energy Profile

First step has higher activation energy (because it is slow)PE for intermediate is lower than reactants (exothermic)PE for product is lower than intermediate (exothermic)Addition of a catalyst will typically lead to at least a 2-step mechanism

Catalysts

  • INCREASES reaction rate by providing an ALTERNATE pathway with LOWER potential energy for the activated complexIncreases rate via:
    Formation of a more stable activated complexIncreased collision frequency*Improved orientation effects Homogeneous - catalyst is the same phase as reactionHeterogeneous - catalyst is a different phase as the reaction

Thermodynamics (7-9% of Exam Score)

Endo VS Exo

  • Endo Required takes energy to break bonds Required Free energy required

  • Freed takes energy when forming bonds +AH *Takes energy to break bonds

EXO-AHV Freedman energy when forming bonds freedTakes energy to break bonds Free energy required

First Law of Thermodynamics

qlost = -qgained Energy cannot be created nor destroyed. It is conserved in a physical or chemical change.

Calorimetry

Heat Transfer Technique - Calorimetry

Equipment - Simple Calorimeter nestles Styrofoam cups-insulate well

Metal at