AP Chemistry Exam

atomic number

The same as the number of protons in the nucleus of an element; it is also the same as the number of electrons surrounding the nucleus of an element when it is neutrally charged.

mass number

The sum of an atom's neutrons and protons

isotopes

Atoms of an element with different numbers of neutrons

Avogadro's number

6.022×10²³ particles per one mole

Moles

grams/molar mass

Standard Temperature and Pressure (STP)

Pressure \= 1 atm
Temperature \= 273 K

Converting from moles to liters

I mole of gas \= 22.4 L

Moles and Solutions

Moles \= (molarity)(liters of solution)

percent composition (mass percents)

The percent by mass of each element that makes up a compound. It is calculated by dividing the mass of each element or component in a compound by the total molar mass for the substance.

empirical formula

- Represents the simplest ratio of one element to another in a compound

- Start by assuming a 100 g sample
- Convert percentages to grams
- Convert grams into moles
- Divide each mole value by the lowest of the values
- These values become the subscripts

molecular formula

- Determine the molar mass of the empirical formula
- Divide that mass into the molar mass
x \= m/e
x \= molar mass/ empirical mass
- Multiply all subscripts in the empirical formula by the value of x

Aufbau principle

States that when building up the electron configuration of an atom, electrons are placed in orbitals, subshells, and shells in order of increasing energy.

Pauli Exclusion Principle

States that the two electrons which share an orbital cannot have the same spin. One electron must spin clockwise, and the other must spin counterclockwise.

Hund's Rule

States that when an electron is added to a subshell, it will always occupy an empty orbital if no one is available. Electrons always occupy orbitals singly if possible and pair up only if no empty orbitals are available.

Coulomb's Law

The amount of energy that an electron has depends on its distance from nucleus of an atom. While on the exam, you will not be required to mathematically calculate the amount of energy a given electron has, you should be able to qualitatively apply Coulomb's Law.

Essentially, the greater the charge of the nucleus, the more energy an electron will have.

Quantum Theory

Max Planck figured out that electromagnetic energy is quantized. That is, for a given frequency of radiation (or light), all possible energies are multiples of a certain unit of energy, called a quantum (mathematically, that's E \= hv). So, energy changes do not occur smoothly but rather in small but specific steps.

Energy and Electromagnetic Radiation

ΔE \= hv \= hc/λ

ΔE \= energy change
h \= Planck's constant, 6.626×10⁻³⁴ J∙s
v \= frequency of the radiation
λ \= wavelength of the radiation
c \= the speed of light, 3.00×10⁸ m/s

Frequency and Wavelength

c \= λv

*Inversely proportional*

c \= speed of light in a vacuum (2.998×10⁸ m/s)
λ \= wavelength of the radiation
v \= frequency of the radiation

ionization energy

The amount of energy necessary to remove an electron from an atom.

photoelectron spectra (PES)

A chart of the amount of ionization energy for all electrons ejected from a nucleus.

The y-axis describes the relative number of electrons that are ejected from a given energy level.

The x-axis shows the binding energy of those electrons.

Gases will most likely act as ideal under what conditions?

High temperature and low pressure

Energy Levels

s-subshell holds two electrons

p-subshell holds six electrons

d-subshell holds 10 electrons

f-subshell holds 14 electrons

electron configuration

The complete description of the energy level and subshell that each electron on an element inhabits

Heisenberg Uncertainty Principle

States that it is impossible to know both the momentum of an electron at a particular instant.

Atomic Radius Trends

Atomic radius decreases across a period

Atomic radius increases down a group

Cations are smaller than their atoms

Ions are larger than their atoms

Ionization energy

The energy required to remove an electron from an atom.

Electronegativity

Refers to how strongly the nucleus of an atom attracts the electrons of other atoms in a bond.

Periodic Trends

Across the periods
- atomic radius decreases
- ionization energy increases
- electronegativity increases

Down the periods
- atomic radius increases
- ionization energy decreases
- electronegativity decreases

Ionic Bonds

An ionic solid is held together by the electrostatic attractions between ions that are next to one another in a lattice structure.

Occurs between a metal and a nonmetal; electrons are not shared, they are given up by one atom and accepted by another.

Substances with ionic bonds are usually solids at room temperature and have very high melting and boiling points.

Ex. NaCl

Factors Affecting Melting Points of Ionic Substances

1. Charge on ions - a greater charge leads to a greater bond energy

Ex. MgO will have a higher melting point than NaCl

2. Size of ions - smaller ions will have greater attraction

Ex. LiF will have a greater melting KBr

Interstitial alloys

Metal atoms with two different radii combine

Ex. In steel, much smaller carbon atoms occupy the interstices of the iron atoms

Substitutional alloy

Forms between atoms of similar radii

Ex. Atoms of zinc are substituted with copper atoms to create an alloy

Covalent bonding

Bonding in which two atoms share electrons. Each atom counts the shared electrons as part of its valence shell to achieve complete outer shells.

The first covalent bond formed between two atoms is called a sigma bond.

Single bonds

Bond designation: One sigma

Bond order: One

Bond length: Longest

Bond energy: Least

Double Bond

Bond designation: One sigma and one pi

Bond order: Two

Bond length: Intermediate

Bond energy: Intermediate

Triple Bond

Bond designation: One sigma and two pi

Bond order: Three

Bond length: Shortest

Bond energy: Greatest

Network (Covalent) Bonds

In a network solid, atoms are held together in a lattice of covalent bonds.

They are very hard and have very high melting and boiling points.

Ex. The most commonly seen network solids are compounds of carbon (such as diamond or graphite) and silicon (SiO₂ quartz)

Hydrogen Bonds

Much stronger than dipole-dipole forces.

Substances that have hydrogen bonds have higher melting and boiling points. Ex. water, H₂O and ammonia, NH₃

*Water is less dense as a solid than as a liquid because its hydrogen bonds force the molecules in ice to form a crystal structure, which keeps them apart than they are in the liquid form

Dipole-Dipole Forces

Forces that occur when the positive end of one polar molecule is attracted to the negative end of another polar molecule.

Molecules with greater polarity have higher melting and boiling points.

Dipole-dipole attractions, however, are relatively weak, and these substances melt and boil at very low temperatures.

London Dispersion Forces

Forces that occur between all molecules.

These very weak attractions occur because of the random motions of electrons on atoms within molecules. At a given moment, a nonpolar molecule might have more electrons on one side than on the other, given it an instantaneous polarity.

Molecules with more electrons will experience will experience greater London dispersion forces, and therefore have generally higher melting and boiling points.

London forces are even weaker than dipole-dipole forces, so substances that have only London dispersion forces melt and boil at extremely low temperatures and tend to be gases at room temperature.

Different types of bonds and their relative melting and boiling points (from highest to lowest)

1. Network Covalent Bonds

2. Ionic Bonds (based on Coulombic attraction)
a. Greater Ion Charge
b. Smaller Atom Size

3. Covalent Bonds (based on molecular polarity)
a. Hydrogen Bonds
b. Non-Hydrogen Bond Dipoles
c. London Dispersion Forces (temporary dipoles)
i. Large molecules are more polarizable because they have more electrons.

How intermolecular forces affect the phase of a substance

1. Substances with weak intermolecular forces (LD), tend to be gases at room temperature.

2. Substances with strong intermolecular forces (HB) tend to be liquids at room temperature.

3. Because ionic bonds are generally significantly stronger tan intermolecular forces in covalent molecules, ionic substances are usually solid at room temperatures.
*Ionic substances do not experience intermolecular forces.*

Vapor Pressure

Arises from the fact that molecules inside a liquid are in constant motion. If those molecules hit the surface of the liquid with enough kinetic energy, they can escape the intermolecular forces holding them to the other molecules and transition them into the gas phase.

This is not to be confused with a liquid boiling. In order for vaporization to occur, no outside energy needs to be added.

Resonance Forms

Incomplete Octets

Some atoms are stable with less than eight electrons in their outer shell.

\
\- Hydrogen only requires two electrons

\
\- Boron is considered to be stable with only six electrons, as in BF₃

Expanded Octets

In molecules that have d subshells available, the central atom can have more than eight valence electrons, but never more than twelve.

- PCl₅

- SF₄

- XeF₄

Formal Charge

If more than one valid Lewis structure exists for a molecule, formal charge can be used to determine the more likely structure.

Standard Enthalpy of Formation

The amount of heat lost or gained when one mole of a compound is formed from its constituent elements.

Enthalpy Change (Hess's Law for ΔH)

The enthalpy change for a reaction is equal to the sum of the enthalpy of formation of all the products minus the sum of the enthalpy of formation of all the reactants.

Valence Shell Electron Pair Repulsion Model

Electrons repel each other, so when atoms come together to form a molecule, the molecule will assume the shape that keeps its different electron pairs as far apart as possible.

Linear Geometry

- Central atom with 2 electron pairs

- Zero lone pairs

- sp hybridization

- Ex. BeCl₂ and CO₂

B - A - B

Trigonal Planar Geometry

- Central atom with three electron pairs

- Zero lone pairs

- sp² hybridization

- 120° bond angles

- Ex. BF₃, SO₃, NO₃⁻, CO₃²⁻

Bent Geometry

- Central atom with three electron pairs

- One lone pair

- sp² hybridization

- 120° bond angle

- Ex. SO₂

Specific Heat Capacity

The amount of heat required to raise the temperature of one mass unit of a substance by 1.00°C

Tetrahedral Geometry

- Central atom has four electron pairs

- Zero lone pairs

- sp³ hybridization

- 109.5° bond angle

- Ex. CH₄, NH₄⁺, ClO₄⁻, SO₄²⁻, PO₄³⁻

Trigonal Pyramidal Geometry

- Central atom has four electron pairs

- One lone pair

- sp³ hybridization

- 109.5° bond angle

- Ex. NH₃, PCl₃, AsH₃, SO₃²⁻

Bent Geometry

- Central atom has four electron pairs

- two lone pair

- sp³ hybridization

- 109.5° bond angle

- Ex. H₂O, OF₂, NH₂⁻

Trigonal Bipyramidal Geometry

- Central atom has 5 electron pairs

- Zero lone pairs

- dsp³ hybridization

- Ex. PCl₅, PF₅

Folded square, seesaw, distorted tetrahedron geometry

- Central atom has 5 electron pairs

- One lone pair

- dsp³ hybridization

- Ex. SF₄, IF₄⁺

T-Shaped Geometry

- Central atom has 5 electron pairs

- Two lone pairs

- dsp³ hybridization

- Ex. ClF₃, ICl₃

Linear Geometry

- Central atom has 5 electron pairs

- Three lone pairs

- dsp³ hybridization

- Ex. XeF₂, I₃⁻

Octahedral Geometry

- Central atom has 6 electron pairs

- Zero lone pairs

- d²sp³ hybridization

- Ex. SF₆

Square Pyramidal

- Central atom has 6 electron pairs

- One lone pair

- d²sp³ hybridization

- Ex. BrF₅, IF₅

Square Planar

- Central atom has 6 electron pairs

- Two lone pairs

- d²sp³ hybridization

- Ex. XeF₄, ICl₄⁻

Entropy

A measure of molecular randomness, or disorder

Kinetic Molecular Theory

- The kinetic energy of an ideal gas is directly proportional to its absolute temperature: The greater the temperature, the greater the average kinetic energy of the gas molecules.

- There are no forces of attraction between the gas molecules in an ideal gas.

- Gas molecules are in constant motion, colliding with one another and with the walls of their container without losing any energy.

The Ideal Gas Equation

PV \= nRT

R \= .08206 Latm/molK

If volume is constant

As pressure increases, temperature increases

Boyle's Law (If temperature is constant)

As pressure increases, volume decreases, and vice versa

Charles' Law (If pressure is constant)

As temperature increases, volume increases

Dalton's Law

Ptotal \= Pa + Pb + Pc + ...

Partial Pressure

Pa \= (Ptotal)(Xa)

Xa \= moles of gas A/total moles of gas

Deviations From Ideal Behavior

At low temperature and/or high pressure, gases behave in a less-than-ideal manner. This is because the assumptions made in the kinetic molecular theory become invalid.

Density

D \= m/v

Molarity (M)

Expresses the concentration of a solution in terms of volume.

M \= moles of solute / liters of solution

Mole Fraction

Mole fraction gives the fraction of moles of a given substance (S) out of the total moles present in a sample.

Mole Fraction (Xa) \= moles of substance S / total number of moles in solution

Solutes and Solvents

"Like dissolves like"

A basic rule to remember which solutes will dissolve in which solvents.

Polar or ionic solutes (such as salt) will dissolve in polar solvents (such as water).

Nonpolar solutes (such as oils) are best dissolved in nonpolar solvents.

When an ionic substance dissolves, it breaks up into ions in a process called dissociation. Free ions in a solution are called electrolytes because they can conduct electricity.

Oxidation

Electron loss

Reduction

Electron gain

Oxidizing agent

Reactant that is reduced (gains electrons)

Reducing agent

Reactant that is oxidized (loses electrons)

Spontaneous

Not requiring an outside source of energy to proceed

Graham's Law

The rate of diffusion of a gas molecule is inversely proportional to the square root of that molecule's mass.

Gibbs Free Energy

The amount of energy in a system that is available to do useful work.

-ΔG is spontaneous

+ΔG is nonspontaneous

When ΔG \= 0 the reaction is at equilibrium

Buffer Solution

A solution consisting of a weak acid plus its conjugate base or a weak base plus its conjugate acid.

This solution resists changes to its pH

Crystalline Solids

Solid that has its atoms arranged in an orderly way.

Amorphous Solid

Solids whose particles have no orderly pattern.

Solubility Rules

1. Compounds with an alkali metal cation (Na⁺, Li⁺, K⁺, etc) or an ammonium cation (NH₄⁺) are always soluble.

2. Compounds with a nitrate (NO₃⁻) anion are always soluble.

Enthalpy Change in Bonds

When bonds are broken, energy is released.

When bonds are formed, energy is absorbed.

Exothermic Reactions

If the products have stronger bonds than reactants, then the products have lower enthalpy than the reactants and are more stable; in this case, energy is released by the reaction, or the reaction is exothermic.

Endothermic Reactions

If the products have weaker bonds than the reactants, then the products have higher enthalpy than the reactants and are less stable; in this case, energy is absorbed by the reaction, or the reaction is exothermic.

Activation Energy

The amount of energy required to reach the transition state, the highest point on the graph. At this point, all reactant bonds have been broken, but no product bonds have been formed, so this is the point in the reaction with the highest energy and lowest stability.

Catalysts

Speed up a reaction by providing the reactants with an alternate pathway that has a lower activation energy.

A catalyst lowers the activation energy, but it has no effect on the energy of the reactants, the energy of the products, or the ΔH of the reaction.

Galvanic Cell (Voltaic Cell)

In a galvanic cell, a favored redox reaction is used to generate a flow of current.

Two half-reactions take place in separate chambers, and the electrons that are released by the oxidation reaction pass through a wire to the chamber where they are consumed in the reduction reaction. That's how the current is created.

If the concentration of the products in a voltaic cell increases, the voltage decreases. If the concentration of the reactants increases, the voltage increases.

Redox in a Galvanic Cell

Oxidation takes place at the anode

Reduction takes place at the cathode

Cathode

Where reduction occurs and the solution is becoming less positively charged, the positive cations from the salt bridge solution flow into the half-cell.

Anode

Where oxidation occurs and the solution is becoming more positively charged, the negative anions from the salt bridge solution flow into the half-cell.

Solving Electroplating Problems

1. If you know the current and time, you can calculate the charge in coulombs.

I \= q/t

I \= current (amperes, A)
q \= charge (coulombs, C)
t \= time (seconds, s)

2. Once you know the charge in coulombs, you know how many electrons were involved in the reaction.

moles of electrons \= (coulombs) / (96,500 coulombs/mol)

3. When you know the number of moles of electrons and you know the half-reaction for the metal, you can find out how many moles of metal plated out.

4. Once you know the number of moles of the metal, you can convert this to the number of grams of the metal.

First Order Rate Laws

Rate \= k[A]

The rate law for a first order reaction uses natural logarithms.

The use of natural logarithms in the rate law creates a linear graph comparing concentration and time.

The slope of the line is given by -k and the y-intercept is given by ln[A]₀

Half-life

Describes the amount of time it takes for half of a sample to react.