Chemistry AP Study Notes 7 (Bonding and Geometry)

Thus far:

1. The Basics
2. Basic Chemical Reactions
3. Reactions in Solution
4. Gases
5. Thermodynamics
6. Electron Orbitals

7. Bonding

• Ionic bonds trade electrons. Covalent bonds share electrons.
• Ionic bonds are a metal and a non-metal. Use the criss-cross method to figure out subscripts. These are polar bonds.
• Use Lewis dot structures to draw shared covalent bonds. These tend to be more non-polar, although they can be partially polar (polar covalent bonds).
• Electronegativity is the measure of the tendency to hold or gain electrons. It increases from bottom left to top right on the periodic table.
• The N - A = S rule is 1) N -- what is the ideal filled valence electron number? (2 or 8); 2) A -- what is the total number of available electrons; 3) S is the total number of electrons that must therefore be shared and S/2 tells the total number of bonds.
• The idea of formal charge helps you determine which of more than one possible structure is the most likely. For each possible structure, take the number of valence electrons for an atom. Subtract the number of electrons that aren't bonded and add half the number of bonded electrons. Make sure the total of all the "formal charges" on each atom add up to the actual charge on the ion.
• The preferred structure is the one with the most zeros, especially on the most electronegative atom, without any like charges next to each other.
• There are a few circumstances where the octet rule does not work.

Molecular Geometry

• The VSEPR theory predicts the shape a molecule will take (valence shell electron pair repulsion). Basically, electron pairs try to move as far away from each other as they can.
• 1) Write the Lewis-dot structure, 2) how many electron pairs are there (count double and triple bonds as a single group, 3) what shape maximizes the distance (this is the geometry of the electron groups), 4) now for drawing purposes, pretend that the non-binding electron groups aren't there and draw the molecular geometry.
• Here are the possibilities. With only two bonding pairs, we have linear geometry (like CO₂).
• With three total electron pairs, we have trigonal planar (all three used, BF₃) and bent (only two used NO₂)
• With four total electron pairs, we have tetrahedral (with all four used, CH₄), trigonal pyramidal (with only three used, NH₃), or bent (with only two used, H₂O).
• With five total electron pairs we have trigonal bipyrimidal (with all five used, PF₅), seesaw (with four used, SF₄), T shaped (with three used, ClF₃), and linear (with two used, XeF₂).
• Finally, with six total electron pairs, we have octohedral (with all six used, SF6), square pyrimidal (with 5 used, ClF₅) and square planar (with 4 used, XeF₄).

Valence Bond Theory

• Explains geometry by hybrid orbitals. 
• Linear is one s and one p orbital (sp hybridization).
• sp² hybridization is an s with two p orbitals. This is trigonal planar.
• sp³ hybridization is an s with three p orbitals. This is tetrahedral.
• sp³d hybridization is an s with three p and one d orbital. This is trigonal bipyrimidal.
• sp³d² hybridization is an s with three p and two d orbitals. This is octohedral.
• Sigma bonds are the straight bonds between atoms. Pi bonds are the second and third bonds in double and triple bonds.

Molecular Orbital Theory

• A theory of covalent bonds that sees the electrons as assigned to the whole molecule rather than the individual atoms.
• Speaks of bonding orbitals and antibonding orbitals.
• A concept called "bond order" is half the bonding orbitals minus the antibonding orbitals.
• The higher the bond order, the shorter and stronger the bond.

In addition

• Resonance structures are instances when, say, a double bond isn't just in one location but moves around, so to speak (e.g., NO₃^-).
• Paramagnetism is an attraction to a magnetic field due to unpaired electrons.
• Diamagnetism is a slight repulsion from a magnetic field due to the presence of paired electrons.

Chemistry AP Study Notes 6 (Orbitals)

The Electron Orbitals

• So the space around the nucleus of atoms has a certain structure. The clouds of probable location take on certain shapes. It's like a seating arrangement for the electrons. As people come in, they are given the next seat.
• There are shells of electrons, like rows of seats. These correspond to the periods or rows on the periodic table. We give them numbers, 1, 2, 3, 4...
• Within any shell, the first two electrons to arrive fill up a spherical orbital or subshell around the nucleus, which can hold two seats. So hydrogen's electron fills the first seat and the second seat is empty. Helium's two electrons entirely fill the first shell, which uniquely only holds two. It is a noble gas because it's outermost shell is completely full.
• A spherical orbital is called an s orbital (the similarity is coincidental). The first two columns of the periodic table are atoms whose outermost orbital involves one or two electrons in this spherical "seating." Group 1 has one electron in that shell. Group two has the spherical part of the shell full.
• After the first two electron seats, the next group of electron seats are also grouped in twos--two up and down, two in and out, and two side to side. So six possible seats perpendicular to each other. This orbital is called the p orbital (again, coincidental). The six groups on the right side of the periodic table are atoms whose outermost shell or valence shell involves electrons in the "p seats."
• When we get to the third row, the third shell, another type of orbital comes into play. However, it doesn't actually show up until the space of the fourth row. These are the transition metals. Ten electrons can fit in this orbital. There are 5 sets of two in interesting flower shapes.
• Finally, there is an f orbital with up to 14 electrons. These correspond to the Lanthanide and Actinoid elements usually placed at the very bottom of the periodic table.

Quantum Theory

• In the year 1900, a scientist by the name of Max Planck suggested that energy might only come in certain packets. So there is the base energy level, then twice that level, three times, etc. This is why there are fixed "seats" around the nucleus of an atom. There is no in between the seats. We say that the energy of an electron is quantized.
•  The starting point for an electron is its ground state. An excited state is when a certain amount of energy is added to the electron so it jumps to the next highest state. The energy between two levels is

ΔE = -2.18 x 10^-18 (1/n²_final – 1/n²_initial)

• In the 1920s, a man named Schrodinger came up with a wave equation to predict the possible size, shapes, and orientations that electron clouds could have around the nucleus. This is where the s, p, d, and f orbitals mentioned above come from. These states correlate to varieties of four quantum numbers.
• First there is the principal quantum number, which has to do with the shells, the rows or periods of the periodic table. n = 1, 2, 3...
• Then there is the angular momentum quantum number, which has to do with the orbitals. One less than n tells you how many orbitals exist for that row. So for the third shell, there can be L = 0, 1, and 2 (s, p, and d orbitals).
• The magnetic quantum number goes from -L to +L. So the p orbital (L = 1) has three options (-1, 0, +1). 
• When you finally take into account the spin quantum number (two options for each magnetic possibility), there are 6 possible electron states for each p orbital.

The Wave Nature of the Electron

• Planck suggested that the packages of energy followed the formula E = hv, where h is Planck's constant: 6.63 x 10^-34 Js and v is the frequency of the energy.
• Frequency is the number of waves that pass a point per second. Related to the frequency is the wavelength, how far the distance is between each crest of a wave. The shorter the wavelength, the higher the frequency. The longer the wavelength, the lower the frequency.
• If you multiple these two together, you get the speed of the wave (meters times cycles/second gives you meters/second for the wave cycles).
• Einstein solidified for us that all electromagnetic waves travel at the same speed, the speed of light, which is 3 x 10⁸ m/s, which is given the symbol c. So c = wavelength times frequency or c = λv.
• The amplitude of a wave is how high it is.
• The electromagnetic spectrum gives us the range of frequencies that electromagnetic waves can have. Radio frequencies are the longest wavelengths and lowest frequencies. Microwaves have slightly shorter wavelengths and slightly higher frequencies.
• Then there is infrared, visible light, ultraviolet, x-rays, and finally gamma rays. Gamma rays have the highest frequencies and the shortest wavelengths.

Chemistry AP Study Notes 5 (Thermodynamics)

Thermodynamics
Enthalpy

• Enthalpy is the heat gained or lost by a system under constant pressure conditions, ΔH. ΔH > 0 if the reaction is endothermic. ΔH < 0 if the reaction is exothermic.
• Exothermic means that the temperature goes up during the reaction. Endothermic means the temperature goes down during the reaction.
• Calorimetry is a technique to measure the heat released or absorbed during a change. That quantity is known as q.
• Heat capacity is the amount of heat needed to change the temperature 1K.

C_p = heat capacity = q/ΔT (units of joules/kelvin)

• Specific heat capacity is the amount of heat needed to raise one gram of a substance 1K.

c = q/(mΔT) (units of joules per gram-kelvin)

• Molar heat capacity is the amount of heat needed to raise one mole of a substance 1K.
• Hess' Law states that if a reaction occurs in steps then the total enthalpy change will equal the totals of the individual steps. 
• You do not have to know the actual steps because heat reactions are a state function. That means that the total only depends on the beginning and end states, not on the pathway used to get there. 
• The heat of formation of a product is symbolized by ΔH_f
• A degree to the right of the ΔH implies a standard state (1 atm, 1 M, etc). ΔH°
• So ΔH°_f gives the total heat of formation when 1 mole of a substance is formed from elements and all the substances are in their standard state. This is the standard enthalpy of formation.
• The ΔH°_f of an element in its standard state is zero.
• The ΔH°_{f rxn} for a reaction is the sum of all the ΔH°_f for the products minus those for the reactants.

Entropy

• The First Law of Thermodynamics is that the total energy of the universe is constant. It amounts to the Law of Conservation of Energy.
• The Second Law of Thermodynamics is the famed entropy law. Entropy is the inevitable overall tendency of a system toward disorder. ΔS_universe = ΔS_system + ΔS_surroundings > 0.
• The entropy increases: 1) when the number of molecules increases during a reaction, 2) with an increase in temperature, 3) when a gas is formed from a liquid or solid, and 4) when a liquid is formed from a solid.
• The standard molar entropy (S°) can be summed up like the standard enthalpy (ΔH°). You take the sum of the entropies of the products and subtract from them the sum of the entropies of the reactants.

Gibbs Free Energy

• Some guidelines for predicting a spontaneous reaction are a negative enthalpy and a positive entropy. These are put together in the Gibbs free energy equation.

ΔG = ΔH - TΔS

• ΔG is the best indicator as to whether a spontaneous reaction will occur.
• If ΔG > 0, the reaction will not be spontaneous. More energy is needed.
• If ΔG < 0, the reaction will be spontaneous.
• If ΔG = 0, the reaction is in equilibrium.
• The standard Gibbs free energy change ΔG° is again the sum of the products minus the sum of the reactants.
• If the concentrations or pressures are not 1, then we need the Gibbs free energy equation for non-standard conditions:

ΔG = ΔG° + ln RT Q or ΔG° + 2.303 log Q

where Q is the ratio of the sum of products over the sum of reactants, the activity quotient.

Chemistry AP Study Notes 4 (Gases)

Thus far:
1. The Basics
2. Basic Chemical Reactions
3. Reactions in Solution

Chapter 5
Gases
Kinetic Molecular Theory, Part I

• 1) Gases are made up of very small particles, 
• 2) in constant, random motion, bouncing into their boundaries (which constitutes pressure), 
• 3) with lots of space between them, 
• 4) colliding randomly and elastically into each other, 
• 5) with the average kinetic energy being proportional to the Kelvin temperature.

Pressure, Volume, Temperature, Amount

• There are clear relationships between the pressure, volume, temperature, and amount of gas.
• Boyle's Law has to do with the relationship between pressure and volume when the temperature is constant. When the pressure goes up, the volume goes down. When the volume goes up, the pressure goes down. These are "inversely proportional." P x V is constant. Also P₁V₁ = P₂V₂.
• Pressure can be measured by a barometer or manometer. One "atmosphere" is sea level pressure. It would raise a column of mercury 760 mm (aka 760 torr-s). The pascal and pounds per square inch are other units of measuring pressure.
• Charles' Law has to do with the relationship between volume and temperature when the pressure is constant. When the temperature goes up, the volume goes up. When the temperature goes down, the volume goes down. These are "directly proportional." V/T is constant. Also V₁/T₁ = V₂/T₂.
• Temperature in such cases is in Kelvin. Kelvin is Celsius plus 273.15.
• Guy-Lussac's Law has to do with the relationship between pressure and temperature when the volume is held constant. When the pressure goes up, the temperature goes up. When the pressure goes down, the temperature goes down. Like volume and temperature, this is a directly proportional relationship. P₁/T₁ = P₂/T₂.
• Avogadro's Law has to do with the relationship between the amount of gas and the volume at a constant temperature and pressure. When the amount goes up, the volume has to go up for the temperature and pressure to stay the same, and vice versa. V₁/n₁ = V₂/n₂.
• We can add a constant and put all the above laws into a single ideal gas equation. The constant to make everything work out is R, the ideal gas constant (0.0821 L-atm/K-mol).

PV = nRT

• Johannes van der Waals made the ideal gas law a little more precise by adjusting the volume to take into account the fact that gas molecules do not have an infinite volume in which to move. He also adjusted the pressure part of the equation to take into account the attraction between molecules. His modified equation was:

(P + an²/V)(V - nb) = nRT

Kinetic Molecular Theory, Part II

• The average velocity of gas particles is the root mean square speed, u_rms.
• It is the square root of 3RT/M, where R is the ideal gas constant, T is the temperature in Kelvins, and M is the molar mass of the gas.
• The kinetic energy of each molecule is 3/2 RT.

Some More Laws

• Dalton's Law says the total pressure of a mixture of gases is just the sum of the individual "partial" pressures.
• You can figure out the partial pressure by multiplying the total pressure by the mole fraction of each gas.
• Graham's Law of Diffusion and Effusion states that the comparative rates of effusion (r1/r2, going through a tiny opening) are equal to the square root of the inverse ratio of the molar masses (M2/M1). Diffusion works similarly (mixing of gases due to their kinetic energy).

Other Details

• You can use the ideal gas law to answer stoichiometric questions. For example, you can find the number of moles of a gas released given the pressure, volume, and temperature. Then using the ratios of an equation, you can solve for grams of reactants and such.
• STP means "standard temperature and pressure."

Chemistry AP Study Notes 3 (Aqueous Solutions)

Thus far:
1. The Basics
2. Basic Chemical Reactions

Chapter 4
Reactions in Aqueous Solutions

• electrolyte (conducts electricity when dissolved in water); non-electrolytes
• cations ("cats are positive") and anions (negative)
• hydration - when substances dissolve into ions that are surrounded in a certain way by water; H₂O is sometimes written over the reaction arrow.
• reversible reactions (double arrow in both directions)
• Some specific types of reactions: 1) precipitation reactions, 2) acid-base reactions, 3) redox reactions (oxidation-reduction). See the five broader types of reaction in the notes on the previous chapter.

Precipitation Reactions

• Precipitation reactions (solid comes out of the reaction) is a double displacement reaction (also called a metathesis reaction).
• solubility - how much solute will dissolve in solvent at a certain temperature
• molecular equation versus ionic equation
• Ions not involved in the overall reaction are called "spectator ions."
• A "net ionic equation" only shows the species that actually take place in the reaction. 

Acid-Base Reactions

• Acid-base reactions. Acids have sour taste (like vinegar). Bases have a bitter taste.
• Arrhenius defined an acid as a substance that produces an H⁺ ion in solution and a base as a substance that produces an OH^- ion in solution.
• Bronsted defined an acid as a proton donor and a base as a proton acceptor.
• the hydronium ion (H₃O⁺)
• monoprotic, diprotic, and triprotic acids
• acid-base neutralization, usually yielding a salt and water. 
• titration is a method for determining the concentration of an acid or base. For example, an acid is prepared with an "indicator" like phenolphthalein (which turns pink in a basic solution--7+ on the ph scale--but is otherwise clear--7- on the ph scale). Drops of a known concentration of a base like NaOH is dripped into the acid until it reaches the endpoint (turns pink), which is the equivalence point (ph of 7).

Oxidation-Reduction Reactions

• Oxidation-reduction reactions include combustion reactions, single replacement reactions, and many double replacement and decomposition reactions.
• In a "redox" reaction, the "oxidized" element loses electrons ("ox-loss") and the "reduced" element gains electrons. The reduced element is called the oxidizing agent, and the oxidized element is called the reducing agent.
• In a sense, you have an oxidation reaction and a reduction reaction taking place simultaneously. For example, solid zinc may oxidize into Zn²⁺ as it dissolves in a solution with copper +2 ions. It is losing electrons so it is being oxidized.
• At the same time, a reduction reaction also takes place. The Cu²⁺ ion becomes solid copper. It is gaining electrons so it is being reduced.
• An "activity series for metals" lists metals in an order of decreasing ease of oxidation (so the metal at the top is most easily oxidized). If a higher metal is put in a solution of a lower metal, there will be a single replacement reaction. The opposite attempt would not react.

Oxidation Numbers

• A tool for balancing redox equations. Don't confuse them with charge.
• The oxidation number of a neutral element is 0.
• The oxidation number on a monoatomic ion is its charge (write the plus or minus after the number).
• The sum of all oxidation numbers in a neutral molecule is zero.
• Alkalis (+1), Alkalines (+2), Halogens (-1), oxygen (-2)

Other Tidbits

• All sodium, potassium, ammonium, and nitrate salts are soluble in water.
• Strong acids include HCl, HBr, HI, HNO₃, HCLO₃, HCLO₄, H₂SO₄
• Cu²⁺ ions are normally blue.
• Bromine solutions tend to be reddish.
• Iodine solutions tend to be brownish in water.
• Carbonates (CO₃^2-) produce carbon dioxide in the presence of an acid.
• Many hydrides (e.g., NaH) react with water to form the hydroxide ion (OH^-) and hydrogen gas.
• Charge is written with number first. Oxidation numbers put the charge first.
• Electrolysis is sometimes used to cause decomposition reactions.
• A complex ion is a metal ion bonded usually with water (called a ligand). So the chromium in chromium nitrate bonds with six water molecules in water. Coordination numbers are the numbers of water (or other) molecules that serve as such ligands. The most common number is 6, but also found are 2 and 4.

Chemistry AP Study Notes 1

What's in a chemistry AP exam? Let me at least try.

Chapter 1
Chemistry: The Study of Change

• the scientific method
• types of mixtures
• states of matter
• physical and chemical properties
• key units of mass, volume, temperature (know conversion)
• density
• scientific notation
• significant figures
• factor-label method

Chapter 2
Atoms, Molecules, and Ions

• Dalton, Thomson, Rutherford, Bohr
• electrons, protons, neutrons
• atomic number, mass number, where they are on the symbol
• periodic table, groups, periods
• molecules, ions
• molecular and empirical formulas
• understanding formulas, naming compounds 
• naming acids, bases