Final Exam Study Guide

The final covers all 21 chapters. Taking them one at a time would mean 21 piles of notes, so this guide groups them into seven themes instead. Each theme pulls together the chapters that share a way of thinking. Measurement and the mole teach you to count. Structure and bonding explain shape. States and solutions handle what matter does in bulk. Change and rate ask how far and how fast. Equilibrium systems hold the balance. Energy and electron transfer set direction. The last theme walks the real elements and the nucleus itself. Work one theme a day and all 21 chapters fit into a week.

Theme 1 · Chapters 1 and 3Measurement and the mole

What to know

Matter is anything with mass that takes up space. In a solid the particles sit in fixed spots, so shape and volume both hold. In a liquid they touch but slide, so volume holds and shape gives way. In a gas they fly apart and fill the container, so neither holds.

Sort every sample three ways. An element holds one kind of atom. A compound holds two or more elements bonded in a fixed ratio. A mixture holds substances that are not bonded, so the ratio can shift. A physical change leaves the substance itself alone, while a chemical change makes new substances.

Every number in chemistry carries a unit, and the unit carries meaning. The significant figures of a measurement are the digits that say something real about its size. Multiplication and division keep the fewest significant figures in the problem. Addition and subtraction keep the fewest decimal places.

Dimensional analysis is the habit that makes unit work safe. Write the number with its unit, then multiply by fractions that cancel what you do not want and leave what you do. If the units come out right, the setup is right.

The mole is a counting word, like a dozen. One mole holds 6.022 × 10²³ particles, which is Avogadro's number. Molar mass is the grams in one mole, read off the periodic table in g/mol. Those two facts build one bridge that almost every calculation in this book walks across.

Percent composition is the share of each element by mass in a compound. An empirical formula gives the smallest whole-number ratio of atoms, and a molecular formula gives the real count. Get the empirical formula from masses or percents, then compare its mass with the measured molar mass to find the multiplier.

Molarity is moles of solute per liter of solution. Dilution keeps the solute and grows the volume, so the moles hold still while the concentration falls.

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Theme 2 · Chapters 2, 6, 7 and 8Structure and bonding

What to know

An atom holds protons and neutrons in a tiny nucleus with electrons spread around it. The proton count is the atomic number Z and it names the element. Isotopes share a proton count and differ in neutrons. The atomic mass on the periodic table is a weighted average over the isotopes as they occur in nature, so the common isotope pulls the average toward itself.

Atoms become ions by losing or gaining electrons. Metals on the left give electrons away to make cations. Nonmetals on the right take them in to make anions. An ionic compound is a lattice of those ions in whatever ratio makes the charges cancel, so the formula is the smallest such ratio. A molecular compound shares electrons instead, and its formula counts the atoms in one molecule.

Light is a wave and a stream of packets at once. Wavelength and frequency are locked together, and each packet carries an energy set by the frequency. Bohr fixed hydrogen's electron into levels with a definite energy each, and the gap between two levels is exactly the energy of the photon that moves an electron between them. That is why a hydrogen lamp gives sharp lines instead of a smear.

Quantum numbers name an orbital. The main level n sets the size, the letter sets the shape as s, p, d or f, and within a subshell the orbitals differ only in direction. An electron configuration lists how the electrons fill those orbitals in order of rising energy. Hund's rule says a subshell fills singly before any orbital doubles up, because two electrons in one orbital repel.

An ionic bond is the pull between opposite charges, and its strength shows up as the lattice energy. Bigger charges and smaller ions both raise it, which is why MgO holds together far harder than NaCl. A covalent bond is a shared pair. How evenly that pair is shared depends on the electronegativity gap, so a bond runs from nonpolar through polar to fully ionic as the gap grows.

A Lewis structure counts valence electrons and spends them to give every atom a full shell, usually an octet. When two or more good structures differ only in where the double bonds sit, the real molecule is a blend of them, and those drawings are resonance forms. Formal charge is the tie-breaker when several structures look legal. Keep the formal charges small and put any negative one on the more electronegative atom.

VSEPR turns a Lewis structure into a shape. Count the electron groups around the central atom, counting each lone pair and each bond as one group whether it is single, double or triple. The groups spread as far apart as they can. Then remove the lone pairs from the picture to read off the shape, because a lone pair takes up more room than a bond and squeezes the remaining angles.

Valence bond theory builds a bond from overlapping orbitals, and hybrid orbitals explain the measured angles. Four groups means sp³ at 109.5°, three means sp² at 120°, and two means sp at 180°. A head-on overlap is a sigma bond and a side-by-side overlap is a pi bond. A single bond is one sigma, a double bond is one sigma plus one pi, and a triple bond is one sigma plus two pi. A sigma bond lets the ends spin and a pi bond does not, which is why a double bond locks a molecule flat.

Molecular orbital theory spreads the electrons over the whole molecule instead. Combining two atomic orbitals gives one bonding level lower in energy and one antibonding level higher. Bond order is the bonding electrons minus the antibonding ones, divided by two. A higher bond order means a shorter and stronger bond. The theory also explains magnetism, since a molecule with unpaired electrons in its orbitals is paramagnetic. Oxygen is the famous case, and liquid oxygen really does cling to a magnet.

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Theme 3 · Chapters 9, 10 and 11States and solutions

What to know

Gas pressure is particles drumming on a wall. More particles, faster particles or a smaller box all raise it. The units all describe the same thing, and 1 atm = 760 torr = 760 mmHg = 101.325 kPa.

The simple gas laws each hold two things still and watch two others trade. Volume rises with temperature, falls as pressure rises, and rises with the amount of gas. The combined gas law packs all of that into one relation for a fixed amount of gas. The ideal gas law then ties all four quantities together at once, and it is the only gas equation you really have to remember.

STP is 0 °C and 1 atm. Put one mole into the ideal gas law at STP and out comes the molar volume, 22.4 L/mol, whatever the gas. So at STP the density of a gas is just its molar mass divided by 22.4.

In a mixture each gas pushes on the wall as if it were alone. Dalton's law adds those partial pressures to get the total, and each gas's share of the pressure equals its share of the moles. Light gases also escape through a pinhole faster than heavy ones, which is Graham's law: the rate goes as one over the square root of the molar mass.

Real gases stray from ideal at high pressure and low temperature, because particles do take up room and do attract each other. The van der Waals constants a and b correct for those two effects.

Heat a solid and a heating curve shows three slopes and two flats. On a slope only the temperature changes, so the heat is mass times specific heat times the temperature change. On a flat only the state changes, so the temperature holds while every joule goes into breaking the forces. The heat for a flat is the mass times the heat of fusion or of vaporization.

Vapor pressure is the push of the vapor sitting above its own liquid in a closed container. It climbs steeply with temperature, and a liquid boils when its vapor pressure reaches the pressure above it. The Clausius-Clapeyron relation puts numbers on that climb. A phase diagram maps which state is stable at each pressure and temperature, with the triple point where all three meet and the critical point where liquid and gas stop being different.

Dissolving takes three steps. Pull the solute apart, open a hole in the solvent, then let the two mix. The first two cost energy and the third pays it back, so the net can go either way. Like dissolves like, since polar solvents handle polar and ionic solutes while nonpolar solvents handle nonpolar ones.

Concentration has several measures and each has its own use. Molarity is per liter of solution and shifts a little with temperature, because volume does. Molality is per kilogram of solvent and never shifts. Mass percent and mole fraction are pure ratios. Density is the bridge between a mass-based measure and a volume-based one.

Colligative properties depend on how many solute particles there are and not on what they are. Solute lowers the vapor pressure, so the boiling point rises and the freezing point falls. The van't Hoff factor i counts the particles each formula unit gives, so NaCl counts twice and CaCl₂ counts three times. Osmotic pressure follows the same logic and is the most sensitive of the four.

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Theme 4 · Chapters 4, 5 and 12Change and rate

What to know

A chemical equation is balanced when every element has the same atom count on both sides. You balance it by changing coefficients only, never subscripts, because changing a subscript changes the substance. Balance the complicated formula first, leave free elements for last, and double everything if a half coefficient turns up.

Most reactions fall into a few families. Combination joins two things into one. Decomposition splits one into two. Single replacement swaps a free element into a compound. Double replacement trades partners, and a precipitation or a neutralization is that pattern. Combustion burns a fuel in oxygen to give carbon dioxide and water.

A redox reaction moves electrons, and you track that with oxidation numbers. A free element is 0. A monatomic ion carries its charge. Oxygen is usually −2 and hydrogen usually +1. The numbers must add to the overall charge on the species. If any number changes across the arrow, the reaction is redox.

The coefficients of a balanced equation are a mole ratio, and that ratio is the only way to cross from one substance to another. So every stoichiometry problem has the same shape. Convert what you are given into moles, cross the arrow with the coefficient ratio, then convert out to whatever the question asks for.

Energy comes in two forms. Kinetic energy is motion and potential energy is stored position. Heat is energy moving because of a temperature gap, and work is energy moving because something was pushed. A system gives off heat in an exothermic change and takes heat in during an endothermic one.

Specific heat is the heat it takes to raise one gram by one degree. Water's value of 4.184 J/g·°C is unusually large, which is why oceans steady the climate and why a water bath is so stable. A calorimeter uses that fact in reverse. Measure the temperature change of a known mass of water and you know the heat the reaction released, with the sign flipped.

Enthalpy change at steady pressure, written ΔH, is the heat of a reaction. It scales with the amount, so doubling the equation doubles ΔH, and reversing the equation flips its sign. Hess's law is the payoff. If several steps add up to your target reaction, their ΔH values add up too, so you can flip, scale and stack known reactions to reach a reaction nobody ever measured.

A standard enthalpy of formation is the ΔH for making one mole of a substance from its elements in their standard states, so it is zero for an element in that form. Then any reaction's ΔH° is the sum over products minus the sum over reactants, each term times its coefficient. Bond energies give a rougher second route, since breaking bonds costs and forming them pays.

Kinetics asks how fast. A rate law links the rate to concentrations through a rate constant and a set of exponents, and those exponents are found by experiment, not read off the equation. The only exception is an elementary step, where the coefficients do give the rate law. Add the exponents and you have the overall order.

An integrated rate law turns a rate into a clock. Each order has its own form, and each form is already the shape of a straight line. So plot the data three ways and only one plot comes out straight. That plot names the order and its slope gives k.

Collision theory says a reaction needs a crash that is hard enough and aimed correctly. The activation energy is the least energy a crash needs, and the top of that hill is the transition state. Note that activation energy is not ΔH. The ΔH is the gap from start to finish, while the activation energy is the height of the hill in between. The Arrhenius equation ties the rate constant to that barrier and the temperature, so two rate constants at two temperatures give you the barrier.

A mechanism is the list of elementary steps a reaction really takes. The slowest step sets the pace, so its rate law is usually the measured one, which is how a mechanism gets tested. A catalyst opens a path with a lower barrier and is remade at the end. It speeds both directions by the same factor, so it changes neither ΔH nor the position of equilibrium.

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Theme 5 · Chapters 13, 14 and 15Equilibrium systems

What to know

At dynamic equilibrium the forward and reverse rates are equal, so the measured amounts hold still while molecules keep reacting both ways. Equal rates do not mean equal amounts. The container must be closed, and you reach the same resting mixture from either side at a given temperature.

The equilibrium constant K is products over reactants, each amount raised to its coefficient from the balanced equation. Pure solids, pure liquids and solvent water stay out, since their crowding cannot change. K carries no units and depends only on temperature. The reaction quotient Q is the same fraction filled with what you have right now, and comparing the two gives the direction: below K it runs forward, above K it runs in reverse.

Le Chatelier's principle is that same test in a hurry. Add a species and the system shifts away from it. Squeeze a gas mixture and it shifts toward the side with fewer moles of gas. Heating shifts an endothermic reaction forward and raises K, and temperature is the only stress that changes K at all. A catalyst and an unreactive gas change nothing about the position.

An ICE table organizes the algebra, with each Change entry equal to the coefficient times x. When K is tiny you may replace (c₀ − x) with c₀, as long as c₀ ÷ K clears about 400 and x ends under five percent of c₀. Sometimes both sides are perfect squares, and then a square root beats the quadratic formula.

Acid-base chemistry is one proton changing hands. An acid donates it, a base accepts it, and a conjugate pair differs by exactly one H⁺. Water does both jobs, so it sets the middle of the scale. The ion-product constant K_w locks the two water ions together at 1.0 × 10^-14 at 25 °C, so pushing one up forces the other down and neither can reach zero.

A buffer holds a weak acid and its conjugate base together in real amounts, so added acid or base is soaked up and the pH barely moves. The Henderson-Hasselbalch equation reads a buffer pH off a ratio, and a buffer works best within about one pH unit of its pK_a. On a titration curve, the half-equivalence point reads pK_a directly, and a weak acid's equivalence point lands above pH 7 because the salt left behind is a base.

Solubility is equilibrium too. K_sp is the constant for a solid breaking into its ions, and the solid is never in the expression. The bridge from K_sp to molar solubility is the salt's ion ratio, so a 1:1 salt gives s², a 1:2 or 2:1 salt gives 4s³, and a 3:2 salt gives 108s⁵. Because of those exponents, two K_sp values can be compared head to head only when the ratios match.

A shared ion pushes the dissolving equilibrium back toward solid, which is the common ion effect. To predict a precipitate, dilute every ion for the combined volume, build Q, and compare it with K_sp. A ligand with a large formation constant strips the metal ion out and dissolves a solid water could not touch. Acid does the same job from the anion side, but only for salts whose anion is the conjugate base of a weak acid. For coupled equilibria, add the equations and multiply the constants, flipping a constant to 1 ÷ K whenever you flip its equation.

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Theme 6 · Chapters 16 and 17Energy and electron transfer

What to know

A change is spontaneous if it keeps going on its own, and that says nothing about speed. Heat release helps but does not decide, since ice melts in a warm room while taking heat in. The missing factor is how spread out the matter and energy end up, measured as entropy. Entropy counts arrangements, and S = k ln W ties it to that count.

The second law is the real test: a change happens when the total entropy of system plus surroundings rises. Either ledger may lose, and only the sum must grow. The surroundings keep score as −ΔH ÷ T, so cold surroundings gain more entropy per joule than warm ones. The third law sets a perfect pure crystal at 0 K to exactly zero entropy, which is why tables can list absolute S° values. Every one of them is positive, including for elements.

Gibbs free energy folds both ledgers into one number for the system alone, as ΔG = ΔH − TΔS. Negative means the forward change is favored, positive means the reverse, and zero means equilibrium. The four sign cases are worth memorizing. Both terms helping means always spontaneous. Both fighting means never. One of each means a switch-over at a crossover temperature.

Free energy also fixes the size of K through ΔG° = −RT ln K. At 298.15 K every 5.71 kJ is one power of ten in K. Keep ΔG° and ΔG apart, since the circle means the standard state while ΔG = ΔG° + RT ln Q describes the mixture you have. Once Q reaches K, the two terms cancel and ΔG is zero.

Electrochemistry turns all of that into a voltage. Oxidation loses electrons and reduction gains them, and they always travel together. Split a redox reaction into half-reactions, balance each one with water for oxygen, H⁺ for hydrogen and electrons for charge, then scale so the electrons cancel. For a basic solution, balance in acid and then add OH^- to both sides.

The hydrogen electrode was defined as exactly 0.000 V so every other half-cell could be measured against it. A high table value means a strong oxidizing agent, and any species high on the table will oxidize anything lower down. A positive E°_cell, a negative ΔG° and a K above 1 are the same fact three times over.

The Nernst equation corrects a potential for real concentrations. Pile up product and Q rises, so the voltage sags. That is a battery's whole life, and a dead battery is simply a cell that reached Q = K. A concentration cell is the limit of the idea, with E°_cell = 0 and the dilute half-cell as the anode.

Electrolysis pays electricity to force a reaction with a negative potential. Faraday's law treats electrons as a reagent measured out with an ammeter and a clock. In water the solvent often reacts instead of the ion you expected, and a real cell needs extra voltage called overpotential. Corrosion is a galvanic cell you did not build, worth 0.84 V for iron in damp air, and a sacrificial anode of zinc or magnesium stops it.

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Theme 7 · Chapters 18, 19, 20 and 21Descriptive and nuclear

What to know

The main groups run from 1 and 2 across to 13 through 18. Two trends explain nearly all of their chemistry. Across a period the nuclear grip tightens, atoms shrink, and the elements shift from giving electrons away to taking them in. Down a group a new shell is added, the grip loosens, and metallic character grows. One quick test places any element: a metal oxide makes a base, a nonmetal oxide makes an acid, and the amphoteric oxides in between react with both.

The d-block metals carry a partly filled d subshell, which is where their color and magnetism come from. In a neutral atom 4s fills before 3d, yet we write 3d first, and chromium and copper each shift one electron to reach a half filled or filled d set. When a cation forms, the 4s electrons always leave first, so d electrons equal the group number minus the charge.

A coordination compound is a metal ion with ligands attached, each donating a lone pair, so the ligand is a Lewis base and the metal is a Lewis acid. The coordination number counts donor atoms, not ligands, so three bidentate ligands give six. Names run cation first, then the ligands in alphabetical order, then the metal with its oxidation number in Roman numerals, and a negative complex takes an -ate ending.

Ligands split the d orbitals into a lower set of three and an upper set of two, separated by Δ. A small Δ leaves the electrons spread out, which is high spin. A large Δ stacks them low, which is low spin, and the choice only exists for d⁴ through d⁷. A d electron can absorb a photon worth exactly Δ, so you see the complementary color of the light that was taken out. Unpaired electrons make a complex paramagnetic, and the magnetic moment gives their count.

Carbon earns its own chapter because it makes four bonds and bonds to itself without complaint. Alkanes are saturated at C_nH_2n+2. Alkenes and rings are C_nH_2n, and alkynes are C_nH_2n-2. Structural isomers share a formula and wire up differently, so they are different substances. Naming always runs longest chain, lowest locants, branches in alphabetical order.

A multiple bond is loose electron density, so reagents attack it. An addition reaction keeps every atom, while substitution throws a second product away. Benzene is the exception that proves the rule, since its six delocalized electrons buy 152 kJ/mol of extra stability, and addition would hand that back. So an aromatic ring substitutes and stays whole.

A functional group sets the behavior and the carbon frame mostly comes along. An O–H bond lets a molecule donate a hydrogen bond, which can move a boiling point by a hundred degrees. The oxidation ladder runs primary alcohol to aldehyde to carboxylic acid, a secondary alcohol stops at the ketone, and a tertiary alcohol refuses. An addition polymer loses nothing, so its repeat unit matches the monomer. A condensation polymer drops water at each link, so each monomer needs two reactive ends.

Finally the nucleus. A nuclide symbol puts the nucleon count A on top and the proton count Z below, so N = A − Z. Stable nuclides crowd into the band of stability, and nothing past Z = 83 is stable. A nucleus weighs less than its separate parts, and that mass defect is its binding energy. Divide by the nucleon count and the value peaks near iron-56 at about 8.79 MeV, which is why heavy nuclei split and light ones fuse.

Alpha decay drops A by 4 and Z by 2. Beta decay raises Z by 1 while A holds. Positron emission and electron capture each lower Z by 1. Gamma emission changes neither. Decay is first order, so one half-life always halves what is left, and nothing you do to a sample changes the rate. A nuclear equation balances on A and Z only, which is exactly why elements can change. For radiation, becquerels measure the source, grays measure energy absorbed, and sieverts measure expected harm.

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