Exam 6 Study Guide

Exam 6 covers chapters 16, 17 and 18. Two of those chapters are about which way a change wants to go. The third one walks the main groups element by element. Chapter 16 gives you entropy and free energy. Chapter 17 puts free energy into a wire and gets a voltage out. Chapter 18 then shows that whole toolkit at work on real elements. Do the worked examples with a pencil first, then take the self-test at the end of each chapter.

Chapter 16Thermodynamics

What to know

A change is spontaneous if it keeps going on its own once it starts. Nothing outside has to drive it. A change that needs steady outside work is nonspontaneous, and it is always the reverse of a spontaneous one.

Spontaneous says nothing about speed. Graphite is the favored form of carbon at room temperature, with ΔG° = −2.9 kJ/mol for diamond turning into it. No ring has ever gone grey. The atoms sit in strong bonds and cannot move. Thermodynamics names the destination. Kinetics sets the travel time.

Heat release helps, but it is not the whole rule. Ice melts in a warm room while soaking heat up. A cold pack does the same. So a second force is at work, and that force is how spread out the matter and the energy end up.

Entropy, written S, measures that spread. A state with many ways to arrange itself has high entropy. Each full arrangement is one microstate. Ludwig Boltzmann turned that counting into a formula, S = k ln W. The log matters here. Multiply the number of ways by ten and S rises by only k ln 10.

The second law of thermodynamics gives the real test. A change is spontaneous when the total entropy of the universe goes up. Two ledgers are open at once, the system and the surroundings. Either one may show a loss. Only the sum has to grow.

The surroundings are enormous, so their temperature barely moves when they take in heat. That makes their entropy change easy to write as −ΔH ÷ T. Read the minus sign with care. Heat that leaves the system lands in the surroundings, so an exothermic change raises their entropy. And look at the T on the bottom. The same joule of heat buys more entropy in a cold room than in a hot one.

The third law of thermodynamics sets the zero point. A perfect crystal of a pure substance at 0 K has an entropy of exactly zero. Each particle sits in one fixed spot, so W = 1 and S = k ln 1 = 0. This is why tables can list a real, absolute standard molar entropy S° for every substance. Every listed value is positive, even for an element.

So ΔS° for a reaction is products minus reactants, each term multiplied by its coefficient. Elements do not drop out, because their S° is not zero. That is the big difference from an enthalpy table. Often the sign is all you need, so count the moles of gas on each side.

Gibbs free energy folds both ledgers into one number for the system alone. Start from the second law, swap in the heat term, then multiply through by −T. Multiplying by a negative number flips the direction of the sign, which is where the minus in the formula comes from.

Free energy also fixes the size of K. A negative ΔG° makes K larger than 1, so products win. A positive ΔG° makes K smaller than 1. A ΔG° of zero gives K = 1. At 298.15 K, every 5.71 kJ of ΔG° moves K by a factor of ten, and that figure is just RT ln 10.

Keep ΔG° and ΔG apart. The circle means the standard state, with each gas at 1 bar and each solute at 1 mol/L. The push you feel at some other mixture is ΔG = ΔG° + RT ln Q. Once Q climbs to K, the log term cancels ΔG° and ΔG drops to zero. That is equilibrium, seen from the free energy side.

In the two switching cases, one temperature marks the turn. Set ΔG to zero and solve. That value is the crossover temperature, and K = 1 there. The method assumes ΔH° and ΔS° hardly drift with temperature, which holds well enough over a few hundred kelvin.

Equations, units and symbols

Worked examples

The traps people fall into

Chapter 17Electrochemistry

What to know

A redox reaction moves electrons from one species to another. Oxidation is the loss of electrons and reduction is the gain. Neither one happens alone. The reducing agent is the one that gets oxidized. The oxidizing agent is the one that gets reduced. Track the move with oxidation numbers. Up means the atom lost electrons. Down means it gained them.

Big redox equations fight back if you balance them by eye. So split them. A half-reaction shows one side of the trade with the electrons written in. Balance each half alone, then scale them so the electrons cancel.

A galvanic cell keeps the two halves apart so the electrons have to travel through a wire. Each beaker plus its electrode is a half-cell. The anode is where oxidation happens. The cathode is where reduction happens. Two short phrases lock it in. An ox: anode, oxidation. Red cat: reduction, cathode. Electrons always leave the anode and travel to the cathode.

Without help, charge piles up and the current stops within seconds. A salt bridge fixes that. It passes ions between the beakers, so neither one builds up charge. In cell notation the anode goes on the left, a single bar is a phase boundary, and a double bar is the bridge. A half-cell with no solid of its own needs an inert electrode such as platinum or graphite.

No single half-cell can be measured on its own, because a voltmeter needs two leads. So chemists picked one as the zero mark. The standard hydrogen electrode is platinum in 1 M H⁺ with H₂ at 1 bar and 25 °C, defined as exactly 0.000 V. Pair any half-cell with it and the reading is that half-cell's standard reduction potential, E°. Every table value is written as a reduction.

High on the table means a strong oxidizing agent. Low on the table means a strong reducing agent. Any species high on the table will oxidize anything lower down. To get the cell potential, take the cathode value minus the anode value, both straight from the table. Do not flip a sign first. The subtraction already handles that.

The Nernst equation corrects the potential for the concentrations you really have. Read its minus sign. Pile up products and Q rises, so the potential drops. Pile up reactants and the potential climbs. That is a battery's whole life story in one line. When Q finally reaches K, the log term cancels E° and the cell reads zero. A dead battery is a cell that reached equilibrium.

A concentration cell is the strange case. Both half-cells use the same couple at different concentrations, so E°_cell is exactly zero. All of its voltage comes from the Nernst term. The dilute half-cell is always the anode, and the cell dies when the two concentrations meet.

Electrolysis runs a cell backward on purpose, using an outside supply to force a reaction with a negative E°_cell. The job names do not change, so oxidation is still at the anode. What flips is the sign on the terminals. In water the solvent often reacts instead of the ion you expected. Real cells also need extra voltage above the calculated value, and that extra is the overpotential.

Faraday's law of electrolysis treats electrons as a reagent you can measure out with an ammeter and a clock. Current times time gives charge. Divide by F to get moles of electrons. Divide by n to get moles of product.

Corrosion is a galvanic cell you did not build. One patch of a damp nail acts as the anode and iron dissolves. Another patch acts as the cathode, where oxygen from the air is reduced. Those two half-cells are worth 0.84 V, so rusting is spontaneous. You can block the water, pick a metal that makes a tight oxide skin, or bolt on a sacrificial anode of zinc or magnesium.

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The traps people fall into

Chapter 18Representative Metals, Metalloids and Nonmetals

What to know

The main group elements fill groups 1, 2 and 13 through 18. They are also called the representative elements. What ties a group together is its outer shell, and that electron count sets the charges and the bond count. Two trends explain nearly all of this chapter. One is size. The other is how tightly the nucleus grips the outer electrons, measured as effective nuclear charge, Z_eff.

Walk across a period and each step adds one proton and one outer electron. The new electron joins a shell that is already there, so it screens badly. Z_eff climbs, atoms shrink, and ionization energy and electronegativity both rise. So the left side hands electrons out and the right side takes them in. That shift is a loss of metallic character.

Go down a group and each step adds a whole new shell. The outer electron sits farther out with more core electrons in the way, so the grip loosens. Metallic character grows down every main group. Group 14 shows it best, running from nonmetal carbon through metalloid silicon down to metallic tin and lead.

You can place an element by how its oxide treats water. A metal oxide is basic and makes a base. A nonmetal oxide is acidic and makes an acid. Between them sits the amphoteric oxide, which reacts with acid and with base. Aluminum oxide is the textbook case, and that one fact puts aluminum right on the metal border.

Boron is the only member of group 13 that is not a metal. It has three valence electrons, one short of a filled set of four bonds. So boron compounds hunt for electron pairs and act as Lewis acids. Diborane solves its shortage with bridging hydrogens in three-center two-electron bonds. Boric acid does not hand over its own proton. It takes a hydroxide from water instead, which leaves an H⁺ behind.

Aluminum is the most plentiful metal in the crust and is never found free. Winning it takes electricity, in the Hall–Héroult process, with alumina dissolved in molten cryolite near 960 °C. The metal then protects itself with a thin tight film of Al₂O₃. Aluminum is amphoteric too, dissolving in strong acid and in strong base and giving hydrogen both times.

Carbon forms more allotropes than any other element. In diamond every carbon bonds to four others at 109.5°, so the whole crystal is one giant molecule that cannot slide and holds no free electron. In graphite each carbon bonds to three others in a flat sheet, and the fourth electron roams above and below. So graphite conducts along its sheets and slides apart in a pencil. Silicon sits below carbon, yet CO₂ is a gas and SiO₂ is rock. Carbon is small enough for strong double bonds. Silicon is not, so it makes four single bonds to oxygen and the solid never ends.

Nitrogen is 78% of the air and almost nothing reacts with it. The N≡N bond is worth 941 kJ/mol and only 110 pm long. Breaking it is the whole problem of nitrogen fixation. The Haber process solves it near 450 °C and 200 atm over iron, which is a deal struck between yield and speed. The Ostwald process then walks ammonia up to nitric acid through NO and NO₂. Nitric acid attacks metals as an oxidizer, not just as an acid, and the product depends on how concentrated it is.

Phosphorus comes in three solids. White phosphorus is built from strained P₄ tetrahedra and catches fire in air near 34 °C. Red phosphorus is a chain polymer safe enough for match strikers, and black phosphorus is layered like graphite. The acids hold the most tested idea in the chapter. Count the O–H groups, not the hydrogens. A hydrogen bonded straight to phosphorus never leaves in water.

Oxygen reacts far more readily than nitrogen, because its double bond is only 498 kJ/mol. Its allotrope ozone is bent, costs energy to make, shields the ground from above and irritates lungs at ground level. Oxygen is almost always −2, but a peroxide holds O₂^2- at −1 each and a superoxide holds O₂^- at −½ each. Adding electrons fills antibonding levels, so the bond order drops and the O–O distance grows.

Sulfur is too big for strong double bonds, so instead of S₂ it builds eight-atom crown rings. Heat them and the rings snap open into chains, which is why molten sulfur thickens instead of thinning. Sulfuric acid comes from the contact process: burn sulfur, oxidize SO₂ over a vanadium oxide catalyst, absorb SO₃ into strong acid, then add water. The third step avoids the acid mist that water alone would throw.

The halogens each have seven outer electrons and each needs one more, so each is a hungry oxidizer. Their appetite falls from fluorine at +2.87 V down to iodine at +0.54 V, and that order predicts every displacement reaction. Three of the four hydrogen halides are strong acids. Hydrofluoric acid is the odd one out, because the H–F bond is worth 569 kJ/mol. Weak does not mean safe, since HF is also the only common acid that eats glass. For the chlorine oxyacids, each extra oxygen makes the acid stronger.

The noble gases have filled outer shells and the highest ionization energies in every period. Still, the heavier ones react. Xenon needs only 1170 kJ/mol to lose an electron, which is about what an oxygen molecule needs. Fluorine is the partner, and the amount you use sets the product. XeF₂ is linear and XeF₄ is square planar, both shaped by extra lone pairs.

Equations, units and symbols

Worked examples

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