Chemistry curriculum

States of matter differ in how far apart their particles are and how freely they move. In a solid the particles are packed and vibrate in place; in a liquid they are close but slide past one another; in a gas they are far apart and move freely. Plasma is a gas so hot that electrons are stripped from the atoms. Hardness has nothing to do with the definition.

An element has one kind of atom, and a compound has elements bonded in a fixed ratio. A mixture keeps its parts' identities and can vary in makeup: uniform throughout in a solution, visibly uneven in a heterogeneous mixture. Separation methods exploit a physical difference, such as filtration for particle size and distillation for boiling point.

A chemical change makes new substances with new identities, such as iron rusting or wood burning. A physical change alters form or state but not identity, such as ice melting or sugar dissolving. How dramatic a change looks is not the test; ask whether the substances present at the end are different ones.

An extensive property depends on how much of a sample you have, such as mass or volume. An intensive property does not, such as density, melting point or color. Because intensive properties are the same for any amount, they are the ones that identify a substance.

Chemistry uses SI units with prefixes, such as grams, liters and moles. Kelvin starts at absolute zero, so a temperature in kelvins is the Celsius value plus 273.15. Gas laws and many formulas need kelvins, because they depend on temperature in proportion to absolute zero, not to the freezing point of water.

Density is mass divided by volume, so it works as a conversion factor in either direction: multiply a volume by density to get a mass, or divide a mass by density to get a volume. For an irregular solid, measure its volume by the rise in water level when it is submerged.

Significant figures show how precisely a number is known. In multiplication and division, the answer keeps as many significant figures as the least precise input. In addition and subtraction, it keeps the decimal places of the least precise input instead. Round only at the end of a calculation.

Treat each conversion as a fraction equal to one and multiply them so the unwanted units cancel. If the units left at the end are the ones the question asks for, the setup is right; if not, a factor is upside down. That check catches errors before any arithmetic is done.

Mass is conserved in a chemical reaction: the products weigh what the reactants weighed. A compound always contains its elements in the same mass ratio, and when two elements form more than one compound, the ratios come in small whole numbers. Those regularities were the first evidence that matter is made of atoms.

Dalton proposed that matter is made of atoms, that atoms of one element are identical, that compounds combine atoms in whole-number ratios, and that reactions rearrange atoms without creating or destroying them. Isotopes later showed atoms of one element can differ in mass, and nuclear reactions showed atoms can change.

Experiments with cathode rays showed they were streams of negatively charged particles much lighter than any atom, and measured their charge-to-mass ratio. Millikan's oil-drop experiment then measured the charge itself, which fixed the electron's mass.

When alpha particles were fired at thin gold foil, most passed straight through but a few bounced back at large angles. Only a tiny, dense, positive nucleus could explain that, so the atom must be mostly empty space with its mass concentrated at the center.

A proton carries one positive charge and a neutron none, and the two have nearly equal mass. Both sit in the nucleus. An electron carries one negative charge, has about 1/1,836 of a proton's mass, and occupies the space around the nucleus.

The atomic number Z counts protons and decides the element. The mass number A counts protons plus neutrons. In a nuclide symbol, A is written top left and Z bottom left, so the neutron count is A minus Z. A neutral atom has as many electrons as protons.

Isotopes are atoms of the same element with different numbers of neutrons. They have the same number of electrons, so their chemistry is nearly identical, but they differ in mass and can differ in nuclear stability: some are radioactive and some are not.

The atomic mass on the periodic table is an average of an element's isotopes, weighted by how abundant each one is. That is why it is rarely a whole number and why no single atom of chlorine has a mass equal to the listed value.

The periodic table arranges elements by atomic number. Rows are periods and columns are groups, and elements in the same group have the same number of outer electrons, so they behave alike. The table also divides into blocks named for the type of orbital being filled.

Metals sit on the left and middle of the table and tend to be shiny, malleable conductors that lose electrons. Nonmetals sit on the upper right and tend to be poor conductors that gain or share electrons. Metalloids along the staircase line between them have mixed properties.

The alkali metals in group 1 are soft and react vigorously with water. The alkaline earth metals in group 2 are less reactive. The halogens in group 17 are reactive nonmetals that form salts with metals. The noble gases in group 18 have full outer shells and barely react at all.

Main-group atoms gain or lose electrons to reach a noble gas's electron count. Group 1 metals form +1 ions and group 2 form +2. Group 17 nonmetals gain one electron to form −1 ions, and group 16 gain two to form −2 ions. Metals lose electrons; nonmetals gain them.

Some ions are groups of atoms bonded together that carry an overall charge, such as nitrate, sulfate, carbonate, phosphate, hydroxide and ammonium. For related oxygen-containing anions, the -ate form has one more oxygen than the -ite form, as in sulfate and sulfite.

In an ionic compound the charges must balance, and that sets the subscripts: one calcium ion with a 2+ charge pairs with two chloride ions, giving CaCl₂. Name the cation first, then the anion, with a single-element anion ending in -ide.

Many transition metals form more than one common ion, so the name includes the charge as a Roman numeral. Iron(II) chloride contains Fe²⁺ and iron(III) chloride contains Fe³⁺. Work out the metal's charge from the anions it is balancing.

Compounds of two nonmetals use Greek prefixes for the atom counts, as in carbon dioxide and dinitrogen tetroxide. Binary acids take the form hydro-…-ic acid, as in hydrochloric acid. Oxyacids follow their anion: an -ate anion gives an -ic acid and an -ite anion gives an -ous acid.

A mole is a counting unit, like a dozen, for 6.022 × 10^23 particles, a number now fixed exactly by definition. Chemists count in moles because reactions combine atoms and molecules by number, while balances measure mass. The mole is the bridge between the two.

Molar mass is the mass of one mole of a substance in grams. Add the atomic masses of every atom in the formula, multiplying by each subscript, and multiply everything inside parentheses by the subscript outside them.

Mass, moles and number of particles are linked by two factors: molar mass converts between grams and moles, and Avogadro's number converts between moles and particles. Always go through moles; there is no direct step from grams to particles.

Percent composition is each element's share of a compound's molar mass. The same arithmetic finds the water in a hydrate: the mass lost on heating, divided by the original mass, gives the fraction of water.

To find an empirical formula, treat percentages as grams in a 100 g sample, convert each to moles, and divide by the smallest number of moles. If a ratio ends near .5, multiply everything by 2 to reach whole numbers; do not round 1.5 to 2.

The molecular formula is a whole-number multiple of the empirical formula. Divide the measured molar mass by the empirical formula's mass to get that multiple, then multiply every subscript by it.

When a compound of carbon and hydrogen burns completely, all its carbon ends up in carbon dioxide and all its hydrogen in water. Weigh those products to find the moles of carbon and hydrogen; any oxygen in the compound is found by subtracting their masses from the sample's mass.

Molarity is moles of solute per liter of solution, the finished mixture, not per liter of solvent added. A solution marked 1 M has one mole of solute in each liter of total volume. Multiply molarity by volume in liters to get moles.

Diluting a solution adds solvent but not solute, so the moles of solute stay the same. That gives M1V1 = M2V2: the concentration falls in proportion as the volume rises. Use it only for dilution, not when a reaction changes the solute.

Mass percent is the mass of solute divided by the mass of solution, times 100. For very dilute solutions, parts per million and parts per billion express the same ratio scaled up, which suits trace contaminants in water.

Molality is moles of solute per kilogram of solvent, and mole fraction is one component's moles divided by the total moles. Both are based on mass or amount rather than volume, so unlike molarity they do not change when the solution expands with temperature.

To prepare a solution of exact molarity, dissolve the measured solute in part of the solvent first, then add solvent until the liquid reaches the mark on a volumetric flask. Adding the full volume of solvent first would give the wrong total volume.

A chemical equation lists reactants on the left and products on the right, with state symbols such as (s), (l), (g) and (aq). Conditions such as heat or a catalyst are written over the arrow.

Balance an equation by changing coefficients, the numbers in front of formulas, until each element has the same count on both sides. Never change a subscript: that changes the substance itself, so the equation would describe a different reaction.

Solubility rules predict which ionic compounds dissolve in water. Compounds of group 1 ions, ammonium and nitrate are generally soluble, and most chlorides are too, with silver, lead and mercury(I) chlorides as the classic exceptions. The rules tell you whether mixing two solutions will form a solid.

When two solutions of soluble salts are mixed, their ions can swap partners. If one new combination is insoluble, it comes out of solution as a solid precipitate. Predict it by pairing each cation with the other anion and checking the solubility rules.

Write soluble strong electrolytes as separate ions, then cancel the spectator ions that appear unchanged on both sides. What remains, the net ionic equation, shows the actual chemical change, such as two ions combining into a precipitate.

An acid reacting with a base produces a salt and, usually, water. With a strong acid and a strong base, the net ionic equation is simply hydrogen ion plus hydroxide ion forming water. Weak acids and bases are written as whole molecules because they are mostly not ionized.

Oxidation numbers track electrons. An element on its own is 0, a simple ion has its charge, oxygen is usually −2 and hydrogen +1, and the numbers in a neutral compound add to zero. The common exceptions are peroxides, where oxygen is −1, and metal hydrides, where hydrogen is −1.

Oxidation is loss of electrons and reduction is gain, and the two always happen together. The species that is oxidized is the reducing agent, because it gives electrons away; the species that is reduced is the oxidizing agent. A rise in oxidation number marks oxidation.

The coefficients of a balanced equation give mole ratios, never mass ratios. Every stoichiometry problem crosses from one substance to another through that mole ratio, so convert to moles first.

To go from grams of one substance to grams of another, convert grams to moles with the first substance's molar mass, apply the mole ratio, then convert moles to grams with the second substance's molar mass. A wrong molar mass at either end silently spoils the result.

The limiting reactant is the one that runs out first, and it alone sets how much product forms. Work out how much product each reactant could make; the smaller amount wins. The other reactant is in excess, and the unused amount is what remains after the reaction.

Theoretical yield is the product the limiting reactant could make in principle. Percent yield is the actual yield divided by the theoretical yield, times 100. Real yields fall short because of side reactions, incomplete reactions and product lost during handling.

For a reaction in solution, multiply molarity by volume in liters to get moles, then use the mole ratio as in any stoichiometry problem. Convert milliliters to liters first; skipping that step is the usual thousandfold error.

In a titration, a solution of known concentration is added until it has exactly reacted with the unknown. At that equivalence point, the moles added, from molarity times volume, combine with the mole ratio to give the moles, and so the concentration, of the unknown.

Energy is the capacity to do work or transfer heat, and it is measured in joules. Heat is energy moving because of a temperature difference; temperature measures how fast the particles move. A large body of water at a low temperature can hold more heat than a cup of boiling water.

The system is the part under study, such as a reaction mixture, and the surroundings are everything else. Signs are read from the system's side: heat flowing into the system is positive. An open system exchanges matter and energy, a closed one only energy, and an isolated one neither.

Specific heat is the energy needed to warm one gram of a substance by one degree, used in q = mcΔT. Water's specific heat is unusually high, so water warms and cools slowly, which moderates coastal climates and makes a pot of water slow to heat.

Calorimetry measures heat by the temperature change it causes in a known mass. A coffee-cup calorimeter works at constant pressure and gives ΔH directly; a sealed bomb calorimeter works at constant volume. Account for the heat absorbed by the calorimeter itself, not just its water.

Enthalpy change, ΔH, is the heat a reaction exchanges at constant pressure. It is written for the balanced equation as written, so doubling the equation doubles ΔH, and reversing it flips the sign.

An exothermic reaction releases heat to the surroundings and has a negative ΔH; an endothermic one absorbs heat and has a positive ΔH. On an energy diagram, the products sit lower than the reactants for an exothermic reaction and higher for an endothermic one.

Enthalpy is a state function, so the total ΔH for a reaction is the same whatever steps it takes. Add known reactions to reach the target equation, reversing a step to flip its sign and multiplying a step to scale its ΔH.

The standard enthalpy of formation is the ΔH for making one mole of a compound from its elements in their standard states, and for those elements it is defined as zero. A reaction's ΔH equals the sum for the products minus the sum for the reactants, each multiplied by its coefficient.

For light, the speed c equals wavelength times frequency, so a shorter wavelength means a higher frequency. Each photon's energy is E = hf, Planck's constant times the frequency f. Short-wavelength light such as ultraviolet therefore carries more energy per photon than red light.

Light ejects electrons from a metal only if its frequency is above a threshold; below it, even very bright light ejects none. Each photon delivers a fixed packet of energy, so it is the frequency, not the brightness, that decides whether an electron escapes. That showed light comes in quanta.

Heated hydrogen gives off light only at certain wavelengths, a line spectrum. Bohr explained it with electron orbits of fixed energy: a photon is emitted when an electron drops between levels, with energy equal to the gap. The model works for hydrogen but fails for atoms with more electrons.

Electrons behave as waves as well as particles, with a wavelength set by their momentum. Because their position and momentum cannot both be known exactly, fixed orbits give way to orbitals: regions where an electron is likely to be found.

Four quantum numbers describe an electron. The principal number n gives the shell and energy level; l, from 0 to n−1, gives the subshell shape; ml, from −l to +l, gives the orbital's orientation; and ms, +1/2 or −1/2, gives the spin.

An s orbital is spherical, a p orbital has two lobes on opposite sides of the nucleus, and d orbitals mostly have four lobes. In atoms with more than one electron, energy depends on both n and l, so within a shell s fills before p and p before d.

The Pauli principle allows at most two electrons in an orbital, and they must have opposite spins. Hund's rule says electrons fill a set of equal-energy orbitals singly, with parallel spins, before any of them pair up.

Electrons fill the lowest available energy levels first, and the periodic table shows the order: reading across each row gives the next subshell to fill. Write the full configuration, or shorten it by starting from the previous noble gas in brackets.

The periodic table divides into s, p, d and f blocks according to the subshell being filled. For main-group elements, the group number tells you the number of valence electrons, the outer electrons that take part in bonding.

A few elements break the simple filling order. Chromium and copper move one electron from the 4s orbital into the 3d set, because a half-filled or completely filled d subshell is especially stable.

When atoms form positive ions, they lose electrons from the shell with the highest n first. For transition metals that means the 4s electrons go before the 3d ones, even though 4s filled first.

Inner electrons shield outer electrons from part of the nucleus's pull. The effective nuclear charge is the net pull an outer electron feels. It rises across a period, as protons are added to the same shell, and it drives nearly every periodic trend.

Atoms get larger down a group, as shells are added, and smaller across a period, as the effective nuclear charge pulls harder. A positive ion is smaller than its parent atom because it has lost electrons, and a negative ion is larger because added electrons repel each other.

Ionization energy, the energy needed to remove an electron, generally rises across a period and falls down a group. It jumps sharply once an inner shell must be broken. Small dips occur between groups 2 and 13 and between groups 15 and 16, where the electron removed is easier to take.

Electron affinity is the energy change when an isolated atom gains an electron. Electronegativity is how strongly an atom attracts shared electrons in a bond. Both generally rise toward the upper right of the table, and fluorine is the most electronegative element.

An ionic bond forms when a metal that loses electrons easily transfers them to a nonmetal that gains them readily. The resulting ions attract in every direction, building a crystal lattice of alternating charges rather than separate molecules. That is why an ionic formula gives a ratio, not a molecule.

Lattice energy is the energy released when gaseous ions come together to form an ionic solid. It follows Coulomb's law: it grows strongly with the size of the ion charges and grows as the ions get smaller and closer. Charge usually matters more than size, so a 2+ and 2− pair outranks a 1+ and 1− pair.

A covalent bond forms when two atoms share a pair of electrons. As the atoms approach, energy falls to a minimum and then rises steeply if they are pushed closer; the distance at that minimum is the bond length, and the depth of the dip is the bond's strength.

When two atoms share electrons unequally, the more electronegative one carries a partial negative charge, making the bond polar. Bonds range continuously from nonpolar, with equal sharing, through polar, to ionic, where an electron is effectively transferred. The electronegativity difference sets the position.

Between the same two atoms, a triple bond is shorter and stronger than a double bond, which is shorter and stronger than a single bond. Down a group, atoms get larger, so their bonds get longer and generally weaker.

In a metal, outer electrons are not tied to any one atom; they form a shared sea around a lattice of positive ions. Those mobile electrons explain why metals conduct electricity and heat, why they can be hammered into shape without shattering, and why they shine.

Main-group atoms tend to bond until each has eight electrons in its outer shell, matching a noble gas. Hydrogen needs only two. The rule predicts many structures well, but it is a guide, not a law: some molecules have fewer than eight around an atom and some have more.

To draw a Lewis structure, count all valence electrons, adjusting for any ion charge. Connect the atoms with single bonds, fill the outer atoms' octets, put leftover electrons on the central atom, and if it still lacks an octet, turn lone pairs into double or triple bonds.

An atom's formal charge is its valence electrons minus its lone-pair electrons minus half its bonding electrons. When several structures are possible, prefer the one with formal charges closest to zero, and with any negative charge on the more electronegative atom.

When more than one valid Lewis structure can be drawn by moving electrons, the real molecule is a blend of them, not a switch between them. In the nitrate ion, each nitrogen-oxygen bond is identical and intermediate between a single and a double bond.

Atoms in period 3 and below can hold more than eight electrons around them, as phosphorus does in PCl₅ and sulfur in SF₆. Atoms in period 2, such as carbon, nitrogen and oxygen, can never exceed eight.

Some atoms are stable with fewer than eight electrons: boron in BF₃ has six, and beryllium compounds can have four. A molecule with an odd number of electrons, such as nitrogen monoxide, must leave one unpaired; such species are called radicals.

VSEPR theory says electron domains around a central atom spread out as far apart as possible. A domain is a lone pair or a bond, and a double or triple bond counts as a single domain. Count the domains first; they set the basic shape.

Electron geometry includes every domain, lone pairs as well as bonds. Molecular geometry describes only where the atoms are. Water has four domains in a tetrahedral arrangement, but with two lone pairs its molecular shape is bent.

Two domains give a linear shape at 180°, three give trigonal planar at 120°, four give tetrahedral at 109.5°, five give trigonal bipyramidal, and six give octahedral at 90°. These ideal angles apply when every domain is a bond to the same kind of atom.

Lone pairs take up more room than bonding pairs, so they squeeze the remaining bond angles below the ideal. In ammonia, with one lone pair, the angle drops below 109.5°, and in water, with two lone pairs, it drops further. Multiple bonds also push neighboring bonds closer together.

A polar bond has a dipole pointing toward its more electronegative atom, with a size that grows with the electronegativity difference. A molecule's overall dipole is the vector sum of its bond dipoles, so direction matters as much as size.

A molecule can have polar bonds and still be nonpolar if its symmetry makes the bond dipoles cancel. Carbon dioxide is linear, so its two C=O dipoles point opposite ways and cancel. Water is bent, so its dipoles add and the molecule is polar.

Valence bond theory describes a covalent bond as the overlap of two atomic orbitals, each holding one electron, so the shared pair sits between the nuclei. Greater overlap generally means a stronger bond.

Atoms mix their atomic orbitals into hybrid orbitals that match the observed shape. The number of electron domains tells you the hybridization: two domains give sp, three give sp², four give sp³, and five and six use d orbitals as well.

A sigma bond forms from head-on overlap along the line between the nuclei; a pi bond forms from side-by-side overlap above and below it. Every single bond is one sigma bond, a double bond is one sigma and one pi, and a triple bond is one sigma and two pi.

A pi bond would break if the two ends twisted, so atoms cannot rotate freely around a double bond. That locks groups on the same side or on opposite sides, giving cis and trans isomers with different properties.

Molecular orbital theory combines atomic orbitals into bonding orbitals, which lower the energy, and antibonding orbitals, which raise it. Bond order is half the difference between bonding and antibonding electrons; a bond order of zero means the molecule does not form.

Molecular orbital theory predicts that O₂ has two unpaired electrons, which makes it paramagnetic: liquid oxygen is drawn into a magnetic field. A simple Lewis structure pairs every electron and so cannot explain that behavior.

Gas pressure is force per unit area from molecules striking a surface. It is measured in atmospheres, torr, millimeters of mercury, bars or pascals; one atmosphere equals 760 torr. A barometer reads atmospheric pressure from the height of a mercury column it can support.

At fixed temperature and amount of gas, pressure and volume are inversely proportional: halve the volume and the pressure doubles. A graph of pressure against volume is therefore a curve, a hyperbola, not a straight line.

At fixed pressure, a gas's volume is proportional to its absolute temperature; at fixed volume, its pressure is. These proportions hold only in kelvins, because doubling a Celsius temperature does not double the absolute temperature.

At the same temperature and pressure, equal volumes of any gases contain equal numbers of particles. So volume is proportional to moles, and gas volumes in a reaction combine in the same ratios as the coefficients.

The ideal gas law, PV = nRT, combines the simple gas laws. R must match your units: about 8.314 J per mole per kelvin for SI work, or about 0.0821 liter-atmospheres per mole per kelvin when pressure is in atmospheres and volume in liters. Temperature is always in kelvins.

At a stated temperature and pressure, one mole of any ideal gas occupies the same volume, so check which standard conditions a problem uses. Rearranging PV = nRT gives a gas's density from its molar mass, or its molar mass from a measured density.

In a gas mixture, each gas exerts its own partial pressure, and the partial pressures add to the total. Each one equals the gas's mole fraction times the total pressure. When a gas is collected over water, subtract water's vapor pressure to get the gas's own pressure.

When gases react at the same temperature and pressure, their volumes are in the same ratio as their moles, so coefficients can be used directly as volume ratios. Otherwise, convert each gas volume to moles with PV = nRT before applying the mole ratio.

Kinetic-molecular theory treats a gas as tiny particles in constant random motion that collide elastically and neither attract nor repel one another, with their own volume negligible. Real gases break these assumptions when the particles are crowded or slow.

The absolute temperature of a gas is proportional to the average kinetic energy of its particles. At the same temperature, every gas has the same average kinetic energy, whatever its molar mass.

Molecules in a gas move at a spread of speeds, described by the Maxwell–Boltzmann distribution. Heating a gas shifts the peak to higher speeds and flattens and widens the curve, so more molecules move fast.

At the same temperature, lighter molecules move faster, because equal average kinetic energy means a smaller mass needs a higher speed. The root-mean-square speed varies inversely with the square root of molar mass.

Graham's law says gases effuse through a tiny hole at rates inversely proportional to the square root of their molar masses. A gas four times lighter escapes twice as fast. The small difference between uranium isotopes in a gaseous compound was once exploited this way to separate them.

Real gases deviate from ideal behavior at high pressure, when particle volume matters, and at low temperature, when attractions matter. The van der Waals equation adds a term a for attractions and a term b for particle volume.

Dispersion forces come from momentary uneven electron distributions that induce dipoles in neighbors. Every substance has them. They grow with molecular size and contact area, so larger molecules, and long chains rather than compact ones, attract each other more strongly.

Polar molecules line up so the positive end of one attracts the negative end of another, which is a dipole-dipole force. An ion attracts the oppositely charged end of polar molecules, an ion-dipole force that lets water surround and dissolve the ions in a salt.

A hydrogen bond forms when hydrogen bonded to nitrogen, oxygen or fluorine is attracted to a lone pair on another such atom. It is an especially strong intermolecular attraction, not a covalent bond, and it gives water its unusually high boiling point.

Stronger intermolecular forces mean a higher boiling point. Compare substances by their dominant force, then by size. Water, ammonia and hydrogen fluoride boil far higher than their size would predict, because of hydrogen bonding.

Viscosity, a liquid's resistance to flow, and surface tension, the energy needed to enlarge its surface, both come from intermolecular attractions. Both decrease as temperature rises, because the molecules move more freely.

Above a liquid in a closed container, molecules escape and return until the rates balance; the pressure of that vapor is the vapor pressure. It rises with temperature, and a liquid boils when its vapor pressure equals the pressure above it. That is why water boils at a lower temperature at high altitude.

A heating curve shows temperature against heat added. On sloped segments, heat raises the temperature of one phase according to its specific heat. On flat plateaus, the temperature stays constant while heat of fusion or vaporization changes the phase.

A phase diagram maps which phase is stable at each pressure and temperature. Lines mark where two phases coexist; at the triple point all three coexist, and beyond the critical point liquid and gas become indistinguishable. Water's solid-liquid line tilts backward, so pressure can melt ice.

Ionic solids are hard and brittle with high melting points; metallic solids conduct and bend; covalent network solids such as diamond are very hard with very high melting points; molecular solids are soft with low melting points. Amorphous solids, such as glass, lack an ordered structure.

A crystal is built from a repeating unit cell. A simple cubic cell holds one atom in total, a body-centered cubic cell two, and a face-centered cubic cell four. Face-centered cubic packs atoms most efficiently of the three, with each atom touching 12 neighbors.

Dissolving breaks attractions among solute particles and among solvent molecules and forms new attractions between solute and solvent. Whether the overall process releases or absorbs heat depends on the balance of those three steps.

Substances with similar intermolecular forces mix: polar and hydrogen-bonding solvents dissolve polar and ionic solutes, and nonpolar solvents dissolve nonpolar solutes. That is why salt dissolves in water and oil does not.

A strong electrolyte breaks completely into ions in water and conducts well, as table salt does. A weak electrolyte forms only a few ions and conducts poorly, as acetic acid does. A nonelectrolyte, such as sugar, dissolves as molecules and does not conduct.

Most solid solutes become more soluble as temperature rises, though a few do not. Gases become less soluble as water warms, which is why warm water holds less dissolved oxygen.

Henry's law says the amount of gas dissolved in a liquid is proportional to that gas's partial pressure above it. A sealed soda holds extra carbon dioxide under pressure, which fizzes out when you open it and the pressure drops.

Raoult's law says the vapor pressure of a solution equals the pure solvent's vapor pressure times the solvent's mole fraction. A nonvolatile solute takes up part of the surface and lowers how much solvent escapes.

A dissolved solute lowers the freezing point and raises the boiling point in proportion to its molality times the number of particles it forms, the van 't Hoff factor. One mole of sodium chloride gives about two moles of particles, so it shifts these points about twice as much as one mole of sugar.

Osmosis is the flow of solvent through a membrane that blocks the solute, from the more dilute side toward the more concentrated side. Osmotic pressure is the pressure needed to stop that flow, and it rises with the solute's concentration.

A reaction rate is the change in concentration of a reactant or product per unit time. Dividing by each substance's coefficient gives one rate for the whole reaction, since a reactant with coefficient 2 is used up twice as fast as one with coefficient 1.

Reactions speed up with higher concentration, higher temperature, more surface area for solids, and a catalyst. The nature of the reactants matters too: reactions that only rearrange ions in solution are often fast, while those breaking strong bonds are slow.

A rate law, rate = k[A]^m[B]^n, gives the rate in terms of concentrations. The exponents, the reaction orders, must be found by experiment; they are not the coefficients of the balanced equation.

To find a reaction's orders, compare experiments in which only one concentration changes. If doubling a concentration doubles the rate, that reactant is first order; if it quadruples the rate, it is second order; if the rate does not change, it is zero order.

Integrated rate laws give concentration against time. For a zero-order reaction a plot of concentration against time is a straight line; for first order, the natural log of concentration is linear; for second order, one over the concentration is linear.

A half-life is the time for a reactant's concentration to fall to half. For a first-order reaction it is constant, whatever the starting amount, which is the signature of first order. For other orders the half-life depends on the concentration.

For particles to react, they must collide with enough energy and in the right orientation. Only a small fraction of collisions meet both conditions, which is why most collisions do not lead to a reaction.

Activation energy is the barrier reactants must climb to reach the transition state. The Arrhenius equation shows the rate constant rising exponentially with temperature, so a modest temperature increase can speed a reaction a lot.

Most reactions happen through a series of elementary steps, and an intermediate formed in one step is used up in a later one. The slowest step sets the overall rate, so the observed rate law reflects that step rather than the overall equation.

A catalyst speeds a reaction by providing a path with a lower activation energy, and it is not used up. Homogeneous catalysts work in the same phase as the reactants, heterogeneous ones offer a surface, and enzymes are biological catalysts. A catalyst does not change the equilibrium position.

At equilibrium, the forward and reverse reactions continue at equal rates, so concentrations stop changing even though molecules keep reacting. Equilibrium means equal rates, not equal concentrations.

The equilibrium constant K is the product concentrations over the reactant concentrations, each raised to its coefficient. A large K means products are favored at equilibrium, and a small K means reactants are favored.

Kc uses molar concentrations and Kp uses partial pressures. They are related by Kp = Kc(RT)^Δn, where Δn is the moles of gas in the products minus the moles of gas in the reactants. When Δn is zero, the two are equal.

The reaction quotient Q has the same form as K but uses current concentrations. If Q is less than K, the reaction moves forward to make more products; if Q is greater than K, it moves backward; if they are equal, it is at equilibrium.

Pure solids and pure liquids are left out of an equilibrium expression. Their concentration is fixed by their density, not by how much is present, so including them would add only a constant.

Le Chatelier's principle says a system at equilibrium shifts to partly undo a change. Add a reactant and it shifts toward products. Compress a gas mixture and it shifts toward the side with fewer gas moles; if both sides have equal gas moles, pressure changes do nothing.

Temperature is the only change that alters the value of K. For an exothermic reaction, treat heat as a product: raising the temperature shifts it toward reactants and lowers K. For an endothermic reaction, heating raises K.

An ICE table tracks initial concentrations, the change written in terms of x, and equilibrium concentrations. When K is small, x is often small enough to ignore beside the starting concentration; check that x is under about 5 percent of it before trusting the shortcut.

Arrhenius defined acids as producing hydrogen ions in water and bases as producing hydroxide ions. Bronsted and Lowry broadened this: an acid donates a proton and a base accepts one. Lewis broadened it again: a base donates an electron pair and an acid accepts it.

When an acid gives up a proton, what remains is its conjugate base; when a base accepts one, it becomes its conjugate acid. Some species, such as water, can do either. A strong acid's conjugate base is too weak to act as a base in water.

Pure water ionizes slightly into hydronium and hydroxide ions. At 25 °C the product of their concentrations, Kw, is 1.0 × 10^-14. Because the product is fixed, raising one concentration lowers the other.

pH is the negative log of the hydronium concentration, so each one-unit drop in pH means ten times more hydronium. At 25 °C, pH plus pOH equals 14, and a neutral solution has a pH of 7. To recover a concentration, raise 10 to the negative pH.

Strong acids, such as hydrochloric, nitric and sulfuric acid, ionize completely in water, and so do strong bases such as sodium hydroxide. For a strong monoprotic acid, the hydronium concentration equals the acid's concentration, so the pH follows directly.

A weak acid ionizes only partly, described by its acid dissociation constant Ka. Find the pH with an equilibrium calculation. Diluting a weak acid increases the percentage that ionizes, even though the pH still rises.

A weak base's strength is described by Kb. For a conjugate acid-base pair, Ka times Kb equals Kw, so the stronger the acid, the weaker its conjugate base.

An acid is stronger when its H–A bond is more polar or weaker, and when the anion left behind is more stable. Among oxyacids, more oxygen atoms and a more electronegative central atom pull electron density away and make the acid stronger.

A salt's solution can be acidic, basic or neutral depending on its parent acid and base. A salt of a strong acid and a weak base is acidic; a salt of a weak acid and a strong base is basic; a salt of a strong acid and a strong base is neutral.

A polyprotic acid loses its protons one at a time, and each step has its own Ka, usually smaller by a large factor than the one before. The first ionization therefore dominates the pH, and later steps can often be ignored.

A buffer is a weak acid together with its conjugate base, or a weak base with its conjugate acid. The weak acid neutralizes added hydroxide and the conjugate base neutralizes added acid, so the pH changes only a little until one component runs out.

The Henderson–Hasselbalch equation gives a buffer's pH: pH = pKa + log of the base concentration over the acid concentration. When the two concentrations are equal, the log term is zero and the pH equals the pKa.

A buffer works best within about one pH unit of its acid's pKa, where both components are present in useful amounts. Its capacity, how much acid or base it can absorb, depends on the actual concentrations, so a dilute buffer with the right ratio still gives out quickly.

When a strong acid is titrated with a strong base, the pH rises slowly, then jumps steeply near the equivalence point, which falls at pH 7 at 25 °C. The products are a neutral salt and water, so nothing pulls the pH away from neutral.

Titrating a weak acid with a strong base gives a buffer region where the pH changes slowly. Halfway to equivalence, the acid and its conjugate base are equal, so the pH equals the pKa. At equivalence the solution holds the conjugate base, so the pH is above 7.

The equivalence point is where the reactants have exactly reacted; the endpoint is where the indicator changes color. Choose an indicator whose color change falls within the steep part of the titration curve, so the two points nearly coincide.

For a slightly soluble salt, the solubility product Ksp is the product of the ion concentrations at equilibrium, each raised to its coefficient. The solid itself is left out of the expression.

Molar solubility is the moles of a salt that dissolve per liter. Let it be s, write each ion's concentration in terms of s, and solve the Ksp expression. For a salt that releases two of one ion, that ion's concentration is 2s, and the term is squared.

Adding a solution that already contains one of a salt's ions lowers how much of the salt dissolves. By Le Chatelier's principle, the extra ion pushes the dissolving equilibrium back toward the solid.

To predict whether a solid forms, calculate the ion product Q from the current concentrations and compare it with Ksp. If Q exceeds Ksp, the solution is oversaturated and a precipitate forms; if Q is smaller, the solid will dissolve.

A salt whose anion is a weak base, such as a carbonate or hydroxide, dissolves more in acid, because the acid removes that anion and pulls the equilibrium toward dissolving. That is how acid erodes limestone and tooth enamel.

A metal ion can bind ligands, molecules or ions with lone pairs, to form a complex ion, a Lewis acid-base reaction described by a formation constant Kf. Forming the complex removes free metal ions, which can dissolve a salt that is otherwise insoluble.

A spontaneous process can happen without continuous outside help. Spontaneous says nothing about speed: diamond turning into graphite is spontaneous, yet it is far too slow to notice.

Entropy measures how many microscopic arrangements are possible for a system's energy and matter. It is more accurate to think of entropy as energy spreading out than as disorder or messiness.

Entropy generally increases when a solid melts or a liquid boils, when a reaction produces more gas molecules than it uses, when temperature rises, and when molecules are larger or more complex.

The second law says the entropy of the universe increases in any spontaneous process. The third law says a perfect crystal at absolute zero has zero entropy, which gives entropy an absolute zero point, unlike enthalpy.

The change in Gibbs free energy, ΔG = ΔH − TΔS, decides spontaneity at constant temperature and pressure. A negative ΔG means the process is spontaneous, a positive one means it is not, and zero means equilibrium.

The signs of ΔH and ΔS decide how spontaneity depends on temperature. If ΔH is negative and ΔS positive, the process is spontaneous at every temperature; if the reverse, at none. When both have the same sign, spontaneity switches at the temperature T = ΔH/ΔS.

The standard free energy change is linked to the equilibrium constant by ΔG° = −RT ln K, so a large K goes with a negative ΔG°. ΔG° refers to standard conditions, while ΔG changes as the reaction proceeds and reaches zero at equilibrium.

To balance a redox reaction, split it into oxidation and reduction half-reactions. Balance atoms other than O and H, then O with water, then H with hydrogen ions, then charge with electrons. In basic solution, add hydroxide to neutralize the hydrogen ions. Scale the halves so electrons cancel.

A galvanic cell turns a spontaneous redox reaction into electric current. Oxidation happens at the anode and reduction at the cathode, and electrons flow through the wire from anode to cathode. A salt bridge lets ions move to keep both sides electrically neutral.

Cell notation writes the anode on the left and the cathode on the right. A single line marks a boundary between phases, and a double line marks the salt bridge.

Standard reduction potentials measure each half-reaction's tendency to gain electrons, relative to the hydrogen electrode set at zero. A cell's standard potential is the cathode's value minus the anode's. Do not multiply a potential by a coefficient: it is an intensive property.

A positive cell potential means the reaction is spontaneous as written. It connects to free energy by ΔG = −nFE, where n is the moles of electrons transferred and F is Faraday's constant, about 96,485 coulombs per mole.

The Nernst equation adjusts a cell's potential for concentrations that are not standard. As the reaction proceeds, the potential falls, reaching zero at equilibrium. A concentration cell, with the same metal on both sides, produces a voltage purely from a concentration difference.

A primary battery is used once, a secondary battery can be recharged, and a fuel cell runs on a continuous fuel supply. Rusting is an electrochemical cell on the metal's surface. Galvanizing coats iron with zinc, and a sacrificial anode of a more reactive metal corrodes in place of the protected metal.

Electrolysis uses electrical energy to drive a reaction that would not happen on its own, as in electroplating. The charge passed, current times time, divided by Faraday's constant gives moles of electrons, which convert to moles and then to mass of metal deposited.

Across a period, elements change from metals with basic oxides to nonmetals with acidic oxides. Down a group, metallic character increases. Those trends predict whether an element's oxide will react with acid or with base.

Alkali metals react with water to form hydroxides and hydrogen gas, more violently going down the group. Alkaline earth metals react less vigorously. Many of these metals and their compounds give characteristic flame colors.

Nonmetal oxides, such as carbon dioxide, sulfur dioxide and nitrogen oxides, dissolve in water to form acids. Each nonmetal has characteristic chemistry, such as carbon's many compounds and nitrogen's several oxidation states.

Halogen reactivity falls down the group, so fluorine is the most reactive. Halogens can combine with each other into interhalogen compounds. Noble gases are very unreactive, but the heavier ones, such as xenon, do form some compounds with fluorine and oxygen.

Transition metals often have several oxidation states, form colored ions, act as catalysts, and can be magnetic. Their partly filled d orbitals are responsible for these properties.

A complex ion has a central metal ion bonded to ligands, molecules or ions that each donate an electron pair. That shared pair forms a coordinate covalent bond. The number of bonds to the metal is its coordination number.

Ligands split a metal's d orbitals into groups of different energy. The complex absorbs light whose energy matches the gap, and you see the complementary color. Strong-field ligands make a larger gap than weak-field ligands, which changes both color and magnetism.

Many biological molecules hold a metal at their core. Hemoglobin's heme groups contain iron that binds oxygen, and chlorophyll contains magnesium. In each case the metal center does the chemical work, and chelating agents bind metals at several points at once.

A functional group is the reactive part of an organic molecule, such as a hydroxyl, carbonyl or carboxyl group. Molecules with the same functional group react in similar ways, whatever the size of their carbon chain.

Alkanes contain only single bonds between carbon atoms, so they are saturated. Structural isomers have the same formula but different connections, and the number of possible isomers grows rapidly as carbon atoms are added.

To name an organic compound, find the longest carbon chain, number it to give substituents the lowest numbers, and list the substituents in alphabetical order with their positions.

Alkenes have a carbon-carbon double bond and alkynes a triple bond, so both are unsaturated. They typically react by addition across the multiple bond. Because a double bond cannot rotate, alkenes can form cis and trans isomers.

Benzene has a ring of six carbon atoms with electrons spread evenly around it, which makes it unusually stable. Aromatic compounds therefore tend to undergo substitution, which keeps the ring intact, rather than addition, which would break it.

Alcohols have an –OH group, so they hydrogen bond with each other and with water, which raises their boiling points and solubility. Ethers have an oxygen between two carbon groups and cannot hydrogen bond with each other, so they boil at lower temperatures.

A carbonyl group is a carbon double bonded to oxygen, which makes it polar. In an aldehyde it sits at the end of a chain, and in a ketone it sits between two carbons. Oxidizing a primary alcohol gives an aldehyde, and a secondary alcohol gives a ketone.

A carboxylic acid has a –COOH group and is a weak acid. Reacting it with an alcohol forms an ester and water. Many esters have fruity smells, and fats and oils are esters of glycerol and fatty acids.

Amines contain nitrogen with a lone pair and act as weak bases. An amide links a carbonyl carbon to nitrogen, the same linkage that joins amino acids in proteins. Addition polymers join monomers without losing atoms, while condensation polymers release a small molecule such as water at each link.

A nuclide symbol shows the mass number at the top left and the atomic number at the bottom left of the element symbol. A nuclear change alters the nucleus and can turn one element into another, while a chemical change only rearranges electrons.

Stable nuclei fall within a band of neutron-to-proton ratios, close to 1 for light elements and rising for heavier ones. A nucleus with too many neutrons tends to undergo beta decay; one with too few tends toward positron emission or electron capture.

Alpha decay emits a helium nucleus; beta decay turns a neutron into a proton and emits an electron; positron emission and electron capture both turn a proton into a neutron. Gamma rays carry off energy without changing the nucleus's identity. Alpha particles are stopped by paper, beta by thin metal, and gamma needs dense shielding.

In a nuclear equation, the mass numbers on both sides add to the same total, and so do the atomic numbers. Use those two sums to identify a missing particle.

Radioactive decay is first order: in each half-life, half of the remaining nuclei decay. Carbon-14 dating compares the carbon-14 left in once-living material with the amount it started with. Each isotope can date only a limited range of ages, set by its half-life.

A nucleus weighs less than its separate protons and neutrons; the missing mass, converted by E = mc², is the binding energy that holds it together. Binding energy per nucleon is highest near iron, so energy is released by fusing nuclei lighter than iron or by splitting much heavier ones.

Fission splits a heavy nucleus and releases neutrons that can sustain a chain reaction, once a critical mass is present; reactors use moderators to slow those neutrons. Fusion joins light nuclei and releases more energy per unit of fuel mass than fission.

Activity counts decays per second. Absorbed dose, in grays, is the energy deposited per kilogram, and equivalent dose, in sieverts, adjusts for how damaging each type of radiation is. Radioactive isotopes are used as tracers, in medical imaging and in radiation therapy.

The four major classes of biological molecules are carbohydrates, lipids, proteins and nucleic acids. Most are polymers built from smaller monomers: sugars, amino acids and nucleotides. A polymer has properties its monomers do not, such as a protein's folded shape.

Monomers join through dehydration reactions, which remove a water molecule for each new bond. Hydrolysis reverses this, adding water to break the bond. Digestion is largely the hydrolysis of large food molecules into their monomers.

Carbohydrates range from simple sugars to long polysaccharides joined by glycosidic links. Starch and cellulose are both chains of glucose, but the links are oriented differently, so the enzymes that break down starch cannot break down cellulose.

Fats are built from glycerol and fatty acids. Saturated fatty acids have no double bonds and pack tightly, so they tend to be solid; unsaturated ones have double bonds that kink the chain, so they tend to be liquid. Phospholipids form the two-layer membranes around cells.

Proteins are chains of amino acids joined by peptide bonds. The sequence of amino acids determines how the chain folds, and the folded shape determines what the protein does.

Enzymes are biological catalysts, usually proteins, that speed reactions by lowering their activation energy. Each fits particular molecules at its active site. Heat or a pH outside its range can change an enzyme's shape, denaturing it so it stops working.

Nucleic acids are chains of nucleotides, each made of a sugar, a phosphate and a base, linked into a sugar-phosphate backbone. DNA uses the sugar deoxyribose and the base thymine; RNA uses ribose and uracil in place of thymine.

Enzymes work best within narrow pH ranges, because pH changes alter their charges and shape. Blood is held within a narrow, slightly basic pH range by buffers, chiefly the carbonic acid and bicarbonate pair.

Carbon forms four bonds and bonds readily to other carbon atoms, building chains, branches and rings. That versatility is why every class of biological molecule has a carbon framework.

Greenhouse gases, such as carbon dioxide, methane and nitrous oxide, absorb heat radiated from Earth's surface and trap it in the atmosphere. Methane traps far more heat per molecule than carbon dioxide but does not stay in the air as long. Burning fossil fuels is the main human source of carbon dioxide.

Sulfur dioxide and nitrogen oxides, released mainly by burning fossil fuels, react with water and oxygen in the air to make sulfuric and nitric acids, which come down in rain, snow and fog. Burning lower-sulfur fuel, or removing sulfur from emissions, reduces it.

Ozone high in the stratosphere absorbs harmful ultraviolet light. Chlorofluorocarbons released at ground level drift up, break apart in sunlight and release chlorine, which destroys ozone in repeated cycles. Ozone near the ground, by contrast, is a harmful pollutant.

Carbon monoxide is dangerous because it binds to hemoglobin and reduces the blood's ability to carry oxygen. Fine particles can lodge deep in the lungs. Smog forms when nitrogen oxides and volatile organic compounds react in sunlight to make ground-level ozone.

Drinking water is cleaned by steps such as filtration, to remove particles, and disinfection, to kill microorganisms. Excess nitrogen and phosphorus from runoff feed algae blooms that, as they decay, can strip the water of the dissolved oxygen fish need.

Some pollutants persist because they resist breaking down. If they also build up in body fat, they bioaccumulate, and their concentration rises at each step up a food chain, which is biomagnification. A molecule's stability is exactly what makes it dangerous here.

Green chemistry designs chemical products and processes to reduce or eliminate hazardous substances. It favors preventing waste rather than cleaning it up, getting more of the starting atoms into the product, using safer solvents and renewable starting materials.

Comparing fuels and technologies means asking where the emissions occur, not only whether a vehicle has a tailpipe. An electric vehicle produces no tailpipe emissions, but the electricity it uses may come from plants that do, so its total depends on how that electricity is generated.

In a lab, eye protection guards against splashes, gloves protect skin from chemicals, and long hair and loose clothing should be secured away from flames and equipment. Choose gloves that resist the specific chemical you are handling, and keep protection on for as long as hazards are present.

Before using a chemical, read its label pictograms and its safety data sheet, which lists hazards, handling precautions and first aid. Each pictogram flags a type of hazard, such as flammable, corrosive or acutely toxic.

Waft vapors toward your nose instead of sniffing directly. Add acid to water, not water to acid, so the heat released goes into the larger volume. Never pipette by mouth, and point a heated test tube away from yourself and others.

Know where the eyewash station, safety shower, fire extinguisher and fire blanket are before you start. For a chemical in the eyes, flush with water at once for an extended time while help is called. Report every spill and injury.

Use a fume hood for anything volatile, toxic or strongly smelling, and work well inside it. A closed storage cabinet does not ventilate; it contains. Never use a fume hood as storage for open containers.

Beakers and Erlenmeyer flasks are for mixing and holding, not precise measuring. A graduated cylinder measures volume moderately well; a buret delivers precise, variable volumes in a titration; a volumetric flask makes exactly one volume for preparing solutions.

Read a liquid level at the bottom of the curved meniscus, with your eye level with it. Tare the balance with the empty container so it reads only the sample. Accuracy is closeness to the true value, while precision is how closely repeated readings agree.

Chemical waste goes into labeled containers, kept separate so incompatible substances do not mix. Broken glass goes in a dedicated container, not the regular trash. The sink drain is not a disposal route for chemicals unless your procedures say a specific substance is safe to pour away.