Unit 1 Beta

Atomic Structure and Properties: the one-page sheet

1.1 Moles and Molar Mass

Chemists count particles in moles of 6.022 × 10²³. The molar mass, the sum of the atomic masses in one particle, has the same number in g/mol as one particle's mass in amu, so it converts a measured mass into moles. Avogadro's number converts moles into particles. Equal masses of different substances hold different numbers of particles.

One mole is 6.022 × 10²³ particles (Avogadro's number). Always say which particles: one mole of water molecules holds three moles of atoms.
Molar mass (g/mol) = the sum of the atomic masses of every atom in one particle. Water: 2(1.008) + 16.00 = 18.02 g/mol.
grams ÷ molar mass = moles; moles × 6.022 × 10²³ = particles. Always go through moles.
Equal masses of different substances hold different numbers of particles: lighter particles, more of them.

chemists count them in groups of 6.022 × 10²³, called a mole the atomic mass on the periodic table is also the molar mass in g/mol dividing a mass by the molar mass gives the amount in moles multiplying moles by 6.022 × 10²³ gives the number of particles

atom: The smallest piece of an element that still has that element's properties.
element: A substance made of only one kind of atom, such as carbon, oxygen or iron.
periodic table: The chart of all the elements in order, with each element's symbol and atomic mass, arranged so that elements with similar properties fall in the same column.
molecule: Two or more atoms held together as one particle, such as a water molecule, H₂O, or an oxygen molecule, O₂.
compound: A substance made of two or more different elements joined in a fixed ratio, such as water (H₂O) or table salt.
atomic mass unit: A unit for the mass of atoms (amu, also called the dalton): one twelfth of the mass of a carbon atom of mass 12, about 1.66 × 10⁻²⁴ g.
atomic mass: The mass of an element's atoms in atomic mass units, as listed on the periodic table; numerically the same as the element's molar mass in g/mol.
mole: The counting unit of chemistry: 6.022 × 10²³ particles of whatever you name (atoms, molecules, ions).
Avogadro's number: 6.022 × 10²³ per mole, the number of particles in one mole.
molar mass: The mass of one mole of a substance, in grams per mole (g/mol); the sum of the atomic masses of every atom in one particle.

1.2 Mass Spectra of Elements

Atoms of one element share an atomic number (protons) but can differ in neutrons; these isotopes have different masses. A mass spectrometer sorts singly charged ions by mass, giving one peak per isotope, with heights showing relative abundance. The atomic mass on the periodic table is the abundance-weighted average of the isotope masses.

An atom has protons and neutrons in its nucleus and electrons around it. The atomic number (protons) identifies the element; the mass number = protons + neutrons.
Isotopes: same element, different numbers of neutrons, so different masses. ³⁵Cl and ³⁷Cl.
In a mass spectrum, each peak is one isotope (as a 1+ ion); its position is the mass and its height the relative abundance.
Average atomic mass = Σ (fraction × isotope mass). It sits closest to the most abundant isotope.

an element can exist as several isotopes with different masses each isotope gives its own peak at its mass the peak heights give the relative abundances the atomic mass on the periodic table is the abundance-weighted average of the isotope masses

proton: A positively charged particle in the nucleus of an atom; the number of protons decides which element an atom is.
neutron: A particle with no charge in the nucleus of an atom, with almost the same mass as a proton.
electron: A tiny negatively charged particle outside the nucleus; it has about 1/1800 of the mass of a proton.
nucleus: The small, dense center of an atom, made of protons and neutrons, which holds almost all of the atom's mass.
atomic number: The number of protons in an atom's nucleus, which identifies the element (carbon is 6, oxygen 8).
mass number: The number of protons plus neutrons in an atom's nucleus, written as in carbon-14 or ¹⁴C.
isotope: Atoms of the same element (same number of protons) with different numbers of neutrons, and so different masses.
ion: An atom or group of atoms with an electric charge, because it has gained or lost electrons.
cation: A positive ion: it has fewer electrons than protons, such as Na⁺.
anion: A negative ion: it has more electrons than protons, such as Cl⁻.
relative abundance: The share of an element's atoms that are one particular isotope, usually given as a percent.
mass spectrum: A graph from a mass spectrometer showing the masses of the ions in a sample and how many of each there are; for an element, one peak per isotope.
mass-to-charge ratio: The mass of an ion divided by its charge (m/z), the quantity a mass spectrometer sorts by; for a 1+ ion it equals the mass.
average atomic mass: The mean mass of an element's atoms, weighting each isotope's mass by its relative abundance; the value on the periodic table.

1.3 Elemental Composition of Pure Substances

A pure compound has a fixed composition by mass. Mass percent is an element's share of the molar mass. To find an empirical formula, convert mass data to moles and reduce to the smallest whole-number ratio. The molar mass then gives the molecular formula, a whole-number multiple of the empirical one.

A pure substance has a fixed composition (law of definite proportions): every sample of water is 11.2% H by mass.
Mass percent of an element = (mass of the element in one formula ÷ molar mass) × 100.
Empirical formula: assume 100 g, convert grams to moles, divide by the smallest, clear fractions (×2 for .5, ×3 for .33).
Molecular formula = empirical formula × n, where n = molar mass ÷ empirical-formula mass.

it always has the same mass percent of each element (law of definite proportions) a mass ratio is not an atom ratio, so masses must be converted to moles that ratio, cleared to whole numbers, is the empirical formula the molar mass is needed to find how many empirical units make one molecule

pure substance: Matter with a fixed composition throughout: an element or a single compound.
law of definite proportions: The law that a given compound always contains the same elements in the same proportions by mass, however it is made.
chemical formula: Element symbols with subscripts that show the ratio of atoms in a substance, such as H₂O (2 H for each O).
mass percent: The share of a compound's mass that comes from one element: the element's mass in one formula divided by the molar mass, times 100.
empirical formula: The simplest whole-number ratio of atoms in a compound, such as CH₂O for glucose.
molecular formula: The actual number of each kind of atom in one molecule, a whole-number multiple of the empirical formula, such as C₆H₁₂O₆.

1.4 Composition of Mixtures

Pure substances have one kind of particle and a fixed composition; mixtures have more than one, in variable proportions, and can be homogeneous or heterogeneous. Elemental analysis measures one element in a sample and uses the pure compound's mass percent to find how much of the compound is present, giving its purity.

A mixture holds two or more substances in proportions that can vary. A homogeneous mixture is uniform throughout; a heterogeneous mixture is not.
In a particulate diagram, a pure substance shows one kind of particle; a mixture shows more than one. What you see and measure in bulk is the macroscopic level.
Elemental analysis: measure the mass of one element, convert it to the compound with the compound's mass percent.
Purity = mass of the wanted compound ÷ mass of the sample × 100.

its composition is fixed, the same in every sample its proportions can vary from sample to sample measuring one element in a sample shows how much of that compound it holds gives the purity, as long as no other part of the mixture holds the same element

mixture: Two or more substances together but not bonded into one kind of particle, in proportions that can vary.
homogeneous mixture: A mixture with the same composition all the way through, such as salt water or air.
heterogeneous mixture: A mixture whose composition differs from place to place, such as sand in water.
purity: The share of a sample, by mass, that is the substance you want: mass of that substance ÷ mass of the sample × 100.
elemental analysis: Measuring how much of an element a sample contains, to identify a compound or to work out how pure a sample is.
particulate diagram: A drawing of a substance at the level of its particles (atoms, molecules, ions), with a key to the symbols.
macroscopic: The scale of things you can see, touch and measure in bulk, such as color, mass or volume, as opposed to the particle level.

1.5 Atomic Structure and Electron Configuration

Electrons are attracted to the nucleus by Coulomb's law: more charge pulls harder and distance weakens the pull. Electrons occupy shells and s, p and d subshells, filled in order of energy. The outer valence electrons are shielded by core electrons, so they are held less tightly. Ionization energy measures how tightly an electron is held.

Coulomb's law: F ∝ q₁q₂/r². Larger charges attract more; greater distance attracts much less. Potential energy ∝ q₁q₂/r.
Electrons sit in shells (n = 1, 2, 3…) made of subshells s, p, d (2, 6, 10 electrons), each made of orbitals holding 2.
Aufbau order: 1s 2s 2p 3s 3p 4s 3d 4p. Na: 1s² 2s² 2p⁶ 3s¹, or [Ne] 3s¹.
Valence electrons are in the outermost shell; core electrons shield them. Ionization energy is the energy to remove an electron.

electrons closer to the nucleus are held more strongly and have lower energy each subshell has its own energy and holds 2, 6 or 10 electrons every atom has a predictable electron configuration they shield the valence electrons, which are held less tightly and take part in chemistry

Coulomb's law: The force between two charges is proportional to the product of the charges divided by the square of the distance between them (F ∝ q₁q₂/r²): opposite charges attract, like charges repel.
potential energy: Stored energy due to position. For two opposite charges it is lower (more negative) the larger the charges and the closer they are, so separating them takes energy.
electron shell: A main energy level of electrons in an atom, numbered n = 1, 2, 3…; higher shells are on average farther from the nucleus.
subshell: A part of an electron shell with its own energy, labeled s, p or d, holding at most 2, 6 or 10 electrons.
orbital: A region around the nucleus where an electron is likely to be found; each holds at most two electrons. An s subshell has 1 orbital, p has 3 and d has 5.
aufbau principle: The rule that electrons fill the lowest-energy open subshell first: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.
electron configuration: A list of an atom's occupied subshells with the number of electrons in each, such as 1s² 2s² 2p⁶ 3s¹ for sodium, or [Ne] 3s¹ in noble gas notation.
valence electron: An electron in the outermost occupied shell of an atom; valence electrons take part in chemical reactions.
core electron: An electron in an inner, filled shell of an atom, closer to the nucleus than the valence electrons.
shielding: The way inner electrons partly cancel the nucleus's pull on outer electrons by repelling them, so outer electrons feel less attraction.
ionization energy: The energy needed to remove an electron from an atom or ion in the gas phase; the first ionization energy removes the most loosely held electron.

1.6 Photoelectron Spectroscopy

Photoelectron spectroscopy ejects electrons with high-energy light and measures each one's binding energy. Each subshell gives one peak: its position shows how tightly the electrons are held and its height how many there are. Inner subshells and higher nuclear charge give higher binding energies, as Coulomb's law predicts.

A photon is a packet of light energy. In photoelectron spectroscopy (PES), high-energy photons eject electrons and the energy each needed is measured.
That energy is the binding energy. One peak per subshell; position = binding energy; height = number of electrons.
Highest binding energy (left) is 1s; lowest (right) is the valence subshell. Within a shell, s is above p.
More protons shift every matching peak to higher energy (Coulomb's law). A new subshell adds a new peak at the low-energy end.

each photon can knock out one electron if it carries enough energy gives the binding energy, how tightly that electron was held they form one peak, whose height counts the electrons inner subshells and heavier elements have peaks at higher binding energy

photon: A single packet of light energy. Higher-energy photons can knock electrons out of atoms.
photoelectron spectroscopy: A method that uses high-energy light to eject electrons from atoms and measures the energy needed to remove each one, giving one peak per subshell.
binding energy: The energy needed to remove an electron from a particular subshell of an atom, a measure of how strongly the nucleus holds it.

1.7 Periodic Trends

Periodic trends follow from Coulomb's law and shielding. Across a period, rising effective nuclear charge pulls valence electrons closer, so radius falls and ionization energy, electronegativity and electron affinity rise. Down a group, added shells increase distance and shielding, reversing these trends. Explanations name protons, shells and core electrons for both atoms.

Effective nuclear charge: the pull a valence electron feels, about protons minus core electrons. It rises across a period and stays similar down a group.
Atomic radius falls across a period and rises down a group. Cations are smaller than their atoms; anions larger (ionic radius).
Ionization energy and electronegativity rise across and fall down. Dips: Mg → Al (new 3p subshell), P → S (paired 3p electrons repel).
Electron affinity is the energy change when an atom gains an electron. Metals (left, middle) hold valence electrons loosely; nonmetals (upper right) tightly.

the effective nuclear charge on the valence electrons rises pulls the valence electrons closer: smaller radius, higher ionization energy and electronegativity valence electrons are farther out and behind more core electrons radius rises and ionization energy and electronegativity fall

periodic trend: A property that changes in a regular way across a period or down a group of the periodic table, such as atomic radius or ionization energy.
group (periodic table): A column of the periodic table (a group or family); its elements have the same number of valence electrons. A row is a period.
effective nuclear charge: The net positive charge a valence electron feels: the nuclear charge reduced by the shielding of the core electrons (roughly protons minus core electrons).
atomic radius: The size of an atom, measured as half the distance between the nuclei of two touching or joined atoms of the element.
ionic radius: The size of an ion. A cation is smaller than its atom, and an anion is larger than its atom.
electronegativity: How strongly an atom attracts electrons that it shares with another atom; it rises across a period and falls down a group.
electron affinity: The energy change when a gaseous atom gains an electron; atoms that attract an added electron strongly release more energy.
metal: An element, on the left or in the middle of the periodic table, that holds its few valence electrons loosely and tends to lose them; nonmetals (upper right) tend to gain electrons, and metalloids lie between.

1.8 Valence Electrons and Ionic Compounds

Main-group metals lose their valence electrons to form cations, and nonmetals gain electrons to form anions, usually reaching a noble gas configuration. Ionic compounds combine cations and anions in the smallest whole-number ratio that makes the total charge zero. Elements in the same group form ions of the same charge and behave alike.

Group 1 → 1+, group 2 → 2+, group 13 → 3+ (Al); group 15 → 3−, group 16 → 2−, group 17 → 1−. Each ion has a noble gas configuration.
An ionic compound is made of cations and anions in the ratio that makes the total charge zero: Ca²⁺ + 2 F⁻ → CaF₂.
Write the cation first; subscripts give the simplest ratio (a formula unit), never 2 : 2.
Elements in a group have the same number of valence electrons, so they form the same ions and react alike.

they lose them to form cations they gain electrons to form anions main-group ions usually end up with a noble gas configuration they combine in the ratio that makes the charges cancel

noble gas configuration: An electron configuration with the same arrangement as a noble gas, such as Na⁺ and F⁻ (both like neon). Particles with the same number of electrons are isoelectronic.
ionic compound: A compound made of cations and anions held together by their opposite charges, in the ratio that makes it neutral; its simplest unit (such as one NaCl) is a formula unit.