Law of conservation of mass: matter can neither be created nor destroyed in a chemical reaction; the total mass of reactants equals the total mass of products. Law of definite proportions: a given chemical compound always contains the same elements combined in the same fixed proportion by mass, irrespective of its source or method of preparation.

Molar mass of CO2 = 12 + 2(16) = 44 g/mol. Number of moles = given mass / molar mass = 11 / 44 = 0.25 mol.

n = m / M

One mole is the amount of a substance that contains as many elementary entities (atoms, molecules, ions) as there are atoms in exactly 12 g of carbon-12. This number of entities is Avogadro's number, N_A = 6.022 x 10^23 mol^-1.

1 mol = 6.022 x 10^23 particles

Molarity (M) is the number of moles of solute dissolved per litre of solution; unit mol/L (or M). Molality (m) is the number of moles of solute dissolved per kilogram of solvent; unit mol/kg (or m). Molality is independent of temperature since it uses mass, whereas molarity changes with temperature because volume changes.

M = n_solute / V(L); m = n_solute / mass_solvent(kg)

Mole fraction of a component = number of moles of that component / total number of moles of all components in the solution; it is dimensionless and the sum of mole fractions equals 1. Mass percent of a component = (mass of the component / total mass of solution) x 100.

x_A = n_A / n_total; mass% = (mass component / total mass) x 100

Wavelength = 4000 Angstrom = 4000 x 10^-10 m = 4 x 10^-7 m. Energy E = hc/lambda = (6.626 x 10^-34 x 3 x 10^8) / (4 x 10^-7) = 1.988 x 10^-25 / 4 x 10^-7 = 4.97 x 10^-19 J.

E = hc / lambda

It is impossible to determine simultaneously and with absolute accuracy both the position and the momentum (or velocity) of a microscopic particle such as an electron. The product of the uncertainties in position (delta x) and momentum (delta p) is at least of the order of h/4pi.

delta x . delta p >= h / 4pi

Wave number (nu bar) = R (1/n1^2 - 1/n2^2) = 1.097 x 10^7 (1/2^2 - 1/3^2) = 1.097 x 10^7 (1/4 - 1/9) = 1.097 x 10^7 x (5/36) = 1.523 x 10^6 m^-1. This is the H-alpha line of the Balmer series.

nu bar = R (1/n1^2 - 1/n2^2)

Pauli's exclusion principle: no two electrons in an atom can have the same set of all four quantum numbers; an orbital can hold at most two electrons with opposite spins. Hund's rule of maximum multiplicity: electron pairing in orbitals of the same subshell (degenerate orbitals) does not occur until each orbital is singly occupied, and all singly filled orbitals have parallel spin.

Aufbau principle: in the ground state of an atom, electrons are filled into orbitals in order of increasing energy, i.e. the lowest energy orbital is filled first. (n + l) rule: the orbital with the lower (n + l) value has lower energy and is filled first; if two orbitals have the same (n + l) value, the one with the lower n is filled first (e.g. 4s (n+l=4) is filled before 3d (n+l=5)).

energy order by increasing (n + l)

Modern periodic law: the physical and chemical properties of elements are a periodic function of their atomic numbers. Mendeleev's law was based on atomic mass, whereas the modern law is based on atomic number (number of protons), which removed anomalies such as the position of argon and potassium.

Nitrogen has the configuration 1s2 2s2 2p3 with a half-filled 2p subshell, which is extra stable due to symmetry and exchange energy, so removing an electron requires more energy. Oxygen (1s2 2s2 2p4) has one paired electron in 2p; removing it relieves electron-electron repulsion and gives a stable half-filled configuration, so less energy is needed. Hence IE1 of nitrogen > oxygen.

Although fluorine is smaller, its 2p subshell is very compact, so the incoming electron experiences strong inter-electronic repulsion from the already crowded 2p electrons. In chlorine, the larger 3p subshell accommodates the incoming electron with less repulsion, so more energy is released. Hence chlorine has a more negative (more exothermic) electron gain enthalpy than fluorine.

Electronegativity is the tendency of an atom in a molecule to attract the shared pair of electrons in a covalent bond towards itself. It increases across a period (as size decreases and nuclear charge increases) and decreases down a group (as size increases). Fluorine is the most electronegative element. The Pauling scale is commonly used.

All four species have 10 electrons (isoelectronic). For isoelectronic species, the greater the nuclear charge (number of protons), the smaller the radius. Nuclear charges: O2- (8), F- (9), Na+ (11), Mg2+ (12). Increasing order of radius: Mg2+ < Na+ < F- < O2-.

An ionic (electrovalent) bond is formed by the complete transfer of one or more electrons from one atom to another, producing oppositely charged ions held by electrostatic attraction (e.g. NaCl). A covalent bond is formed by the mutual sharing of electron pairs between atoms (e.g. H2 or Cl2). Ionic bonds form between metals and non-metals; covalent bonds form between non-metals.

Both molecules are based on sp3 hybridisation with an ideal angle of 109.5 deg. NH3 has one lone pair, while H2O has two lone pairs. Lone pair-lone pair repulsion is stronger than lone pair-bond pair repulsion, and water has an extra lone pair, so its bond pairs are pushed closer together. Hence the bond angle of H2O (104.5 deg) is smaller than that of NH3 (107 deg).

N2 has 14 electrons. Number of bonding electrons Nb = 10 and antibonding electrons Na = 4. Bond order = (Nb - Na)/2 = (10 - 4)/2 = 3. This corresponds to a nitrogen-nitrogen triple bond, which explains the very high stability and bond dissociation energy of N2.

Bond order = (Nb - Na)/2

A coordinate bond is a covalent bond in which the shared pair of electrons is contributed by only one of the two bonded atoms (the donor). In the ammonium ion (NH4+), nitrogen in NH3 has a lone pair which it donates to a proton (H+) that has no electrons, forming the fourth N-H bond as a coordinate bond. Once formed, all four N-H bonds are identical.

NH3 + H+ -> NH4+

A hydrogen bond is a weak electrostatic attraction between a hydrogen atom covalently bonded to a highly electronegative atom (F, O or N) and the lone pair of another electronegative atom. Conditions: hydrogen must be attached to a small, highly electronegative atom. Types: intermolecular hydrogen bonding (between different molecules, e.g. in water and HF) and intramolecular hydrogen bonding (within the same molecule, e.g. o-nitrophenol).