IB Chemistry Data Booklet | Study to Learn

Reference section

Constants and Conventions

Molar gas constant

R = 8.31\ \text{J K}^{-1}\text{mol}^{-1}

Appears in the ideal gas law and anywhere pressure, volume, temperature, and moles need to be related. Use T in kelvin and SI units for p and V (Pa, m³) with this value of R, or convert your other units to match it first.

$R$: molar gas constant = 8.31 J K⁻¹mol⁻¹

Avogadro's constant

N_A = 6.02\times10^{23}\ \text{mol}^{-1}

The number of particles — atoms, molecules, ions, or formula units — in exactly one mole of any substance. It's the conversion factor between a particle count N and an amount in moles n, via n = N/N_A.

$N_A$: Avogadro's constant = 6.02×10²³ mol⁻¹

Standard temperature and pressure (STP)

T = 273\ \text{K}\ (0\,^{\circ}\text{C}) \qquad p = 1.00\times10^{5}\ \text{Pa} \qquad V_m = 22.7\ \text{dm}^3\text{mol}^{-1}

IB's definition of STP (and the resulting molar volume of 22.7 dm³ mol⁻¹) differs from the older convention some textbooks still use, which gives 22.4 dm³ mol⁻¹ — use 22.7 unless a question explicitly states otherwise.

$T$: standard temperature = 273 K (0 °C)
$p$: standard pressure = 1.00×10⁵ Pa
$V_m$: molar volume of an ideal gas at STP = 22.7 dm³ mol⁻¹

Reference section

A · Structure 1: Particulate Nature

Amount of substance (the mole)

n = \frac{N}{N_A} \qquad n = \frac{m}{M}

The mole links a countable number of particles to a measurable mass. Use n = N/N_A when starting from a particle count, and n = m/M when starting from a measured mass — both give the same amount of substance n, so they can be set equal to each other when converting between the two.

$n$: amount of substance (mol)
$N$: number of particles (atoms, molecules, ions, or formula units)
$N_A$: Avogadro's constant = 6.02×10²³ mol⁻¹
$m$: mass (g)
$M$: molar mass (g mol⁻¹)

Ideal gas law

pV = nRT

Relates the four measurable properties of a gas sample in a single equation. Always convert temperature to kelvin first; use SI units (Pa, m³) with R = 8.31 J K⁻¹mol⁻¹, or convert consistently if working in kPa/dm³.

$p$: pressure (Pa)
$V$: volume (m³)
$n$: amount of substance (mol)
$R$: molar gas constant (J K⁻¹mol⁻¹)
$T$: absolute temperature (K)

Empirical and molecular formula

n = \frac{M_{molecular}}{M_{empirical}} \qquad \text{molecular formula} = (\text{empirical formula})_n

The empirical formula gives the simplest whole-number ratio of atoms in a compound; the molecular formula is a whole-number multiple n of it. Find the empirical formula first from percentage composition or combustion data, then use a given molar mass to find n and scale up.

$n$: whole-number multiplier linking the two formulas
$M_molecular$: molar mass of the actual molecule (g mol⁻¹)
$M_empirical$: molar mass of the empirical formula unit (g mol⁻¹)

Reference section

B · Structure 2: Bonding and Structure

Electronegativity difference and bond polarity

\Delta EN = |EN_A - EN_B|

Comparing the electronegativity values of two bonded atoms predicts how evenly the shared electron pair is distributed. As a rough guide: ΔEN below about 0.4 gives an essentially nonpolar covalent bond, 0.4–1.8 a polar covalent bond, and above about 1.8 the bond is better described as ionic — these are guidelines, not hard cutoffs.

$ΔEN$: electronegativity difference between the two bonded atoms (Pauling scale, dimensionless)
$EN_A, EN_B$: electronegativity values of atoms A and B (Pauling scale)

VSEPR electron-domain geometry

2\ \text{domains: } 180^{\circ} \qquad 3\ \text{domains: } 120^{\circ} \qquad 4\ \text{domains: } 109.5^{\circ} \qquad 5\ \text{domains: } 90^{\circ}/120^{\circ} \qquad 6\ \text{domains: } 90^{\circ}

Electron domains (bonding pairs and lone pairs) around a central atom spread out to minimise repulsion, which fixes the ideal bond angle for a given number of domains. A lone pair repels more strongly than a bonding pair, so measured bond angles compress slightly below these ideal values whenever lone pairs are present.

$2 domains$: linear geometry, 180°
$3 domains$: trigonal planar, 120°
$4 domains$: tetrahedral, 109.5°
$5 domains$: trigonal bipyramidal, 90° and 120°
$6 domains$: octahedral, 90°

Lattice enthalpy trend

\Delta H_{lattice} \propto \frac{|q_+ \times q_-|}{r_+ + r_-}

Lattice enthalpy isn't usually calculated directly from this proportionality, but it explains the trend across compounds: lattice enthalpy becomes more exothermic (larger magnitude) with higher ionic charges and smaller ionic radii, since both increase the electrostatic attraction between neighbouring ions.

$ΔH_lattice$: lattice enthalpy — energy released forming one mole of ionic solid from its gaseous ions (kJ mol⁻¹)
$q_+, q_-$: charges on the cation and anion
$r_+, r_-$: ionic radii of the cation and anion (pm)

Reference section

C · Structure 3: Classification of Matter

General formulas of homologous series

\text{Alkanes: } C_nH_{2n+2} \qquad \text{Alkenes: } C_nH_{2n} \qquad \text{Alcohols: } C_nH_{2n+1}OH \qquad \text{Carboxylic acids: } C_nH_{2n+1}COOH

Every member of a homologous series fits the same general formula and differs from its neighbour by one CH₂ unit, which is why members show a gradual, predictable trend in physical properties like boiling point as chain length increases. n is the number of carbon atoms in the longest chain.

$n$: number of carbon atoms in the chain (n = 1, 2, 3, …)

Periodic trends

\text{Across a period: } Z_{eff}\uparrow,\ r_{atomic}\downarrow,\ IE_1\uparrow,\ EN\uparrow \qquad \text{Down a group: } r_{atomic}\uparrow,\ IE_1\downarrow,\ EN\downarrow

All four trends trace back to the same two competing factors: increasing nuclear charge (pulling outer electrons in) versus increasing shielding from extra inner shells (pushing them out). Across a period shielding stays roughly constant while nuclear charge rises; down a group, added electron shells dominate instead.

$Z_eff$: effective nuclear charge felt by the outer (valence) electrons
$r_atomic$: atomic radius
$IE_1$: first ionisation energy
$EN$: electronegativity

IUPAC nomenclature reference

\text{meth-}(C_1)\ \ \text{eth-}(C_2)\ \ \text{prop-}(C_3)\ \ \text{but-}(C_4)\ \ \text{pent-}(C_5)\ \ \text{hex-}(C_6) \qquad \text{suffixes: -ane, -ene, -yne, -anol, -anoic acid, -anal, -anone}

A systematic name is built from a stem showing chain length plus a suffix showing the principal (highest-priority) functional group, with a locant number when its position needs specifying. Any other substituent is named as a prefix, listed alphabetically with its own locant.

$stem$: indicates the number of carbon atoms in the longest chain containing the principal functional group
$suffix$: indicates the principal functional group present
$locant$: number identifying the position of a functional group or substituent on the chain

Reference section

D · Reactivity 1: What Drives Reactions?

Enthalpy change from calorimetry

q = mc\Delta T \qquad \Delta H = -\frac{q}{n}

The standard way to determine an enthalpy change experimentally: measure the heat absorbed or released by a surrounding known mass of solution (q), then divide by the moles of the limiting reactant to get a molar enthalpy change. The minus sign reflects that heat released to the surroundings (q positive) corresponds to an exothermic, negative ΔH for the reaction itself.

$q$: heat energy transferred to or from the surroundings (J)
$m$: mass of the solution being heated or cooled (g)
$c$: specific heat capacity of the solution, often approximated as that of water = 4.18 J g⁻¹K⁻¹
$ΔT$: temperature change of the solution (K or °C)
$ΔH$: molar enthalpy change of the reaction (kJ mol⁻¹)
$n$: moles of the limiting reactant (mol)

Hess's Law

\Delta H_{rxn} = \sum \Delta H_f^{\circ}(\text{products}) - \sum \Delta H_f^{\circ}(\text{reactants})

Enthalpy is a state function, so the overall enthalpy change for a reaction is the same regardless of the route taken between reactants and products. This lets you calculate a ΔH that's difficult to measure directly by combining known standard enthalpies of formation (or other measurable steps) algebraically.

$ΔH_rxn$: enthalpy change of the overall reaction (kJ mol⁻¹)
$ΔH_f°$: standard enthalpy of formation of a species (kJ mol⁻¹); zero by definition for an element in its standard state

Bond enthalpies

\Delta H \approx \sum BE(\text{bonds broken}) - \sum BE(\text{bonds formed})

Breaking bonds always requires energy input; forming bonds always releases energy, so this is essentially Hess's law applied at the level of individual bonds. It only gives an approximate ΔH, because tabulated bond enthalpies are averages taken across many different compounds, not exact values for the specific molecule in the question.

$ΔH$: enthalpy change of reaction, estimated from bond enthalpies (kJ mol⁻¹)
$BE$: average bond enthalpy of a given bond type (kJ mol⁻¹)

Born–Haber cycle (lattice enthalpy)

\Delta H_f^{\circ} = \Delta H_{atomisation} + \Delta H_{IE} + \Delta H_{EA} + \Delta H_{lattice}

A Born–Haber cycle applies Hess's law to the formation of an ionic compound, breaking it into steps that are each individually measurable (atomisation, ionisation, electron affinity) except for lattice enthalpy, which is found by making it the unknown that balances the cycle. Every route around the cycle must sum to the same overall enthalpy change.

$ΔH_f°$: standard enthalpy of formation of the ionic compound (kJ mol⁻¹)
$ΔH_atomisation$: enthalpy to convert the elements into gaseous atoms (kJ mol⁻¹)
$ΔH_IE$: ionisation enthalpy/energy of the metal (kJ mol⁻¹)
$ΔH_EA$: electron affinity of the non-metal (kJ mol⁻¹)
$ΔH_lattice$: lattice enthalpy — formation of the ionic solid from gaseous ions (kJ mol⁻¹)

Entropy and Gibbs free energy

\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} \qquad \Delta G = \Delta H - T\Delta S

A reaction is spontaneous (thermodynamically feasible) when ΔG < 0. Because ΔG combines an enthalpy term with a temperature-dependent entropy term, an endothermic reaction (ΔH > 0) can still become spontaneous above some temperature if ΔS is sufficiently positive — set ΔG = 0 and solve for T to find that switching temperature.

$ΔS_total, ΔS_system, ΔS_surroundings$: entropy changes of the universe, system, and surroundings (J K⁻¹mol⁻¹)
$ΔG$: Gibbs free energy change (kJ mol⁻¹) — the reaction is spontaneous when ΔG < 0
$ΔH$: enthalpy change of the system (kJ mol⁻¹)
$T$: absolute temperature (K)

Reference section

E · Reactivity 2: How Much, How Fast, How Far?

Stoichiometric mole ratios

\frac{n_A}{n_B} = \frac{\text{coefficient of A}}{\text{coefficient of B}}

The balanced chemical equation gives the exact mole ratio in which reactants combine and products form. Convert all given quantities to moles first, apply the ratio from the balanced equation to find the unknown amount, then convert back to whatever units the question asks for.

$n_A, n_B$: amount in moles of species A and B in the balanced equation (mol)

Concentration and dilution

c = \frac{n}{V} \qquad c_1V_1 = c_2V_2

c = n/V converts between concentration, moles, and volume of a solution. c₁V₁ = c₂V₂ applies when a solution is diluted (or mixed with more of the same solute) since the moles of solute stay fixed while only the volume changes.

$c$: concentration (mol dm⁻³)
$n$: amount of solute (mol)
$V$: volume of solution (dm³)
$c_1, V_1$: concentration and volume before dilution
$c_2, V_2$: concentration and volume after dilution

Limiting reagent and percentage yield

\%\ yield = \frac{\text{actual yield}}{\text{theoretical yield}}\times100

The limiting reagent is found by dividing the moles of each reactant by its coefficient in the balanced equation — whichever gives the smallest value runs out first and caps the theoretical yield. Percentage yield is essentially always below 100% in practice, due to side reactions, incomplete reactions, or losses during purification.

$% yield$: percentage yield of product actually obtained
$actual yield$: mass (or moles) of product actually obtained
$theoretical yield$: maximum possible mass (or moles) of product, calculated from the limiting reagent

Rate law and order of reaction

rate = k[A]^m[B]^n

The exponents m and n — the orders of reaction with respect to each reactant — must be found experimentally from rate data; they cannot be read directly off the balanced equation's coefficients. The overall order is m + n, and the units of the rate constant k depend on that overall order.

$rate$: reaction rate (mol dm⁻³ s⁻¹)
$k$: rate constant (units depend on overall order)
$[A], [B]$: concentrations of reactants A and B (mol dm⁻³)
$m, n$: orders of reaction with respect to A and B (found experimentally, not from the equation)

Equilibrium constant, Kᴄ

K_c = \frac{[\text{products}]^{\text{stoich. coeff.}}}{[\text{reactants}]^{\text{stoich. coeff.}}}

Kc is calculated from equilibrium concentrations, each raised to the power of its coefficient in the balanced equation. A large Kc (≫1) favours products at equilibrium; a small Kc (≪1) favours reactants. Kc is constant at a given temperature and unaffected by initial concentrations, total pressure, or a catalyst.

$K_c$: equilibrium constant expressed in terms of concentration (units vary with the reaction)
$[products], [reactants]$: equilibrium concentrations of products and reactants (mol dm⁻³), each raised to its stoichiometric coefficient

Equilibrium constant, Kₚ

K_p = \frac{(p_{products})^{\text{stoich. coeff.}}}{(p_{reactants})^{\text{stoich. coeff.}}} \qquad K_p = K_c(RT)^{\Delta n}

Kp is used for equilibria involving gases, replacing concentration with partial pressure. It relates back to Kc through Δn, the change in moles of gas between products and reactants — when Δn = 0, Kp and Kc are numerically equal (in consistent units).

$K_p$: equilibrium constant expressed in terms of partial pressure
$p$: partial pressure of a gaseous species
$K_c$: equilibrium constant in terms of concentration
$R$: molar gas constant
$T$: absolute temperature (K)
$Δn$: change in moles of gas = (moles of gaseous products) − (moles of gaseous reactants)

Reference section

F · Reactivity 3: Mechanisms of Change

pH, pOH, and Kᴡ

pH = -\log[H^+] \qquad pOH = -\log[OH^-] \qquad K_w = [H^+][OH^-] \qquad pH + pOH = 14

Kw = 1.00×10⁻¹⁴ at 25°C defines the relationship between [H⁺] and [OH⁻] in any aqueous solution, not just neutral water. pH + pOH = 14 follows from taking −log of the Kw expression, and only holds exactly at 25°C since Kw itself changes with temperature.

$pH$: measure of acidity = −log[H⁺]
$pOH$: measure of alkalinity = −log[OH⁻]
$[H⁺], [OH⁻]$: hydrogen ion and hydroxide ion concentrations (mol dm⁻³)
$K_w$: ionic product of water = 1.00×10⁻¹⁴ at 25°C

Weak acid dissociation, Kₐ

K_a = \frac{[H^+][A^-]}{[HA]} \qquad pK_a = -\log K_a

Ka measures how far a weak acid dissociates in water — a larger Ka (smaller pKa) means a stronger acid. Unlike a strong acid, a weak acid's [H⁺] can't be assumed equal to its initial concentration and must be worked out from Ka using an ICE table.

$K_a$: acid dissociation constant (mol dm⁻³)
$[H^+], [A^-], [HA]$: equilibrium concentrations of hydrogen ion, conjugate base, and undissociated acid (mol dm⁻³)
$pK_a$: −log K_a; a smaller pKa means a stronger acid

Henderson–Hasselbalch buffer equation

pH = pK_a + \log\frac{[A^-]}{[HA]}

Gives the pH of a buffer solution directly from the ratio of conjugate base to weak acid present, without needing a full ICE table. A buffer resists pH change most effectively when [A⁻] and [HA] are roughly equal — that is, when pH ≈ pKa.

$pH$: pH of the buffer solution
$pK_a$: −log K_a of the weak acid component
$[A^-]$: concentration of the conjugate base (mol dm⁻³)
$[HA]$: concentration of the undissociated weak acid (mol dm⁻³)

Oxidation states and redox

\text{oxidation: loss of electrons (O.N. increases)} \qquad \text{reduction: gain of electrons (O.N. decreases)}

Assigning an oxidation number (O.N.) to every atom before and after a reaction is the fastest way to spot a redox reaction and identify which species is oxidised and which is reduced, even when no explicit electron transfer is written out. Balancing a redox half-equation means balancing atoms first, then charge, by adding electrons.

$O.N.$: oxidation number/state of an atom in a compound or ion

Standard cell potential

E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode} \qquad \Delta G^{\circ} = -nFE^{\circ}_{cell}

A positive E°cell (built from the more positive reduction potential as the cathode) indicates a spontaneous cell reaction, consistent with the negative ΔG° it produces. Standard electrode potentials are always tabulated as reduction potentials — flip the sign when a half-equation runs as an oxidation instead.

$E°_cell$: standard cell potential (V)
$E°_cathode, E°_anode$: standard reduction potentials of the cathode and anode half-cells (V)
$ΔG°$: standard Gibbs free energy change of the cell reaction (J mol⁻¹)
$n$: number of moles of electrons transferred in the balanced equation
$F$: Faraday constant = 96 500 C mol⁻¹

Nernst equation

E_{cell} = E^{\circ}_{cell} - \frac{RT}{nF}\ln Q

Extends the standard cell potential to non-standard conditions — concentrations or gas pressures other than 1 mol dm⁻³ / 1 atm. As a cell reaction proceeds and Q drifts away from its standard value, Ecell falls away from E°cell, which is why real cells lose voltage as they discharge.

$E_cell$: cell potential under non-standard conditions (V)
$E°_cell$: standard cell potential (V)
$R$: molar gas constant
$T$: absolute temperature (K)
$n$: number of moles of electrons transferred
$F$: Faraday constant = 96 500 C mol⁻¹
$Q$: reaction quotient (same form as the equilibrium constant expression, but using current, non-equilibrium concentrations)