Equation sheet

Atomic structure

$E$ = energy · $\nu$ = frequency · $\lambda$ = wavelength · $F$ = force · $q$ = charge · $r$ = separation

• $E = h\nu$
  Energy of a photon3.11–3.12 Light, spectra and photons1.6 Measuring the shells
• $c = \lambda\nu$
  Wavelength and frequency3.11–3.12 Light, spectra and photons
• $\displaystyle F_\text{coulombic} \propto \frac{q_1q_2}{r^2}$
  Coulomb’s law1.5 Electrons in shells1.6 Measuring the shells1.7 Periodic trends

Gases, liquids and solutions

$P$ = pressure · $V$ = volume · $T$ = temperature · $n$ = number of moles · $X$ = mole fraction · $m$ = mass · $\boldsymbol{M}$ = molar mass · $D$ = density · $KE$ = kinetic energy · $v$ = velocity · $M$ = molarity · $A$ = absorbance · $\varepsilon$ = molar absorptivity · $b$ = path length · $c$ = concentration

• $\displaystyle \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
  Combined gas law3.4 The ideal gas law
• $PV = nRT$
  Ideal gas law3.4 The ideal gas law3.6 Deviation from ideal behavior
• $\displaystyle P_A = P_\text{total}\times X_A,\ \text{where } X_A = \frac{\text{moles A}}{\text{total moles}}$
  Partial pressure and mole fraction3.4 The ideal gas law
• $P_\text{total} = P_A + P_B + P_C + \dots$
  Dalton’s law3.4 The ideal gas law
• $\displaystyle n = \frac{m}{\boldsymbol{M}}$
  Moles from mass1.1 Counting atoms by weighing4.5 Stoichiometry
• $\displaystyle D = \frac{m}{V}$
  Densitynot shown yet
• $KE = \tfrac12mv^2$
  Kinetic energy3.5 Kinetic molecular theory
• $\displaystyle M = \frac{n_\text{solute}}{\mathrm{L}_\text{solution}}$
  Molarity3.7–3.8 Solutions and their particles4.5 Stoichiometry
• $A = \varepsilon bc$
  Beer–Lambert law3.13 The Beer–Lambert law

Kinetics

$k$ = rate constant · $t$ = time · $t_{1/2}$ = half-life

• $[\mathrm{A}]_t - [\mathrm{A}]_0 = -kt$
  Zero-order integrated rate law5.3 Concentration over time
• $\ln[\mathrm{A}]_t - \ln[\mathrm{A}]_0 = -kt$
  First-order integrated rate law5.3 Concentration over time
• $\displaystyle \frac{1}{[\mathrm{A}]_t} - \frac{1}{[\mathrm{A}]_0} = kt$
  Second-order integrated rate law5.3 Concentration over time
• $\displaystyle t_{1/2} = \frac{0.693}{k}$
  Half-life, first order5.3 Concentration over time

Equilibrium

$K_c$ = molar concentrations · $K_p$ = gas pressures · $K_w$ = water · $K_a$ = acid · $K_b$ = base

• $\displaystyle K_c = \frac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{A}]^a[\mathrm{B}]^b},\ \text{where } a\mathrm{A} + b\mathrm{B} \rightleftharpoons c\mathrm{C} + d\mathrm{D}$
  Equilibrium constant, concentrations7.3 The reaction quotient and K7.4 Calculating K7.5 The size of K
• $\displaystyle K_p = \frac{(P_\mathrm{C})^c(P_\mathrm{D})^d}{(P_\mathrm{A})^a(P_\mathrm{B})^b}$
  Equilibrium constant, pressures7.3 The reaction quotient and K7.4 Calculating K
• $K_w = [\mathrm{H_3O^+}][\mathrm{OH^-}] = 1.0\times10^{-14}\ \text{at}\ 25^\circ\mathrm{C}$
  Water8.1 Water, pH and pOH8.3 Weak acids and bases
• $\mathrm{p}K_w = 14 = \mathrm{pH} + \mathrm{pOH}\ \text{at}\ 25^\circ\mathrm{C}$
  pH and pOH at 25 °C8.1 Water, pH and pOH
• $\mathrm{pH} = -\log[\mathrm{H_3O^+}] \qquad \mathrm{pOH} = -\log[\mathrm{OH^-}]$
  pH and pOH8.1 Water, pH and pOH8.2 Strong acids and bases8.3 Weak acids and bases
• $\displaystyle K_a = \frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]} \qquad K_b = \frac{[\mathrm{OH^-}][\mathrm{HB^+}]}{[\mathrm{B}]}$
  Acid and base ionization constants8.3 Weak acids and bases8.7 pH and pKa
• $\mathrm{p}K_a = -\log K_a \qquad \mathrm{p}K_b = -\log K_b$
  pKₐ and pK_b8.7 pH and pKa8.5 Titrations
• $K_w = K_a\times K_b \qquad \mathrm{p}K_w = \mathrm{p}K_a + \mathrm{p}K_b$
  Conjugate pairs8.3 Weak acids and bases
• $\displaystyle \mathrm{pH} = \mathrm{p}K_a + \log\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}$
  Henderson–Hasselbalch equation8.9 The Henderson–Hasselbalch equation8.8 Buffers

Thermodynamics and electrochemistry

$q$ = heat · $m$ = mass · $c$ = specific heat capacity · $T$ = temperature · $S^\circ$ = standard entropy · $H^\circ$ = standard enthalpy · $G^\circ$ = standard Gibbs free energy · $R$ = gas constant · $K$ = equilibrium constant · $n$ = number of moles of electrons · $E^\circ$ = standard potential · $I$ = current (amperes) · $q$ = charge (coulombs) · $t$ = time (seconds) · $Q$ = reaction quotient

• $q = mc\Delta T$
  Heat6.4 Heat capacity and calorimetry6.3 Heat transfer and thermal equilibrium
• $\Delta H^\circ_\text{reaction} = \sum\Delta H^\circ_{f\,\text{products}} - \sum\Delta H^\circ_{f\,\text{reactants}}$
  Enthalpy change from enthalpies of formation6.8 Enthalpy of formation
• $\Delta S^\circ_\text{reaction} = \sum S^\circ_\text{products} - \sum S^\circ_\text{reactants}$
  Entropy change9.2 Absolute entropy and entropy change
• $\Delta G^\circ_\text{reaction} = \sum\Delta G^\circ_{f\,\text{products}} - \sum\Delta G^\circ_{f\,\text{reactants}}$
  Free energy change from free energies of formation9.3 Gibbs free energy
• $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$
  Gibbs free energy9.3 Gibbs free energy9.4 Thermodynamic and kinetic control9.6 Free energy of dissolution
• $\Delta G^\circ = -RT\ln K$
  Free energy and K9.5 Free energy and equilibrium
• $\Delta G^\circ = -nFE^\circ$
  Free energy and cell potential9.9 Cell potential and free energy
• $\displaystyle I = \frac{q}{t}$
  Current9.11 Electrolysis and Faraday’s law
• $\displaystyle E_\text{cell} = E^\circ_\text{cell} - \frac{RT}{nF}\ln Q$
  Cell potential away from standard conditions (Nernst)9.10 Cell potential under nonstandard conditions