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Formula Sheet
Every constant and equation used on this site, in one place. Print it, bookmark it, or keep it open beside your homework.
Physical Constants
| Constant | Symbol | Value |
|---|
| Avogadro's number | $N_A$ | $6.022 \times 10^{23}\ \text{mol}^{-1}$ |
| Gas constant | $R$ | $8.314\ \text{J/mol·K} = 0.08206\ \text{L·atm/mol·K}$ |
| Planck's constant | $h$ | $6.626 \times 10^{-34}\ \text{J·s}$ |
| Speed of light | $c$ | $3.00 \times 10^8\ \text{m/s}$ |
| Elementary charge | $e$ | $1.602 \times 10^{-19}\ \text{C}$ |
| Faraday constant | $F$ | $96{,}485\ \text{C/mol}$ |
| Boltzmann constant | $k_B$ | $1.381 \times 10^{-23}\ \text{J/K}$ |
| Electron mass | $m_e$ | $9.109 \times 10^{-31}\ \text{kg}$ |
| Proton mass | $m_p$ | $1.673 \times 10^{-27}\ \text{kg}$ |
| Neutron mass | $m_n$ | $1.675 \times 10^{-27}\ \text{kg}$ |
| Atomic mass unit | $1\ \text{amu}$ | $1.6605 \times 10^{-27}\ \text{kg}$ |
| Rydberg constant | $R_H$ | $1.097 \times 10^7\ \text{m}^{-1}$ ($2.18 \times 10^{-18}$ J) |
| Ion product of water (25 °C) | $K_w$ | $1.0 \times 10^{-14}$ |
| Standard pressure | $1\ \text{atm}$ | $101.325\ \text{kPa} = 760\ \text{mmHg} = 760\ \text{torr}$ |
| Absolute zero | $0\ \text{K}$ | $-273.15\ \text{°C}$ |
Unit Conversions
| Conversion | Relation |
|---|
| Temperature | $K = \text{°C} + 273.15$ |
| Length | $1\ \text{Å} = 10^{-10}\ \text{m}$; $1\ \text{nm} = 10^{-9}\ \text{m}$ |
| Volume | $1\ \text{L} = 1000\ \text{mL} = 1000\ \text{cm}^3$ |
| Energy | $1\ \text{cal} = 4.184\ \text{J}$; $1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$ |
| Pressure | $1\ \text{atm} = 101.325\ \text{kPa} = 760\ \text{mmHg}$ |
| Mass | $1\ \text{amu} = 1.6605 \times 10^{-27}\ \text{kg}$ |
Stoichiometry
| Equation | Use |
|---|
| $$n = \frac{m}{M}$$ | Moles from mass (M = molar mass) |
| $$\text{Percent yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\%$$ | Reaction efficiency |
| $$M_1V_1 = M_2V_2$$ | Dilution |
| $$\text{Average mass} = \sum (\text{fraction} \times \text{isotope mass})$$ | Average atomic mass |
Gases
| Equation | Use |
|---|
| $$PV = nRT$$ | Ideal gas law |
| $$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$ | Combined gas law |
| $$P_{\text{total}} = P_1 + P_2 + \cdots$$ | Dalton's law of partial pressures |
| $$\frac{\text{rate}_1}{\text{rate}_2} = \sqrt{\frac{M_2}{M_1}}$$ | Graham's law of effusion |
Thermochemistry and Thermodynamics
| Equation | Use |
|---|
| $$q = mc\Delta T$$ | Heat from a temperature change |
| $$\Delta H^\circ_{rxn} = \sum n\,\Delta H^\circ_f(\text{products}) - \sum n\,\Delta H^\circ_f(\text{reactants})$$ | Standard enthalpy of reaction |
| $$\Delta G = \Delta H - T\Delta S$$ | Gibbs free energy (spontaneity) |
| $$\Delta G^\circ = -RT \ln K$$ | Free energy and the equilibrium constant |
Kinetics
| Equation | Use |
|---|
| $$\text{rate} = k[\text{A}]^m[\text{B}]^n$$ | Rate law (orders from experiment) |
| $$t_{1/2} = \frac{0.693}{k}$$ | Half-life, first-order reactions |
| $$k = Ae^{-E_a/RT}$$ | Arrhenius equation |
| $$\ln\frac{k_2}{k_1} = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$ | Rate constants at two temperatures |
Equilibrium
| Equation | Use |
|---|
| $$K_{eq} = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$$ | Equilibrium constant |
| $$K_{sp} = [\text{cation}]^a[\text{anion}]^b$$ | Solubility product (solids omitted) |
| $$\Delta G^\circ = -RT \ln K$$ | Free energy and K |
Acids and Bases
| Equation | Use |
|---|
| $$\text{pH} = -\log[\text{H}_3\text{O}^+] \qquad \text{pOH} = -\log[\text{OH}^-]$$ | pH and pOH |
| $$\text{pH} + \text{pOH} = 14.00 \quad (25\,^\circ\text{C})$$ | pH–pOH relation |
| $$K_a \cdot K_b = K_w$$ | Conjugate acid–base pairs |
| $$\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}$$ | Henderson–Hasselbalch (buffers) |
Electrochemistry
| Equation | Use |
|---|
| $$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$ | Standard cell potential |
| $$\Delta G^\circ = -nFE^\circ$$ | Free energy from cell potential |
| $$E = E^\circ - \frac{0.0592}{n}\log Q \quad (25\,^\circ\text{C})$$ | Nernst equation |
Solutions
| Equation | Use |
|---|
| $$M = \frac{n_{\text{solute}}}{V_{\text{solution (L)}}} \qquad m = \frac{n_{\text{solute}}}{\text{kg solvent}}$$ | Molarity and molality |
| $$\Delta T_f = iK_f m \qquad \Delta T_b = iK_b m \qquad \pi = iMRT$$ | Colligative properties |
| $$C = k_H P$$ | Henry's law (gas solubility) |
| $$P = X \cdot P^\circ$$ | Raoult's law (vapour pressure) |