Chemistry formula sheet

Chemistry All Chemistry tools

• Collision Theory and Activation Energy Simulator

  See how few molecules clear the activation barrier, and why heating changes that so violently.

  Arrhenius (1889), with collision theory of reaction rates

  $$k = Ae^{-E_a/RT}$$

• Titration Curve Calculator

  An exact titration curve, with the equivalence pH and the indicator to match it.

  Acid-base equilibrium, after Henderson (1908) and Hasselbalch (1917)

  $$[\mathrm{H^+}] + [\mathrm{M^+}] = [\mathrm{A^-}] + [\mathrm{OH^-}]$$

• Radioactive Decay Simulator

  Individual nuclei decaying at random, against the curve the formula predicts.

  Rutherford and Soddy (1902), exponential decay law

  $$N = N_0 e^{-\lambda t}$$

• Molarity Calculator

  Solve for any one of concentration, mass, molar mass or volume, with units from nM to M.

  IUPAC definition of amount concentration

  $$c = \frac{n}{V} = \frac{m}{M \cdot V}$$

• Dilution Calculator

  Stock and diluent volumes for any target concentration, plus full serial dilution plans.

  Conservation of amount of substance on dilution

  $$c_1 V_1 = c_2 V_2$$

• Molar Mass Calculator

  Type any formula, including hydrates, and get molar mass, percent composition and grams to moles or particles.

  IUPAC standard atomic weights

  $$M = \sum_i n_i A_{r,i}$$

• pH Calculator

  pH, pOH, [H⁺] and [OH⁻] for strong or weak acids and bases, solved exactly.

  Sorensen (1909), definition of pH

  $$\mathrm{pH} = -\log_{10}[\mathrm{H^+}]$$

• Henderson-Hasselbalch Calculator

  Buffer pH from the acid-base ratio, or the ratio needed for a target pH.

  Henderson (1908) and Hasselbalch (1917)

  $$\mathrm{pH} = \mathrm{p}K_a + \log_{10}\frac{[A^-]}{[HA]}$$

• Percent Solution Calculator

  Percent w/v to g/L, mg/mL or ppm, and the mass to weigh out.

  Mass and volume concentration definitions

  $$\%\,\mathrm{w/v} = \frac{m_{\mathrm{g}}}{V_{\mathrm{mL}}} \times 100$$

• Beer-Lambert Law Calculator

  Concentration from absorbance, or any other term in A = εlc.

  Bouguer (1729), Lambert (1760) and Beer (1852)

  $$A = \varepsilon l c$$

• Half-Life Calculator

  Remaining amount, elapsed time or half-life for any decay process.

  Exponential decay, Rutherford and Soddy (1902)

  $$N = N_0 \left(\tfrac{1}{2}\right)^{t/t_{1/2}}$$

• Titration Calculator

  Find an unknown concentration from endpoint volume, with the stoichiometric ratio applied.

  Stoichiometric equivalence at the end point

  $$r\,c_1 V_1 = c_2 V_2$$

• Percent Yield Calculator

  Percent yield from actual and theoretical mass, with the shortfall.

  Definition of percentage yield

  $$\%\,\text{yield} = \frac{m_{\text{actual}}}{m_{\text{theoretical}}} \times 100$$

• Rf Value Calculator

  Rf from spot and solvent front distances, or either distance from Rf.

  IUPAC chromatography nomenclature (Ettre, 1993)

  $$R_f = \frac{d_{\text{spot}}}{d_{\text{solvent front}}}$$

• Atom Economy Calculator

  Percent atom economy from product and reactant molar masses, with the waste.

  Trost, The atom economy, Science (1991)

  $$\text{atom economy} = \frac{n\,M_{\text{product}}}{\sum n_i M_{\text{reactant},i}} \times 100\%$$

• Bond Enthalpy Calculator

  ΔH from bonds broken minus bonds formed, with a table of bond energies.

  Bond energies from OpenStax Chemistry 2e (2019), Table 7.2

  $$\Delta H \approx \sum D_{\text{broken}} - \sum D_{\text{formed}}$$

• Average Atomic Mass Calculator

  Average atomic mass from isotopes, or an isotope’s abundance from Ar.

  IUPAC definition of atomic weight; NIST isotopic compositions

  $$A_r = \frac{\sum_i m_i\,p_i}{100}$$

• Empirical Formula Calculator

  Empirical formula from composition, plus the molecular formula from molar mass.

  Law of definite proportions, Proust (1797)

  $$\text{ratio}_i = \frac{m_i / A_{r,i}}{\min_j (m_j / A_{r,j})}$$

• Limiting Reagent Calculator

  Limiting reagent, theoretical yield and percent yield in one pass.

  Reaction stoichiometry

  $$\text{extent} = \min_i \frac{n_i}{\nu_i}$$

• VSEPR Molecular Geometry

  Lone pairs drawn, so the shape has a visible reason.

  Gillespie and Nyholm (1957)

  $$\text{steric number} = n_{\text{bond}} + n_{\text{lone}}, \quad \vec{\mu}_{\text{net}} = \sum_i \hat{b}_i$$

• Crystal Lattice Explorer

  Unit cells you can turn, and the contact line that sets the maths.

  Close packing of spheres, after Kepler (1611) and Barlow (1883)

  $$\text{packing} = \frac{Z\,\pi f^{3}}{6}, \quad \rho = \frac{Z M}{N_A a^{3}}$$

• Titration Lab Simulator

  A burette, an indicator and an exact pH meter, with your endpoint measured against equivalence.

  Indicator equilibrium, after Henderson (1908) and Hasselbalch (1917)

  $$\mathrm{pH} = \mathrm{p}K_{\text{In}} + \log_{10}\frac{[\mathrm{In^-}]}{[\mathrm{HIn}]}$$

• Chemical Equation Balancer

  Balance any equation, ions and half-equations included, with the working and an atom count.

  Conservation matrix Aν = 0, IUPAC Green Book (2007) after Alberty (1991)

  $$\sum_j A_{ij}\,\nu_j = 0, \quad \sum_j z_j\,\nu_j = 0$$

• Rutherford Scattering Simulator

  Alphas fired at a nucleus: their exact paths, angles and closest approach, and the counts against Rutherford’s formula.

  Rutherford (1911), tested by Geiger and Marsden (1913)

  $$d = \frac{2Ze^{2}}{4\pi\varepsilon_0K}, \quad \tan\frac{\theta}{2} = \frac{d}{2b}, \quad N(\theta) \propto \frac{1}{\left(\sin\frac{\theta}{2}\right)^{4}}$$

• Galvanic Cell Simulator

  Two metals, two solutions and a salt bridge, run down while the voltage falls and the electrodes change mass.

  Nernst (1889), and Faraday’s laws of electrolysis (1834)

  $$E = E^\circ - \frac{RT}{nF}\ln Q, \quad \Delta m = \frac{ItM}{zF}$$

• Arrhenius Equation Calculator

  Find a reaction’s activation energy from two rate constants, or its rate constant at a new temperature.

  Arrhenius (1889), rate constants and temperature

  $$k = A\,e^{-E_a/(RT)}, \quad \ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$

• Bohr Model and Hydrogen Spectrum Simulator

  Jump an electron between Bohr orbits and read the photon’s energy, wavelength and series.

  Bohr (1913), with the Rydberg formula (1888)

  $$E_n = -13.6\,\frac{Z^{2}}{n^{2}}\ \text{eV}, \quad \frac{1}{\lambda} = R Z^{2}\left(\frac{1}{n_1^{2}} - \frac{1}{n_2^{2}}\right)$$

• Atomic Orbitals Visualizer

  Orbital shapes from the exact wavefunction, turnable, with every node counted.

  Schrödinger (1926), the hydrogen atom solved exactly

  $$\psi = R_{n\ell}(r)\,Y_{\ell m}(\theta, \phi), \quad P(r) = r^{2}R_{n\ell}(r)^{2}, \quad n - \ell - 1 \text{ radial nodes}, \quad \ell \text{ angular nodes}$$

• Integrated Rate Law Calculator

  Concentration, time, rate constant and half-life at zero, first and second order, and the order from data.

  Integrated rate laws, OpenStax Chemistry 2e (2019), section 12.4

  $$[A] = [A]_0 - kt, \quad \ln[A] = \ln[A]_0 - kt, \quad \frac{1}{[A]} = \frac{1}{[A]_0} + kt$$

• Electron Configuration Calculator

  Configurations of elements and ions in full and noble gas notation, with orbital boxes and unpaired electrons.

  Madelung (1936) and Hund (1925), with ion ground states from the NIST Atomic Spectra Database

  $$N = 2(2\ell + 1), \quad \mu = \sqrt{n(n + 2)}\,\mu_{\text{B}}$$

• Freezing Point Depression Calculator

  ΔT = i K m for freezing and boiling points, solved for the change, molality, i or molar mass.

  Raoult (1882) and van ’t Hoff (1887)

  $$\Delta T_f = i K_f m, \quad \Delta T_b = i K_b m$$

• Protons, Neutrons and Electrons Calculator

  Protons, neutrons and electrons for any isotope or ion, with the nuclide symbol.

  IUPAC definitions of atomic number and mass number

  $$p = Z, \quad n = A - Z, \quad e = Z - q$$

• Nernst Equation Calculator

  Cell potential from two half-reactions at any concentration and temperature, with the free energy, K and the working.

  Nernst (1889), with the IUPAC Green Book’s cell conventions

  $$E = E^\circ - \frac{RT}{nF}\ln Q, \quad \Delta G^\circ = -nFE^\circ = -RT\ln K$$

• Stoichiometry Calculator

  Grams to grams, moles and gas volumes through a balanced equation.

  IUPAC Green Book, stoichiometric numbers and amount of substance

  $$n_{\text{B}} = n_{\text{A}}\frac{\nu_{\text{B}}}{\nu_{\text{A}}}, \quad n = \frac{m}{M} = \frac{PV}{RT} = cV$$

• ICE Table Calculator

  Fill in an ICE table, solve for x exactly and test the small-x shortcut, or find K from equilibrium amounts.

  Guldberg and Waage (1864), law of mass action

  $$K_c = \frac{[\mathrm{C}]^{c}[\mathrm{D}]^{d}}{[\mathrm{A}]^{a}[\mathrm{B}]^{b}}$$

• Born-Haber Cycle Calculator

  Lattice enthalpy or enthalpy of formation, with the Born-Haber cycle drawn to scale and every step labelled.

  Born and Haber (1919); data from NIST, with oxygen’s second electron affinity from Huheey’s Inorganic Chemistry

  $$\Delta_{\text{f}} H = \sum \Delta_{\text{at}} H + \sum \text{IE} + \sum \text{EA} + \Delta_{\text{latt}} H$$

• NMR Splitting Pattern Visualizer

  Choose neighbours and coupling constants to draw the splitting tree and see the multiplet it makes, line by line.

  Gutowsky, McCall and Slichter, J. Chem. Phys. 21, 279 (1953)

  $$\text{lines} = (n_A + 1)(n_B + 1)(n_C + 1)$$

• Molecular Orbital Diagram Visualizer

  Molecular orbital diagrams from H2 to Ne2, filled by Aufbau and Hund’s rule, with bond order and magnetism read off.

  Mulliken (1928) and Lennard-Jones (1929), with the orbital order of OpenStax Chemistry 2e

  $$\text{bond order} = \tfrac{1}{2}\left(n_{\text{bonding}} - n_{\text{antibonding}}\right)$$

• HPLC and GC Chromatography Simulator

  Watch two to four analytes separate on an HPLC or GC column, with retention times, plate count and resolution.

  IUPAC chromatography nomenclature (Ettre, 1993)

  $$R_s = \frac{2(t_{R2} - t_{R1})}{w_1 + w_2}$$

• Cyclohexane Chair Conformation Explorer

  Flip a substituted cyclohexane chair and see which chair wins, by how many kJ/mol, and the ratio at any temperature.

  A-values from McMurry, Organic Chemistry (OpenStax, 2023), Table 4.1

  $$\Delta G^\circ = G_{\text{B}} - G_{\text{A}} = -RT\ln K$$

• R and S Configuration Explorer

  Rank four groups by the CIP rules, turn the stereocentre until group 4 points away, and read R or S from the arrow.

  Cahn, Ingold and Prelog (1966); IUPAC 2013, rule P-92

  $$(\vec{r}_1 \times \vec{r}_2) \cdot \vec{r}_3 < 0 \;\Rightarrow\; \text{R}, \qquad > 0 \;\Rightarrow\; \text{S}$$

• Crystal Field Splitting Visualizer

  Split the d orbitals in three geometries, fill them with electrons and see when Δ beats the pairing energy.

  Bethe (1929) and Van Vleck (1932), crystal field theory

  $$\mathrm{CFSE} = (-0.4x + 0.6y)\,\Delta_o + mP$$

• Photoelectron Spectroscopy Visualizer

  One peak per subshell for any atom from H to Kr, read off as a configuration, with a second element to compare.

  Einstein (1905); binding energies from Carlson (1975), Table A1.A, after Lotz (1970)

  $$E_{\text{binding}} = h\nu - E_{\text{kinetic}}$$

• Flame Test and Emission Spectrum Simulator

  Hold a salt in the flame, see its colour, and split it into the lines and bands that make it.

  Kirchhoff and Bunsen (1860), Chemical Analysis by Spectrum Observations

  $$\Delta E = \frac{hc}{\lambda}$$

• Lewis Structure Generator

  Type a formula or ion and watch its Lewis structure build, with formal charges and resonance.

  Formal charge, OpenStax Chemistry 2e (2019), section 7.4

  $$\text{FC} = V - N - \tfrac{B}{2}$$

• Newman Projection and Conformation Explorer

  Turn a C−C bond and watch the Newman projection, the sawhorse and the energy curve follow.

  Interaction energies from McMurry, Organic Chemistry (OpenStax, 2023), Table 3.5

  $$\frac{N_{\text{gauche}}}{N_{\text{anti}}} = 2\,e^{-\Delta E/RT}$$