Chemistry equations in Markdown to PDF

# Chemistry and life sciences

## Reactions and equilibrium

$ \mathrm{2\,H_2 + O_2 \longrightarrow 2\,H_2O} \qquad \mathrm{N_2 + 3\,H_2 \rightleftharpoons 2\,NH_3} \qquad \mathrm{CaCO_3 \overset{\Delta}{\longrightarrow} CaO + CO_2} $

For $a\mathrm{A} + b\mathrm{B} \rightleftharpoons c\mathrm{C} + d\mathrm{D}$ the equilibrium constant and the reaction quotient are

$ K_c = \frac{[\mathrm{C}]^c\,[\mathrm{D}]^d}{[\mathrm{A}]^a\,[\mathrm{B}]^b} \qquad \Delta G = \Delta G^{\circ} + RT \ln Q \qquad \Delta G^{\circ} = -RT \ln K $

## Kinetics

Rate laws, the Arrhenius equation and the half-life of a first-order process:

$ r = k\,[\mathrm{A}]^m [\mathrm{B}]^n \qquad k = A\, e^{-E_a / RT} \qquad \ln \frac{k_2}{k_1} = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \qquad t_{1/2} = \frac{\ln 2}{k} $

Michaelis-Menten enzyme kinetics and its linearized form:

$ v = \frac{V_{\max}\,[\mathrm{S}]}{K_m + [\mathrm{S}]} \qquad \frac{1}{v} = \frac{K_m}{V_{\max}} \cdot \frac{1}{[\mathrm{S}]} + \frac{1}{V_{\max}} $

## Acids, bases and electrochemistry

$ \mathrm{pH} = -\log_{10} [\mathrm{H^+}] \qquad \mathrm{pH} = \mathrm{p}K_a + \log_{10} \frac{[\mathrm{A^-}]}{[\mathrm{HA}]} \qquad K_w = [\mathrm{H^+}][\mathrm{OH^-}] = 10^{-14} \text{ at } 25\ ^\circ\mathrm{C} $

$ E = E^{\circ} - \frac{RT}{nF} \ln Q \qquad \Delta G^{\circ} = -nFE^{\circ} \qquad \mathrm{Zn} + \mathrm{Cu^{2+}} \longrightarrow \mathrm{Zn^{2+}} + \mathrm{Cu} $

## Gases and solutions

$ pV = nRT \qquad \left( p + \frac{a n^2}{V^2} \right)(V - nb) = nRT \qquad A = \varepsilon\, \ell\, c \qquad \Pi = i\, c\, R\, T $

## Nuclear and radiological

$ N(t) = N_0\, e^{-\lambda t} \qquad A(t) = \lambda N(t) \qquad E = \Delta m\, c^2 \qquad {}^{14}_{6}\mathrm{C} \longrightarrow {}^{14}_{7}\mathrm{N} + e^- + \bar{\nu}_e $

## Population and pharmacology

Logistic growth, and the one-compartment model with first-order elimination:

$ \frac{\mathrm{d}N}{\mathrm{d}t} = rN \left( 1 - \frac{N}{K} \right) \qquad C(t) = \frac{D}{V_d}\, e^{-k_e t} \qquad t_{1/2} = \frac{0.693\, V_d}{\mathrm{CL}} \qquad \mathrm{AUC} = \int_0^{\infty} C(t)\,\mathrm{d}t = \frac{D}{\mathrm{CL}} $

Hardy-Weinberg equilibrium for two alleles with frequencies $p$ and $q$:

$ p^2 + 2pq + q^2 = 1, \qquad p + q = 1 $

| Quantity | Symbol | Typical value |
|:---------|:------:|:--------------|
| Gas constant | $R$ | $8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$ |
| Faraday constant | $F$ | $96\,485\ \mathrm{C\,mol^{-1}}$ |
| Avogadro constant | $N_A$ | $6.022 \times 10^{23}\ \mathrm{mol^{-1}}$ |
| Half-life of carbon-14 | $t_{1/2}$ | $5{,}730$ years |