Chemistry Formulas and Reactions

\documentclass{article}
\usepackage[version=4]{mhchem}

\begin{document}

\section{Chemical Formulas}

% Simple formulas
Water: \ce{H2O}

Sulfuric acid: \ce{H2SO4}

Methane: \ce{CH4}

% Complex formulas with charges
Hydronium ion: \ce{H3O+}

Sulfate ion: \ce{SO4^2-}

Ammonium: \ce{NH4+}

% Isotopes
Carbon-14: \ce{^14C}

Uranium-235: \ce{^235U}

Deuterium oxide: \ce{^2H2O}

% States of matter
Solid sodium chloride: \ce{NaCl_{(s)}}

Aqueous hydrochloric acid: \ce{HCl_{(aq)}}

Gaseous carbon dioxide: \ce{CO2_{(g)}}

Liquid water: \ce{H2O_{(l)}}

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\documentclass{article}
\usepackage[version=4]{mhchem}

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\section{Chemical Reactions}

% Simple reaction
\ce{2H2 + O2 -> 2H2O}

% Reversible reaction
\ce{N2 + 3H2 <=> 2NH3}

% Equilibrium with conditions
\ce{CaCO3_{(s)} <=>[\Delta] CaO_{(s)} + CO2_{(g)}}

% Multiple steps
\begin{align}
\ce{CH4 + 2O2 &-> CO2 + 2H2O} \\
\ce{2H2 + O2 &-> 2H2O} \\
\ce{C + O2 &-> CO2}
\end{align}

\section{Complex Reactions}

% Precipitation reaction
\ce{AgNO3_{(aq)} + NaCl_{(aq)} -> AgCl_{(s)} v + NaNO3_{(aq)}}

% Acid-base reaction
\ce{HCl_{(aq)} + NaOH_{(aq)} -> NaCl_{(aq)} + H2O_{(l)}}

% Oxidation-reduction
\ce{Zn_{(s)} + Cu^2+_{(aq)} -> Zn^2+_{(aq)} + Cu_{(s)}}

% Organic reaction with mechanism
\ce{CH3CH2OH ->[H2SO4][\Delta] CH2=CH2 + H2O}

% Enzyme-catalyzed reaction
\ce{glucose + O2 ->[enzyme] CO2 + H2O + ATP}

\section{Reaction Mechanisms}

% Nucleophilic substitution
\ce{R-X + Nu^- -> R-Nu + X^-}

% Addition reaction
\ce{CH2=CH2 + HBr -> CH3CH2Br}

% Elimination reaction
\ce{CH3CH2Br + OH^- -> CH2=CH2 + Br^- + H2O}

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\documentclass{article}
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\usepackage{amsmath}

\begin{document}

\section{Advanced Chemical Notation}

% Coordination compounds
Hexaamminecobalt(III) chloride: \ce{[Co(NH3)6]Cl3}

Potassium hexacyanoferrate(II): \ce{K4[Fe(CN)6]}

% Transition states
\ce{A + B ->[TS] P}

% Catalysts above arrows
\ce{benzene ->[AlCl3] methylbenzene}

\ce{ethene + H2 ->[Ni][\Delta] ethane}

% Multiple arrows
\ce{A ->[k1] B ->[k2] C}

\ce{reactants <=>[\ce{k_{forward}}][\ce{k_{reverse}}] products}

% Electron configurations
Ground state oxygen: \ce{[He] 2s^2 2p^4}

Excited state carbon: \ce{[He] 2s^1 2p^3}

\section{Thermodynamic Notation}

% Enthalpy changes
\ce{CH4_{(g)} + 2O2_{(g)} -> CO2_{(g)} + 2H2O_{(l)}} \quad $\Delta H = -890$ kJ/mol

% Equilibrium expressions
\ce{N2_{(g)} + 3H2_{(g)} <=> 2NH3_{(g)}} \quad $K_c = \frac{[\ce{NH3}]^2}{[\ce{N2}][\ce{H2}]^3}$

% Rate expressions
Rate = $k[\ce{A}]^m[\ce{B}]^n$

\section{Biochemical Notation}

% Amino acids
Glycine: \ce{NH2CH2COOH}

Alanine: \ce{NH2CH(CH3)COOH}

% Phosphorylation
\ce{ATP + H2O -> ADP + Pi + energy}

% DNA bases
Adenine: \ce{C5H5N5}

Guanine: \ce{C5H5N5O}

\end{document}

\documentclass{article}
\usepackage{chemfig}

\begin{document}

\section{Basic Molecular Structures}

% Simple molecules
Methane: \chemfig{C(-[1]H)(-[3]H)(-[5]H)(-[7]H)}

Water: \chemfig{H-O-H}

Ammonia: \chemfig{N(-[1]H)(-[5]H)(-[7]H)}

% Linear molecules
Ethane: \chemfig{H_3C-CH_3}

Propane: \chemfig{H_3C-CH_2-CH_3}

% Branched molecules
Isobutane: \chemfig{H_3C-CH(-[2]CH_3)-CH_3}

% Double bonds
Ethene: \chemfig{H_2C=CH_2}

Carbon dioxide: \chemfig{O=C=O}

% Triple bonds
Ethyne: \chemfig{HC~CH}

Hydrogen cyanide: \chemfig{H-C~N}

\section{Cyclic Structures}

% Cyclohexane
\chemfig{*6(------)}

% Benzene
\chemfig{*6(=-==-=)}

% Cyclopentane
\chemfig{*5(-----)}

% Substituted benzene
Toluene: \chemfig{*6(=-=(-CH_3)-=)}

Phenol: \chemfig{*6(=-=(-OH)-=)}

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\documentclass{article}
\usepackage{chemfig}

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\section{Complex Organic Molecules}

% Glucose
Glucose: \chemfig{HO-[1,0.5,2]?<[7,0.7]OH>[1,0.7]?<[2,0.5]OH>[3,0.7]?<[4]OH>[4,0.7]?<[3,0.5]OH>[7,0.7]?(-[1,0.3]O-[7,0.3]?)}

% Caffeine
Caffeine: \chemfig{*6((-N*5(-(-CH_3)-N=-N(-CH_3)-))=N-=(-N(-CH_3))=*6(-(-=O)-N(-CH_3)-(-=O)-N=-=))}

% Cholesterol (simplified)
Cholesterol: \chemfig{*6((-*6(-----(-OH)))---(-*5(---(-*6(------))--))-(-(=)-(-[1])-([7]))---)}

\section{Functional Groups}

% Alcohol
Primary alcohol: \chemfig{R-CH_2-OH}

Secondary alcohol: \chemfig{R-CH(-[2]OH)-R'}

Tertiary alcohol: \chemfig{R-C(-[2]OH)(-[6]R')(-[7]R'')}

% Carbonyl compounds
Aldehyde: \chemfig{R-C(=[2]O)-H}

Ketone: \chemfig{R-C(=[2]O)-R'}

% Carboxylic acid derivatives
Carboxylic acid: \chemfig{R-C(=[2]O)-OH}

Ester: \chemfig{R-C(=[2]O)-O-R'}

Amide: \chemfig{R-C(=[2]O)-N(-[6]H)-H}

% Aromatic functional groups
Aniline: \chemfig{*6(=-=(-NH_2)-=)}

Benzoic acid: \chemfig{*6(=-=(-C(=[2]O)-OH)-=)}

\section{Stereochemistry}

% Wedge and dash bonds
Tetrahedral carbon: \chemfig{C(-[1,,,1]H)(-[3,,,2]Cl)(-[5]Br)(-[7]F)}

% Chair conformation
Cyclohexane chair: \chemfig{*6((-[2]H)(-[6]H)-(-[2]H)(-[6]H)-(-[2]H)(-[6]H)---)}

% Newman projection
Newman projection: \chemfig{*6((-H)(-H)(-H)-*6((-H)(-H)(-H)---)---)}

\end{document}

\documentclass{article}
\usepackage{chemfig}
\usepackage[version=4]{mhchem}

\begin{document}

\section{Organic Reaction Schemes}

% SN2 reaction
\schemestart
\chemfig{H_3C-CH_2-Br}
\+
\chemfig{OH^{-}}
\arrow{->[SN2]}
\chemfig{H_3C-CH_2-OH}
\+
\chemfig{Br^{-}}
\schemestop

% Addition reaction
\schemestart
\chemfig{H_2C=CH_2}
\+
\chemfig{HBr}
\arrow{->}
\chemfig{H_3C-CH_2Br}
\schemestop

% Multistep synthesis
\schemestart
\chemfig{*6(=-=(-CH_3)-=)}
\arrow{->[KMnO_4][H^+, heat]}
\chemfig{*6(=-=(-C(=[2]O)-OH)-=)}
\arrow{->[SOCl_2]}
\chemfig{*6(=-=(-C(=[2]O)-Cl)-=)}
\arrow{->[NH_3]}
\chemfig{*6(=-=(-C(=[2]O)-NH_2)-=)}
\schemestop

\section{Biochemical Pathways}

% Glycolysis step
\schemestart
\chemfig{glucose}
\arrow{->[hexokinase][ATP, Mg^{2+}]}
\chemfig{glucose-6-phosphate}
\arrow{->[phosphoglucose isomerase]}
\chemfig{fructose-6-phosphate}
\schemestop

% Peptide bond formation
\schemestart
\chemfig{H_2N-CH(-[6]R_1)-C(=[2]O)-OH}
\+
\chemfig{H_2N-CH(-[6]R_2)-C(=[2]O)-OH}
\arrow{->[condensation][-H_2O]}
\chemfig{H_2N-CH(-[6]R_1)-C(=[2]O)-NH-CH(-[6]R_2)-C(=[2]O)-OH}
\schemestop

\section{Coordination Chemistry}

% Octahedral complex
Octahedral \ce{[Co(NH3)6]^3+}:
\chemfig{Co(-[0]NH_3)(-[60]NH_3)(-[120]NH_3)(-[180]NH_3)(-[240]NH_3)(-[300]NH_3)}

% Square planar complex
Square planar \ce{[PtCl4]^2-}:
\chemfig{Pt(-[0]Cl)(-[90]Cl)(-[180]Cl)(-[270]Cl)}

% Chelating ligand
EDTA complex:
\chemfig{(-[1]OOC-CH_2)_2N-CH_2-CH_2-N(-[7]CH_2-COO)_2}

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\section{NMR Spectroscopy}

% Chemical shifts
\ce{^1H} NMR (400 MHz, CDCl$_3$): $\delta$ 7.26 (s, 5H, Ph), 3.85 (s, 3H, OCH$_3$), 2.45 (t, 2H, CH$_2$)

\ce{^13C} NMR (100 MHz, CDCl$_3$): $\delta$ 170.2 (C=O), 128.5 (Ar-C), 55.2 (OCH$_3$), 34.1 (CH$_2$)

% Coupling constants
\ce{^1H} NMR: $\delta$ 6.95 (d, $J$ = 8.0 Hz, 2H), 4.12 (q, $J$ = 7.2 Hz, 2H)

% Two-dimensional NMR
COSY, HSQC, and HMBC correlations confirm the structure.

\section{IR Spectroscopy}

IR (KBr): $\tilde{\nu}$ = \SI{3300}{\per\centi\meter} (O-H stretch), \SI{1720}{\per\centi\meter} (C=O stretch), \SI{1600}{\per\centi\meter} (C=C stretch)

FT-IR (neat): \SI{2950}{\per\centi\meter} (C-H stretch), \SI{1735}{\per\centi\meter} (ester C=O), \SI{1250}{\per\centi\meter} (C-O stretch)

\section{Mass Spectrometry}

MS (EI, 70 eV): $m/z$ (\%) = 180 (M$^+$, 45), 152 (M$^+$ - CO, 100), 124 (M$^+$ - 2CO, 75)

HRMS (ESI): $m/z$ calculated for \ce{C10H12NO2} [M+H]$^+$ 178.0868, found 178.0865

\section{Elemental Analysis}

Anal. Calculated for \ce{C15H14N2O3}: C, 66.66; H, 5.22; N, 10.36. Found: C, 66.58; H, 5.18; N, 10.41.

\section{Crystallography}

Crystal data: \ce{C12H10N2O}, $M$ = 198.22, monoclinic, space group $P2_1/c$, $a$ = \SI{7.123}{\angstrom}, $b$ = \SI{15.456}{\angstrom}, $c$ = \SI{9.876}{\angstrom}, $\beta$ = 105.23°, $V$ = \SI{1045.2}{\angstrom\cubed}, $Z$ = 4.

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\section{Thermodynamics}

% Standard formation enthalpies
$\Delta_f H^\circ$ (\ce{H2O}, l) = \SI{-285.8}{\kilo\joule\per\mole}

$\Delta_f H^\circ$ (\ce{CO2}, g) = \SI{-393.5}{\kilo\joule\per\mole}

% Gibbs free energy
$\Delta G = \Delta H - T\Delta S$

For the reaction \ce{N2 + 3H2 <=> 2NH3}:
$\Delta G^\circ = -2 \times \SI{16.5}{\kilo\joule\per\mole} = \SI{-33.0}{\kilo\joule\per\mole}$

% Equilibrium constant
$K_p = \frac{P_{\ce{NH3}}^2}{P_{\ce{N2}} \cdot P_{\ce{H2}}^3}$

$\ln K = -\frac{\Delta G^\circ}{RT}$

\section{Chemical Kinetics}

% Rate laws
For \ce{A + B -> C}, the rate law is:
\[
\text{Rate} = k[\ce{A}]^m[\ce{B}]^n
\]

% Integrated rate laws
First order: $\ln[\ce{A}] = \ln[\ce{A}]_0 - kt$

Second order: $\frac{1}{[\ce{A}]} = \frac{1}{[\ce{A}]_0} + kt$

% Arrhenius equation
$k = A e^{-E_a/RT}$

$\ln k = \ln A - \frac{E_a}{RT}$

\section{Electrochemistry}

% Nernst equation
$E = E^\circ - \frac{RT}{nF} \ln Q$

At 298 K: $E = E^\circ - \frac{0.0592}{n} \log Q$

% Standard reduction potentials
\ce{Cu^2+ + 2e^- -> Cu} \quad $E^\circ = +\SI{0.34}{\volt}$

\ce{Zn^2+ + 2e^- -> Zn} \quad $E^\circ = -\SI{0.76}{\volt}$

% Cell notation
\ce{Zn | Zn^2+ (1 M) || Cu^2+ (1 M) | Cu}

$E_{\text{cell}}^\circ = E_{\text{cathode}}^\circ - E_{\text{anode}}^\circ = 0.34 - (-0.76) = \SI{1.10}{\volt}$

\section{Quantum Chemistry}

% Schrödinger equation
$\hat{H}\Psi = E\Psi$

% Hydrogen atom wavefunctions
$\Psi_{1s} = \frac{1}{\sqrt{\pi a_0^3}} e^{-r/a_0}$

% Molecular orbitals
For \ce{H2^+}: $\Psi_{\pm} = \frac{1}{\sqrt{2 \pm 2S}}(\phi_A \pm \phi_B)$

% Electronic configurations
\ce{C}: $1s^2 2s^2 2p^2$

\ce{Fe^3+}: $[\ce{Ar}] 3d^5$

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\documentclass{article}
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\usepackage{chemfig}
\usepackage{modiagram}

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\section{Package Comparison}

\begin{tabular}{|l|l|l|}
\hline
\textbf{Package} & \textbf{Best For} & \textbf{Examples} \\
\hline
mhchem & Chemical equations & \ce{H2SO4}, \ce{A + B -> C} \\
& Formulas with charges & \ce{NH4+}, \ce{SO4^2-} \\
& Reaction arrows & \ce{A <=> B} \\
\hline
chemfig & Molecular structures & Benzene rings, stereochemistry \\
& Organic molecules & Complex natural products \\
& Reaction schemes & Multi-step syntheses \\
\hline
modiagram & Molecular orbitals & MO diagrams \\
& Electronic structure & Energy level diagrams \\
\hline
\end{tabular}

\section{Molecular Orbital Diagrams}

% Simple MO diagram for H2
\begin{modiagram}[labels]
\atom[N]{left}{1s}
\atom[N]{right}{1s}
\molecule[N]{
1sigma = {0; pair}
}
\end{modiagram}

% More complex example for O2
\begin{modiagram}[labels]
\atom[O]{left}{2s, 2p = {;pair,up,up}}
\atom[O]{right}{2s, 2p = {;pair,up,up}}
\molecule[O2]{
2sigma = {0; pair},
2sigma* = {1.5; },
2piy = {-1; pair},
2piz = {-1; pair},
2pix = {0.5; up, up},
2pix* = {2; }
}
\end{modiagram}

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\documentclass{article}
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% Custom commands for common notation
\newcommand{\conc}[1]{[\ce{#1}]}
\newcommand{\std}{\circ}

\begin{document}

\title{Synthesis and Characterization of Novel Organic Compounds}
\author{Chemistry Department}
\maketitle

\section{Experimental}

\subsection{Synthesis of Compound 1}

To a solution of \ce{benzaldehyde} (\SI{1.06}{\gram}, \SI{10.0}{\milli\mole}) in dry \ce{CH2Cl2} (\SI{20}{\milli\liter}) was added \ce{NaBH4} (\SI{0.38}{\gram}, \SI{10.0}{\milli\mole}) at \SI{0}{\celsius}. The reaction mixture was stirred for \SI{2}{\hour} at room temperature.

\schemestart
\chemfig{*6(=-=(-CHO)-=)}
\arrow{->[NaBH_4][CH_2Cl_2, rt]}
\chemfig{*6(=-=(-CH_2OH)-=)}
\schemestop

\subsection{Characterization}

\textbf{Compound 1}: Colorless oil. Yield: \SI{92}{\percent}.

\textbf{\ce{^1H} NMR} (400 MHz, CDCl$_3$): $\delta$ 7.38-7.28 (m, 5H, Ar-H), 4.68 (s, 2H, CH$_2$), 2.15 (br s, 1H, OH).

\textbf{\ce{^13C} NMR} (100 MHz, CDCl$_3$): $\delta$ 140.8, 128.4, 127.6, 126.9, 65.1.

\textbf{IR} (neat): $\tilde{\nu}$ = \SI{3330}{\per\centi\meter} (O-H), \SI{3030}{\per\centi\meter} (Ar-H), \SI{2924}{\per\centi\meter} (C-H), \SI{1496}{\per\centi\meter}, \SI{1454}{\per\centi\meter} (Ar).

\textbf{MS} (EI): $m/z$ (\%) = 108 (M$^+$, 25), 79 (100), 77 (85).

\section{Results and Discussion}

The reaction proceeded via a nucleophilic addition mechanism:

\begin{align}
\ce{C6H5CHO + BH4^- &-> C6H5CH2O^-BH3} \\
\ce{C6H5CH2O^-BH3 + H2O &-> C6H5CH2OH + B(OH)3 + H2}
\end{align}

The equilibrium constant for the hydride transfer is:
\[
K_{eq} = \frac{\conc{C6H5CH2O^-BH3}}{\conc{C6H5CHO}\conc{BH4^-}}
\]

Thermodynamic analysis shows $\Delta G\std = \SI{-15.2}{\kilo\joule\per\mole}$ for this transformation at \SI{298}{\kelvin}.

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