Formula Sheet
Every key formula of the course on one page, grouped by chapter, with a link back to the section that develops it.
Chapter 1 · Solutions
Percentages and ppm§ 1.1 →
$\text{mass \%}=\dfrac{m_{\text{component}}}{m_{\text{solution}}}\times100$, $\ \text{w/v \%}=\dfrac{\text{g solute}}{\text{mL solution}}\times100$, $\ \text{ppm}=\dfrac{\text{parts of component}}{\text{total parts}}\times10^{6}$
Mole fraction§ 1.1 →
$x_{2}=\dfrac{n_{2}}{n_{1}+n_{2}},\quad x_{1}+x_{2}=1$ (no unit; temperature-independent)
Molarity and molality§ 1.1 →
$M=\dfrac{n_{2}}{V_{\text{solution}}/\mathrm{L}}\ \mathrm{mol\,L^{-1}}$ (changes with $T$); $\ m=\dfrac{n_{2}}{\text{mass of solvent}/\mathrm{kg}}\ \mathrm{mol\,kg^{-1}}$ (does not)
Converting units ($d$ in $\mathrm{g\,mL^{-1}}$, molar masses in $\mathrm{g\,mol^{-1}}$, $w$ = mass fraction of solute)§ 1.1 →
$M=\dfrac{1000\,d\,w}{M_{2}},\qquad m=\dfrac{1000\,M}{1000\,d-M\,M_{2}},\qquad x_{2}=\dfrac{m\,M_{1}}{1000+m\,M_{1}}$
Henry's law§ 1.1 →
$p=K_{H}\,x$ at constant $T$ (dilute solution, gas not reacting with the solvent); larger $K_{H}$ ⇒ less soluble; $K_{H}$ rises with $T$
Raoult's law (volatile components, ideal solution)§ 1.2 →
$p_{1}=x_{1}\,p_{1}^{\circ},\quad p_{2}=x_{2}\,p_{2}^{\circ}$ (constant $T$)
Total vapour pressure of an ideal binary solution§ 1.2 →
$p_{\text{total}}=x_{1}p_{1}^{\circ}+x_{2}p_{2}^{\circ}=p_{1}^{\circ}+\left(p_{2}^{\circ}-p_{1}^{\circ}\right)x_{2}$
Vapour composition (ideal solution)§ 1.2 →
$y_{1}=\dfrac{x_{1}p_{1}^{\circ}}{p_{\text{total}}},\qquad \dfrac{1}{p_{\text{total}}}=\dfrac{y_{1}}{p_{1}^{\circ}}+\dfrac{y_{2}}{p_{2}^{\circ}}$
Non-volatile solute (dilute, no dissociation)§ 1.2 →
$p_{1}=x_{1}\,p_{1}^{\circ},\quad \Delta p_{1}=p_{1}^{\circ}-p_{1}=x_{2}\,p_{1}^{\circ}$
Ideal and non-ideal solutions§ 1.2 →
Ideal: $\Delta_{mix}H=0$, $\Delta_{mix}V=0$. Positive deviation: $p\gt p_{\text{Raoult}}$, $\Delta_{mix}H\gt0$, $\Delta_{mix}V\gt0$ (minimum-boiling azeotrope). Negative deviation: $p\lt p_{\text{Raoult}}$, $\Delta_{mix}H\lt0$, $\Delta_{mix}V\lt0$ (maximum-boiling azeotrope).
Relative lowering of vapour pressure (non-volatile solute)§ 1.3 →
$\dfrac{p_{1}^{\circ}-p_{1}}{p_{1}^{\circ}}=x_{2}=\dfrac{n_{2}}{n_{1}+n_{2}}\approx\dfrac{w_{2}M_{1}}{M_{2}w_{1}}$ (dilute)
Elevation of boiling point ($w$ in g)§ 1.3 →
$\Delta T_{b}=K_{b}\,m=\dfrac{K_{b}\times1000\,w_{2}}{M_{2}\,w_{1}},\qquad K_{b}=\dfrac{RM_{1}(T_{b}^{\circ})^{2}}{1000\,\Delta_{vap}H}$
Depression of freezing point ($w$ in g)§ 1.3 →
$\Delta T_{f}=K_{f}\,m=\dfrac{K_{f}\times1000\,w_{2}}{M_{2}\,w_{1}},\qquad K_{f}=\dfrac{RM_{1}(T_{f}^{\circ})^{2}}{1000\,\Delta_{fus}H}$
Osmotic pressure ($R=0.083\ \mathrm{L\,bar\,mol^{-1}\,K^{-1}}$)§ 1.3 →
$\pi=CRT=\dfrac{n_{2}RT}{V},\qquad M_{2}=\dfrac{w_{2}RT}{\pi V}$
van 't Hoff factor§ 1.3 →
$i=\dfrac{\text{normal }M}{\text{abnormal }M}$; dissociation into $\nu$ particles: $i=1+(\nu-1)\alpha$; association into $n$-mers: $i=1-\left(1-\tfrac1n\right)\beta$
Modified equations§ 1.3 →
$\Delta T_{b}=iK_{b}m,\quad \Delta T_{f}=iK_{f}m,\quad \pi=iCRT$
Chapter 2 · Electrochemistry
Daniell cell§ 2.1 →
$\mathrm{Zn(s)\,|\,Zn^{2+}(aq)\,\|\,Cu^{2+}(aq)\,|\,Cu(s)}$; $\ \mathrm{Zn(s)+Cu^{2+}(aq)\rightarrow Zn^{2+}(aq)+Cu(s)}$, $E^{\circ}_{cell}=1.10\ \mathrm{V}$
Cell notation§ 2.1 →
anode (oxidation, $-$) on the left $\|$ cathode (reduction, $+$) on the right; $|$ = phase boundary, $\|$ = salt bridge; inert Pt for gas or ion–ion couples
Standard hydrogen electrode§ 2.1 →
$\mathrm{Pt(s)\,|\,H_{2}(g,\ 1\ bar)\,|\,H^{+}(aq,\ 1\ M)}$, $\ \mathrm{2H^{+}(aq)+2e^{-}\rightarrow H_{2}(g)}$, $\ E^{\circ}=0.00\ \mathrm{V}$ by definition
Standard EMF (both values are standard reduction potentials; never multiply $E^{\circ}$ by coefficients)§ 2.1 →
$E^{\circ}_{cell}=E^{\circ}_{R}-E^{\circ}_{L}=E^{\circ}_{\text{cathode}}-E^{\circ}_{\text{anode}}$; $\ E^{\circ}_{cell}\gt0$ ⇒ spontaneous as written
Reading the electrochemical series§ 2.1 →
higher $E^{\circ}$ ⇒ stronger oxidising agent; lower $E^{\circ}$ ⇒ stronger reducing agent; a metal displaces the ions of metals above it; metals with $E^{\circ}\lt0$ liberate $\mathrm{H_{2}}$ from $1\ \mathrm{M}$ acid
Nernst equation for an electrode (Ox + $ne^{-}$ → Red; solids = 1, gases in bar)§ 2.2 →
$E=E^{\circ}-\dfrac{2.303RT}{nF}\log\dfrac{[\text{Red}]}{[\text{Ox}]}$; at 298 K $\ E_{\mathrm{M^{n+}/M}}=E^{\circ}-\dfrac{0.059}{n}\log\dfrac{1}{[\mathrm{M^{n+}}]}$
Nernst equation for a cell ($n$ = electrons in the balanced cell reaction)§ 2.2 →
$E_{cell}=E^{\circ}_{cell}-\dfrac{0.059}{n}\log Q$ at 298 K; Daniell: $E_{cell}=1.10-\dfrac{0.059}{2}\log\dfrac{[\mathrm{Zn^{2+}}]}{[\mathrm{Cu^{2+}}]}$
Hydrogen electrode ($p_{\mathrm{H_{2}}}=1$ bar, 298 K)§ 2.2 →
$E_{\mathrm{H^{+}/H_{2}}}=-0.059\,\mathrm{pH}$
EMF and Gibbs energy ($F=96\,487\ \mathrm{C\,mol^{-1}}$)§ 2.2 →
$\Delta_{r}G=-nFE_{cell}$, $\ \Delta_{r}G^{\circ}=-nFE^{\circ}_{cell}$ (J mol⁻¹)
Standard EMF and equilibrium constant (298 K)§ 2.2 →
$\log K_{c}=\dfrac{nE^{\circ}_{cell}}{0.059}$, $\ \Delta_{r}G^{\circ}=-2.303RT\log K_{c}$; $\ E^{\circ}\gt0\iff\Delta_{r}G^{\circ}\lt0\iff K\gt1$
Resistance, conductance, conductivity§ 2.3 →
$R=\rho\dfrac{l}{A}$, $\ G=\dfrac{1}{R}\ (\mathrm{S})$, $\ \kappa=\dfrac{1}{\rho}\ (\mathrm{S\,cm^{-1}})$; $\ 1\ \mathrm{S\,m^{-1}}=0.01\ \mathrm{S\,cm^{-1}}$
Cell constant§ 2.3 →
$G^{*}=\dfrac{l}{A}=R\,\kappa$, $\ \kappa=\dfrac{G^{*}}{R}$ (calibrate with standard $\mathrm{KCl}$)
Molar conductivity ($\kappa$ in $\mathrm{S\,cm^{-1}}$, $c$ in $\mathrm{mol\,L^{-1}}$)§ 2.3 →
$\Lambda_{m}=\dfrac{\kappa}{c}=\dfrac{\kappa\times1000}{c}\ \mathrm{S\,cm^{2}\,mol^{-1}}$; $\ 1\ \mathrm{S\,m^{2}\,mol^{-1}}=10^{4}\ \mathrm{S\,cm^{2}\,mol^{-1}}$
Strong electrolytes (dilute)§ 2.3 →
$\Lambda_{m}=\Lambda_{m}^{\circ}-A\sqrt{c}$; intercept of $\Lambda_{m}$ vs $\sqrt{c}$ gives $\Lambda_{m}^{\circ}$
Kohlrausch's law§ 2.3 →
$\Lambda_{m}^{\circ}=\nu_{+}\lambda_{+}^{\circ}+\nu_{-}\lambda_{-}^{\circ}$; $\ \Lambda_{m}^{\circ}(\mathrm{CH_{3}COOH})=\Lambda_{m}^{\circ}(\mathrm{CH_{3}COONa})+\Lambda_{m}^{\circ}(\mathrm{HCl})-\Lambda_{m}^{\circ}(\mathrm{NaCl})$
Weak electrolytes§ 2.3 →
$\alpha=\dfrac{\Lambda_{m}}{\Lambda_{m}^{\circ}}$, $\ K_{a}=\dfrac{c\,\alpha^{2}}{1-\alpha}$
Faraday's laws ($t$ in seconds, $n$ = electrons per formula unit, $F=96\,487\ \mathrm{C\,mol^{-1}}$)§ 2.4 →
$Q=It$, $\ \text{mol}\ e^{-}=\dfrac{Q}{F}$, $\ m=\dfrac{M\,I\,t}{nF}=Z\,I\,t$, $\ Z=\dfrac{M}{nF}$
Cells in series (same charge)§ 2.4 →
$\dfrac{m_{1}}{m_{2}}=\dfrac{M_{1}/n_{1}}{M_{2}/n_{2}}$
Water at the electrodes§ 2.4 →
$\mathrm{2H_{2}O+2e^{-}\rightarrow H_{2}+2OH^{-}}$ ($-0.83\ \mathrm{V}$); $\ \mathrm{2H_{2}O\rightarrow O_{2}+4H^{+}+4e^{-}}$ ($E^{\circ}=+1.23\ \mathrm{V}$); brine: $\mathrm{H_{2}}$ and $\mathrm{Cl_{2}}$ (overpotential)
Lead storage battery (discharge)§ 2.4 →
$\mathrm{Pb(s)+PbO_{2}(s)+2H_{2}SO_{4}(aq)\rightarrow 2PbSO_{4}(s)+2H_{2}O(l)}$, about $2\ \mathrm{V}$ per cell
Primary cells§ 2.4 →
dry cell $\approx1.5\ \mathrm{V}$: $\mathrm{MnO_{2}+NH_{4}^{+}+e^{-}\rightarrow MnO(OH)+NH_{3}}$; mercury cell $1.35\ \mathrm{V}$: $\mathrm{Zn(Hg)+HgO\rightarrow ZnO+Hg}$
Fuel cell and rusting§ 2.4 →
$\mathrm{2H_{2}(g)+O_{2}(g)\rightarrow 2H_{2}O(l)}$, $E^{\circ}=1.23\ \mathrm{V}$; rusting: $\mathrm{2Fe+O_{2}+4H^{+}\rightarrow 2Fe^{2+}+2H_{2}O}$, $E^{\circ}_{cell}=1.67\ \mathrm{V}$
Chapter 3 · Chemical Kinetics
Average and instantaneous rate§ 3.1 →
$r_{av}=-\dfrac{\Delta[\mathrm{R}]}{\Delta t}=\dfrac{\Delta[\mathrm{P}]}{\Delta t}$ (chord), $\ r_{inst}=-\dfrac{d[\mathrm{R}]}{dt}=\dfrac{d[\mathrm{P}]}{dt}$ (tangent)
Rate of reaction for $a\mathrm{A}+b\mathrm{B}\rightarrow c\mathrm{C}+d\mathrm{D}$§ 3.1 →
$\text{rate}=-\dfrac{1}{a}\dfrac{d[\mathrm{A}]}{dt}=-\dfrac{1}{b}\dfrac{d[\mathrm{B}]}{dt}=\dfrac{1}{c}\dfrac{d[\mathrm{C}]}{dt}=\dfrac{1}{d}\dfrac{d[\mathrm{D}]}{dt}$
Rate law and order§ 3.1 →
$\text{rate}=k[\mathrm{A}]^{x}[\mathrm{B}]^{y}$; order $=x+y$ (from experiment, may be 0 or fractional)
Units of $k$ for order $n$§ 3.1 →
$\mathrm{(mol\,L^{-1})^{1-n}\,s^{-1}}$: zero $\mathrm{mol\,L^{-1}\,s^{-1}}$, first $\mathrm{s^{-1}}$, second $\mathrm{L\,mol^{-1}\,s^{-1}}$
Order from two initial rates (other concentrations fixed)§ 3.1 →
$x=\dfrac{\log(r_{2}/r_{1})}{\log([\mathrm{A}]_{2}/[\mathrm{A}]_{1})}$
Zero order§ 3.2 →
$[\mathrm{R}]=[\mathrm{R}]_{0}-kt$, $\ t_{1/2}=\dfrac{[\mathrm{R}]_{0}}{2k}$ (until $[\mathrm{R}]=0$ at $t=[\mathrm{R}]_{0}/k$)
First order§ 3.2 →
$[\mathrm{R}]=[\mathrm{R}]_{0}e^{-kt}$, $\ k=\dfrac{2.303}{t}\log\dfrac{[\mathrm{R}]_{0}}{[\mathrm{R}]}=\dfrac{2.303}{t_{2}-t_{1}}\log\dfrac{[\mathrm{R}]_{1}}{[\mathrm{R}]_{2}}$
First-order half-life§ 3.2 →
$t_{1/2}=\dfrac{0.693}{k}$ (independent of $[\mathrm{R}]_{0}$); after $n$ half-lives $[\mathrm{R}]=[\mathrm{R}]_{0}/2^{n}$; $\ t_{99.9\%}\approx10\,t_{1/2}$
Gas phase $\mathrm{A(g)\rightarrow B(g)+C(g)}$, constant $V$§ 3.2 →
$p_{\mathrm{A}}=2p_{0}-p_{t}$, $\ k=\dfrac{2.303}{t}\log\dfrac{p_{0}}{2p_{0}-p_{t}}$
Pseudo-first-order (B in large excess)§ 3.2 →
$\text{rate}=k'[\mathrm{A}][\mathrm{B}]=k[\mathrm{A}]$, $\ k=k'[\mathrm{B}]$
Arrhenius equation§ 3.3 →
$k=A\,e^{-E_{a}/RT}$; $\ \ln k=\ln A-\dfrac{E_{a}}{RT}$ (slope of $\ln k$ vs $1/T$ $=-E_{a}/R$)
Two temperatures ($R=8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}$, $T$ in K)§ 3.3 →
$\log\dfrac{k_{2}}{k_{1}}=\dfrac{E_{a}}{2.303R}\left(\dfrac{T_{2}-T_{1}}{T_{1}T_{2}}\right)$
Temperature coefficient§ 3.3 →
$\dfrac{k_{T+10}}{k_{T}}\approx2$–$3$; rise of $n\times10\ \mathrm{K}$ multiplies $k$ by about $(\text{coefficient})^{n}$
Effect of a catalyst (same $A$, same $T$)§ 3.3 →
$\dfrac{k_{cat}}{k}=e^{(E_{a}-E_{a,cat})/RT}$; $\Delta_{r}H$, $\Delta_{r}G$ and $K$ unchanged
Collision theory§ 3.3 →
$\text{rate}=P\,Z_{\mathrm{AB}}\,e^{-E_{a}/RT}$ ($P$ = steric factor)
Chapter 4 · The d- and f-Block Elements
Configurations of the 3d series (exceptions Cr, Cu)§ 4.1 →
$\mathrm{[Ar]\,3d^{x}\,4s^{2}}$ ($x=1$ Sc … $10$ Zn); $\ \mathrm{Cr}:\mathrm{[Ar]\,3d^{5}\,4s^{1}}$, $\ \mathrm{Cu}:\mathrm{[Ar]\,3d^{10}\,4s^{1}}$
d-electron count of a 3d ion $\mathrm{M^{q+}}$ (4s lost first)§ 4.1 →
$d^{\,Z-18-q}$, e.g. $\mathrm{Fe^{3+}}$: $26-18-3=5$
Spin-only magnetic moment ($n$ unpaired electrons)§ 4.1 →
$\mu=\sqrt{n(n+2)}\ \mathrm{BM}$: $1.73,\ 2.83,\ 3.87,\ 4.90,\ 5.92$ for $n=1$–$5$
Unpaired electrons, $d^{m}$ ion in water§ 4.1 →
$n=m$ for $m\le5$; $\ n=10-m$ for $m\ge5$
Key $E^{\circ}$ values of the 3d series§ 4.1 →
$E^{\circ}_{\mathrm{Cu^{2+}/Cu}}=+0.34\ \mathrm{V}$ (only positive); $E^{\circ}_{\mathrm{Mn^{3+}/Mn^{2+}}}=+1.57$, $E^{\circ}_{\mathrm{Co^{3+}/Co^{2+}}}=+1.97$, $E^{\circ}_{\mathrm{Fe^{3+}/Fe^{2+}}}=+0.77$, $E^{\circ}_{\mathrm{Cr^{3+}/Cr^{2+}}}=-0.41\ \mathrm{V}$
Chromate–dichromate equilibrium (Cr stays +6)§ 4.2 →
$\mathrm{2CrO_{4}^{2-}(aq)+2H^{+}(aq)\rightleftharpoons Cr_{2}O_{7}^{2-}(aq)+H_{2}O(l)}$
Dichromate in acid ($E^{\circ}=+1.33\ \mathrm{V}$, $n=6$)§ 4.2 →
$\mathrm{Cr_{2}O_{7}^{2-}+14H^{+}+6e^{-}\rightarrow2Cr^{3+}+7H_{2}O}$
Permanganate in acid ($E^{\circ}=+1.52\ \mathrm{V}$, $n=5$)§ 4.2 →
$\mathrm{MnO_{4}^{-}+8H^{+}+5e^{-}\rightarrow Mn^{2+}+4H_{2}O}$
Permanganate, neutral ($n=3$) and strongly alkaline ($n=1$)§ 4.2 →
$\mathrm{MnO_{4}^{-}+2H_{2}O+3e^{-}\rightarrow MnO_{2}+4OH^{-}}$; $\ \mathrm{MnO_{4}^{-}+e^{-}\rightarrow MnO_{4}^{2-}}$
Redox titration: electrons lost = electrons gained§ 4.2 →
$n_{\text{ox}}\times(\text{mol oxidant})=n_{\text{red}}\times(\text{mol reductant})$
Making permanganate: fusion, then disproportionation§ 4.2 →
$\mathrm{2MnO_{2}+4KOH+O_{2}\rightarrow2K_{2}MnO_{4}+2H_{2}O}$; $\ \mathrm{3MnO_{4}^{2-}+4H^{+}\rightarrow2MnO_{4}^{-}+MnO_{2}+2H_{2}O}$
Lanthanoid atoms (5d¹ only in La, Ce, Gd, Lu)§ 4.3 →
$\mathrm{[Xe]\,4f^{1-14}\,5d^{0-1}\,6s^{2}}$; usually $\mathrm{[Xe]\,4f^{\,Z-56}\,6s^{2}}$
Lanthanoid $+3$ ions§ 4.3 →
$\mathrm{Ln^{3+}}=\mathrm{[Xe]\,4f^{\,Z-57}}$; unpaired $=n$ ($n\le7$), $14-n$ ($n\ge7$)
Actinoids: configuration and highest states§ 4.3 →
$\mathrm{[Rn]\,5f^{1-14}\,6d^{0-1}\,7s^{2}}$ (Th: $6d^{2}7s^{2}$); highest: Th $+4$, Pa $+5$, U $+6$, Np/Pu $+7$
Lanthanoid contraction and consequences§ 4.3 →
$r(\mathrm{La^{3+}})=103\ \mathrm{pm}\rightarrow r(\mathrm{Lu^{3+}})=86\ \mathrm{pm}$; $\ \mathrm{Zr}\ 160\approx\mathrm{Hf}\ 159\ \mathrm{pm}$; basicity $\mathrm{La(OH)_{3}}\gt\cdots\gt\mathrm{Lu(OH)_{3}}$
Unusual lanthanoid oxidation states§ 4.3 →
$\mathrm{Ce^{4+}}$ ($f^{0}$, oxidant, $E^{\circ}=+1.74\ \mathrm{V}$); $\mathrm{Eu^{2+}}$ ($f^{7}$), $\mathrm{Yb^{2+}}$ ($f^{14}$) reductants
Chapter 5 · Coordination Compounds
Werner's valences§ 5.1 →
primary = oxidation state (ionisable); secondary = coordination number (non-ionisable); mol AgCl per mol = chlorides outside $[\ ]$
Oxidation number of the central atom§ 5.1 →
$x+\sum(\text{ligand charges})=\text{charge of the entity}$
Coordination number§ 5.1 →
$\text{CN}=\sum(\text{number of ligands}\times\text{denticity})$; e.g. $\mathrm{[Fe(C_{2}O_{4})_{3}]^{3-}}$: $3\times2=6$
IUPAC name of a complex§ 5.1 →
cation first; ligands alphabetical (prefixes ignored), anionic ones -ido/-ato/-ito; aqua, ammine, carbonyl; di-/tri- or bis-/tris-(…); metal (+ -ate if anion: ferrate, cuprate, argentate, aurate) + (Roman oxidation state)
Formula of a coordination entity§ 5.1 →
$[\text{metal}\,(\text{ligands alphabetical by formula})]^{\text{charge}}$, e.g. $\mathrm{[CoCl_{2}(en)_{2}]^{+}}$
Geometrical isomers (count)§ 5.2 →
square planar: $\mathrm{MA_{2}B_{2}}$, $\mathrm{MA_{2}BC}$ 2; $\mathrm{MABCD}$ 3 · tetrahedral: none · octahedral: $\mathrm{MA_{4}B_{2}}$ 2 (cis/trans); $\mathrm{MA_{3}B_{3}}$ 2 (fac/mer); $\mathrm{M(AA)_{2}B_{2}}$ 2
Total stereoisomers§ 5.2 →
geometrical isomers $+$ number of them that are chiral: $\mathrm{[M(AA)_{3}]}$ 2; $\mathrm{[M(AA)_{2}B_{2}]}$ 3; $\mathrm{[M(AA)_{2}BC]}$ 3; $\mathrm{[MA_{2}B_{2}(AA)]}$ 4
Chirality test§ 5.2 →
a mirror plane through the complex $\Rightarrow$ achiral; none $\Rightarrow$ chiral ($d$, $l$ pair). Planar complexes: achiral.
Structural isomerism§ 5.2 →
linkage (ambidentate donor atom) · coordination (ligands swap between cation and anion) · ionisation (ligand ⇄ counter ion) · solvate/hydrate (water inside ⇄ outside)
VBT hybridisation and shape§ 5.3 →
$sp$ linear · $sp^{3}$ tetrahedral · $dsp^{2}$ square planar · $d^{2}sp^{3}$ octahedral (inner, low-spin) · $sp^{3}d^{2}$ octahedral (outer, high-spin)
Octahedral splitting§ 5.3 →
$e_{g}$: $+0.6\,\Delta_{o}$; $\ t_{2g}$: $-0.4\,\Delta_{o}$
Tetrahedral splitting§ 5.3 →
$t_{2}$: $+0.4\,\Delta_{t}$; $\ e$: $-0.6\,\Delta_{t}$; $\ \Delta_{t}=\tfrac49\Delta_{o}$ (always high-spin)
CFSE (octahedral $t_{2g}^{x}e_{g}^{y}$)§ 5.3 →
$\text{CFSE}=(-0.4x+0.6y)\Delta_{o}$ $+\ P$ per extra pair; low-spin if $\Delta_{o}\gt P$, high-spin if $\Delta_{o}\lt P$ ($d^{4}$–$d^{7}$ only)
Splitting from the absorbed wavelength§ 5.3 →
$\Delta=\dfrac{N_{A}hc}{\lambda}=\dfrac{1.196\times10^{5}}{\lambda/\mathrm{nm}}\ \mathrm{kJ\,mol^{-1}}$; colour seen = complement of colour absorbed
Spectrochemical series§ 5.3 →
$\mathrm{I^{-}\lt Br^{-}\lt Cl^{-}\lt F^{-}\lt OH^{-}\lt C_{2}O_{4}^{2-}\lt H_{2}O\lt NH_{3}\lt en\lt CN^{-}\lt CO}$
Chapter 6 · Haloalkanes and Haloarenes
Alcohols → haloalkanes§ 6.1 →
$\mathrm{ROH+HCl\xrightarrow{ZnCl_{2}}RCl+H_{2}O}$; $\ \mathrm{3ROH+PX_{3}\rightarrow3RX+H_{3}PO_{3}}$; $\ \mathrm{ROH+PCl_{5}\rightarrow RCl+POCl_{3}+HCl}$; $\ \mathrm{ROH+SOCl_{2}\rightarrow RCl+SO_{2}+HCl}$ (best: gaseous by-products). Reactivity with HX: 3° > 2° > 1°.
Halogen exchange§ 6.1 →
Finkelstein: $\mathrm{RX+NaI\xrightarrow{\text{dry acetone}}RI+NaX\downarrow}$ (X = Cl, Br). Swarts: $\mathrm{RX+AgF\rightarrow RF+AgX}$ (or $\mathrm{Hg_{2}F_{2}}$, $\mathrm{CoF_{2}}$, $\mathrm{SbF_{3}}$).
Haloarenes from diazonium salts§ 6.1 →
$\mathrm{ArN_{2}^{+}X^{-}\xrightarrow{Cu_{2}X_{2}}ArX+N_{2}}$ (Sandmeyer, X = Cl, Br); $\ \mathrm{ArN_{2}^{+}Cl^{-}+KI\rightarrow ArI+KCl+N_{2}}$
C–X bond trends§ 6.1 →
Length: C–F < C–Cl < C–Br < C–I; bond enthalpy (and resistance to breaking): C–F > C–Cl > C–Br > C–I. Dipole moment: $\mathrm{CH_{3}Cl}$ largest.
Radical halogenation: product share§ 6.1 →
share of product $i$ $=\dfrac{n_{i}r_{i}}{\sum n_{j}r_{j}}$ ($n$ = number of equivalent H, $r$ = reactivity per H; Cl at room temperature ≈ 1 : 3.8 : 5 for 1° : 2° : 3°)
SN2§ 6.2 →
$\text{rate}=k[\mathrm{RX}][\mathrm{Nu^{-}}]$; one step, backside attack, inversion. Reactivity: $\mathrm{CH_{3}X\gt1^{\circ}\gt2^{\circ}\gg3^{\circ}}$.
SN1§ 6.2 →
$\text{rate}=k[\mathrm{RX}]$; slow ionisation to $\mathrm{R^{+}}$, then fast attack; racemisation. Reactivity: $\mathrm{3^{\circ}\gt2^{\circ}\gt1^{\circ}\gt CH_{3}X}$; allylic, benzylic fast.
Leaving-group order (SN1 and SN2)§ 6.2 →
$\mathrm{R{-}I\gt R{-}Br\gt R{-}Cl\gg R{-}F}$
Ambident nucleophiles§ 6.2 →
$\mathrm{RX+KCN\rightarrow RCN}$; $\ \mathrm{RX+AgCN\rightarrow RNC}$; $\ \mathrm{RX+KNO_{2}\rightarrow R{-}ONO}$; $\ \mathrm{RX+AgNO_{2}\rightarrow R{-}NO_{2}}$
Rotation of an enantiomer mixture§ 6.2 →
$\alpha=(2f-1)\,\alpha_{\text{pure}}$ ($f$ = fraction of the $(+)$ enantiomer); racemic ($f=\tfrac12$): $\alpha=0$
β-Elimination and Saytzeff's rule§ 6.3 →
$\mathrm{RCH_{2}CH_{2}X\xrightarrow{\text{alc. KOH},\ \Delta}RCH{=}CH_{2}}$; major alkene = most substituted. Ease: 3° > 2° > 1°.
Grignard reagent§ 6.3 →
$\mathrm{RX+Mg\xrightarrow{\text{dry ether}}RMgX}$; $\ \mathrm{RMgX+H_{2}O\rightarrow RH+Mg(OH)X}$
Coupling with sodium (dry ether)§ 6.3 →
Wurtz: $\mathrm{2RX+2Na\rightarrow R{-}R+2NaX}$; Wurtz–Fittig: $\mathrm{ArX+RX+2Na\rightarrow Ar{-}R+2NaX}$; Fittig: $\mathrm{2ArX+2Na\rightarrow Ar{-}Ar+2NaX}$
ArCl → ArOH (o/p-NO₂ activates)§ 6.3 →
$\mathrm{C_{6}H_{5}Cl}$: $623\ \mathrm{K}$, $300\ \mathrm{atm}$; 4-nitro: $443\ \mathrm{K}$; 2,4-dinitro: $368\ \mathrm{K}$; 2,4,6-trinitro: $323\ \mathrm{K}$ (water)
Ozone destruction by Cl atoms§ 6.3 →
$\mathrm{Cl^{\bullet}+O_{3}\rightarrow ClO^{\bullet}+O_{2}}$; $\ \mathrm{ClO^{\bullet}+O\rightarrow Cl^{\bullet}+O_{2}}$; net $\mathrm{O_{3}+O\rightarrow2O_{2}}$
Chloroform in air and light§ 6.3 →
$\mathrm{2CHCl_{3}+O_{2}\rightarrow2COCl_{2}+2HCl}$ (store in dark, full bottles)
Chapter 7 · Alcohols, Phenols and Ethers
Classifying alcohols§ 7.1 →
Count the carbons on the carbinol carbon: $\mathrm{RCH_{2}OH}$ 1°, $\mathrm{R_{2}CHOH}$ 2°, $\mathrm{R_{3}COH}$ 3°; $\mathrm{OH}$ on a ring carbon: phenol
Alcohols from alkenes§ 7.1 →
$\mathrm{CH_{3}CH{=}CH_{2}\xrightarrow{H_{2}O/H^{+}}CH_{3}CH(OH)CH_{3}}$ (Markovnikov); $\ \mathrm{CH_{3}CH{=}CH_{2}\xrightarrow{(i)\,B_{2}H_{6}\ (ii)\,H_{2}O_{2}/OH^{-}}CH_{3}CH_{2}CH_{2}OH}$
Alcohols from carbonyl compounds§ 7.1 →
Reduction: aldehyde → 1°, ketone → 2°. $\mathrm{RMgX}$ then $\mathrm{H_{2}O}$: $\mathrm{HCHO}$ → 1°, $\mathrm{R'CHO}$ → 2°, $\mathrm{R'COR''}$ → 3°
Phenol from cumene§ 7.1 →
$\mathrm{C_{6}H_{5}CH(CH_{3})_{2}\xrightarrow{O_{2}}C_{6}H_{5}C(CH_{3})_{2}OOH\xrightarrow{H^{+}/H_{2}O}C_{6}H_{5}OH+CH_{3}COCH_{3}}$
Boiling points (similar $M$)§ 7.1 →
alcohol $\gg$ ether $\approx$ alkane (hydrogen bonding); unbranched $\gt$ branched isomer
Acid strength ($\mathrm{p}K_{a}$, approx.)§ 7.2 →
picric acid $0.5$ $\lt$ 4-nitrophenol $7.1$ $\lt$ 3-nitrophenol $8.3$ $\lt$ phenol $10.0$ $\lt$ cresols $\approx10.2$ $\lt$ water $15.7$ $\lt$ ethanol $15.9$; alcohols 1° $\gt$ 2° $\gt$ 3°
Lucas test ($\mathrm{ZnCl_{2}}$ + conc. $\mathrm{HCl}$)§ 7.2 →
3°: cloudy at once · 2°: within about 5 min · 1°: no turbidity at room temperature
Dehydration (ease 3° $\gt$ 2° $\gt$ 1°)§ 7.2 →
$\mathrm{CH_{3}CH_{2}OH\xrightarrow[443\ K]{conc.\ H_{2}SO_{4}}CH_{2}{=}CH_{2}+H_{2}O}$; at $413\ \mathrm{K}$ (excess ethanol): $\mathrm{C_{2}H_{5}OC_{2}H_{5}}$
Oxidation of alcohols§ 7.2 →
1° → aldehyde (PCC; Cu, 573 K) → acid ($\mathrm{KMnO_{4}/H^{+}}$); 2° → ketone; 3° resists (Cu, 573 K: alkene)
Phenol: named reactions and tests§ 7.2 →
$\mathrm{C_{6}H_{5}ONa}\xrightarrow{(i)\,\mathrm{CO_{2}}\ (ii)\,\mathrm{H^{+}}}$ salicylic acid (Kolbe); $\ \mathrm{C_{6}H_{5}OH}\xrightarrow{\mathrm{CHCl_{3}/NaOH},\ \mathrm{H^{+}}}$ salicylaldehyde (Reimer–Tiemann); bromine water → 2,4,6-tribromophenol (white)
Commercial alcohols§ 7.2 →
$\mathrm{C_{6}H_{12}O_{6}\xrightarrow{zymase}2C_{2}H_{5}OH+2CO_{2}}$; $\ \mathrm{CO+2H_{2}\xrightarrow{ZnO{-}Cr_{2}O_{3}}CH_{3}OH}$
Ethers from 1° alcohols§ 7.3 →
$\mathrm{2C_{2}H_{5}OH\xrightarrow[413\ K]{conc.\ H_{2}SO_{4}}C_{2}H_{5}OC_{2}H_{5}+H_{2}O}$ (443 K: ethene)
Williamson synthesis ($\mathrm{S_{N}2}$)§ 7.3 →
$\mathrm{RX+R'ONa\rightarrow ROR'+NaX}$: RX methyl or 1° (3° RX → alkene; ArX no reaction); aryl ethers: $\mathrm{ArONa+RX}$
Cleavage by HI ($\mathrm{HI\gt HBr\gt HCl}$)§ 7.3 →
$\mathrm{CH_{3}OR\rightarrow CH_{3}I+ROH}$ (R 1°/2°); $\ \mathrm{(CH_{3})_{3}COCH_{3}\rightarrow(CH_{3})_{3}CI+CH_{3}OH}$; $\ \mathrm{C_{6}H_{5}OCH_{3}\rightarrow C_{6}H_{5}OH+CH_{3}I}$
Anisole: o/p substitution§ 7.3 →
$\mathrm{Br_{2}}$/ethanoic acid, $\mathrm{CH_{3}Cl}$ or $\mathrm{CH_{3}COCl}$/$\mathrm{AlCl_{3}}$, $\mathrm{HNO_{3}/H_{2}SO_{4}}$ → mainly the 4-substituted anisole
Chapter 8 · Aldehydes, Ketones and Carboxylic Acids
Aldehydes and ketones§ 8.1 →
$\mathrm{R{-}CHO}$ (-al), $\ \mathrm{R{-}CO{-}R'}$ (-one); open-chain, saturated: $\mathrm{C_{n}H_{2n}O}$; $\mathrm{\overset{\delta+}{C}{=}\overset{\delta-}{O}}$, $sp^{2}$, $120^{\circ}$
General methods§ 8.1 →
$\mathrm{RCH_{2}OH\xrightarrow{PCC}RCHO}$; $\ \mathrm{R_{2}CHOH\xrightarrow{K_{2}Cr_{2}O_{7}/H^{+}}R_{2}CO}$; $\ $Cu, 573 K (dehydrogenation); $\ \mathrm{R_{2}C{=}CR'_{2}\xrightarrow{O_{3};\ Zn/H_{2}O}R_{2}CO+R'_{2}CO}$; $\ \mathrm{RC{\equiv}CH\xrightarrow{HgSO_{4},\ H_{2}SO_{4}}RCOCH_{3}}$ (only $\mathrm{HC{\equiv}CH}$ gives $\mathrm{CH_{3}CHO}$)
Stopping at the aldehyde§ 8.1 →
$\mathrm{RCOCl\xrightarrow{H_{2},\ Pd{-}BaSO_{4}}RCHO}$ (Rosenmund); $\ \mathrm{RCN\xrightarrow{SnCl_{2}/HCl;\ H_{3}O^{+}}RCHO}$ (Stephen); $\ \mathrm{RCN\ or\ RCOOR'\xrightarrow{DIBAL{-}H;\ H_{2}O}RCHO}$
Aromatic aldehydes§ 8.1 →
$\mathrm{C_{6}H_{5}CH_{3}\xrightarrow{CrO_{2}Cl_{2}/CS_{2};\ H_{3}O^{+}}C_{6}H_{5}CHO}$ (Etard); $\ \mathrm{C_{6}H_{5}CH_{3}\xrightarrow{Cl_{2},\ h\nu}C_{6}H_{5}CHCl_{2}\xrightarrow{H_{2}O,\ 373\ K}C_{6}H_{5}CHO}$; $\ \mathrm{C_{6}H_{6}\xrightarrow{CO,\ HCl,\ AlCl_{3}/CuCl}C_{6}H_{5}CHO}$ (Gattermann–Koch)
Ketones§ 8.1 →
$\mathrm{2R'COCl+R_{2}Cd\rightarrow2R'COR+CdCl_{2}}$; $\ \mathrm{RCN+R'MgX\xrightarrow{ether;\ H_{3}O^{+}}RCOR'}$; $\ \mathrm{ArH+RCOCl\xrightarrow{anhyd.\ AlCl_{3}}ArCOR+HCl}$
Nucleophilic addition§ 8.2 →
$\mathrm{{>}C{=}O+HCN\xrightarrow{OH^{-}}{>}C(OH)CN}$; $\ \mathrm{{>}C{=}O+NaHSO_{3}\rightleftharpoons{>}C(OH)SO_{3}Na}$; $\ \mathrm{{>}C{=}O\xrightarrow{R'MgX;\ H_{2}O}{>}C(R')OH}$; $\ \mathrm{RCHO\xrightarrow{2R'OH,\ dry\ HCl}RCH(OR')_{2}}$. Reactivity: $\mathrm{HCHO\gt RCHO\gt R_{2}CO}$; aromatic below aliphatic
Addition–elimination ($\mathrm{H_{2}N{-}Z}$, pH ≈ 4)§ 8.2 →
$\mathrm{{>}C{=}O+H_{2}N{-}Z\rightleftharpoons{>}C{=}N{-}Z+H_{2}O}$ ($\mathrm{Z=OH}$ oxime, $\mathrm{NH_{2}}$ hydrazone, $\mathrm{NHCONH_{2}}$ semicarbazone, $\mathrm{NHC_{6}H_{3}(NO_{2})_{2}}$ 2,4-DNP derivative)
Reduction§ 8.2 →
$\mathrm{RCHO\rightarrow RCH_{2}OH}$, $\ \mathrm{R_{2}CO\rightarrow R_{2}CHOH}$ ($\mathrm{NaBH_{4}}$, $\mathrm{LiAlH_{4}}$, $\mathrm{H_{2}/Ni}$); $\ \mathrm{{>}C{=}O\rightarrow{>}CH_{2}}$: Zn–Hg/conc. HCl (Clemmensen) or $\mathrm{NH_{2}NH_{2}}$; KOH, ethylene glycol, heat (Wolff–Kishner)
Tests§ 8.2 →
$\mathrm{RCHO+2[Ag(NH_{3})_{2}]^{+}+3OH^{-}\rightarrow RCOO^{-}+2Ag+2H_{2}O+4NH_{3}}$; $\ \mathrm{RCHO+2Cu^{2+}+5OH^{-}\rightarrow RCOO^{-}+Cu_{2}O+3H_{2}O}$ (not ArCHO); $\ \mathrm{RCOCH_{3}+3I_{2}+4NaOH\rightarrow RCOONa+CHI_{3}+3NaI+3H_{2}O}$
α-Hydrogen and Cannizzaro§ 8.2 →
$\mathrm{2CH_{3}CHO\xrightarrow{dil.\ NaOH}CH_{3}CH(OH)CH_{2}CHO\xrightarrow{\Delta}CH_{3}CH{=}CHCHO}$; cross aldol, both with α-H: 4 products; $\ \mathrm{2ArCHO\xrightarrow{conc.\ NaOH}ArCH_{2}OH+ArCOO^{-}}$ (no α-H)
Preparing carboxylic acids§ 8.3 →
$\mathrm{RCH_{2}OH,\ RCHO\xrightarrow{[O]}RCOOH}$; $\ \mathrm{C_{6}H_{5}R\xrightarrow{KMnO_{4}/KOH;\ H_{3}O^{+}}C_{6}H_{5}COOH}$ (benzylic H needed); $\ \mathrm{RCN\xrightarrow{H_{3}O^{+}}RCOOH}$; $\ \mathrm{RMgX\xrightarrow{CO_{2};\ H_{3}O^{+}}RCOOH}$ (one C more); esters, acyl chlorides, anhydrides by hydrolysis
Acid strength§ 8.3 →
$K_{a}=\dfrac{[\mathrm{RCOO^{-}}][\mathrm{H_{3}O^{+}}]}{[\mathrm{RCOOH}]}$, $\ \mathrm{p}K_{a}=-\log K_{a}$; weak acid: $[\mathrm{H_{3}O^{+}}]\approx\sqrt{K_{a}C}$ if under ~5% ionised
Acidity order (approximate pKa)§ 8.3 →
$\mathrm{CF_{3}COOH}$ (0.23) > $\mathrm{CCl_{3}COOH}$ (0.64) > $\mathrm{CHCl_{2}COOH}$ (1.26) > $\mathrm{FCH_{2}COOH}$ (2.59) > $\mathrm{ClCH_{2}COOH}$ (2.87) > $\mathrm{HCOOH}$ (3.75) > $\mathrm{C_{6}H_{5}COOH}$ (4.19) > $\mathrm{CH_{3}COOH}$ (4.76) > phenol (10) > ethanol (≈16)
O–H and C–OH reactions§ 8.3 →
$\mathrm{RCOOH+NaHCO_{3}\rightarrow RCOONa+H_{2}O+CO_{2}}$; $\ \mathrm{RCOOH+SOCl_{2}\rightarrow RCOCl+SO_{2}+HCl}$; $\ \mathrm{RCOOH+R'OH\overset{H^{+}}{\rightleftharpoons}RCOOR'+H_{2}O}$; $\ \mathrm{2RCOOH\xrightarrow{P_{2}O_{5}}(RCO)_{2}O}$; $\ \mathrm{RCOONH_{4}\xrightarrow{\Delta}RCONH_{2}}$
–COOH group reactions§ 8.3 →
$\mathrm{RCOOH\xrightarrow{LiAlH_{4};\ H_{3}O^{+}}RCH_{2}OH}$; $\ \mathrm{RCOONa\xrightarrow{NaOH/CaO,\ \Delta}RH}$; $\ \mathrm{2RCOO^{-}\xrightarrow{\text{electrolysis}}R{-}R+2CO_{2}}$ (Kolbe); $\ \mathrm{RCH_{2}COOH\xrightarrow{X_{2}/\text{red P};\ H_{2}O}RCH(X)COOH}$ (HVZ)
Chapter 9 · Amines
Classes of amines§ 9.1 →
1° $\mathrm{RNH_{2}}$ · 2° $\mathrm{R_{2}NH}$ · 3° $\mathrm{R_{3}N}$ · quaternary salt $\mathrm{R_{4}N^{+}X^{-}}$ (count carbons on N)
Amines by reduction§ 9.1 →
$\mathrm{ArNO_{2}\xrightarrow{H_{2}/Pd\ or\ Fe/HCl}ArNH_{2}}$; $\ \mathrm{RCN\xrightarrow{LiAlH_{4}}RCH_{2}NH_{2}}$; $\ \mathrm{RCONH_{2}\xrightarrow{LiAlH_{4}}RCH_{2}NH_{2}}$
Ammonolysis (gives a mixture)§ 9.1 →
$\mathrm{RX\xrightarrow{NH_{3}}RNH_{2}\xrightarrow{RX}R_{2}NH\xrightarrow{RX}R_{3}N\xrightarrow{RX}R_{4}N^{+}X^{-}}$; reactivity $\mathrm{RI\gt RBr\gt RCl}$
Gabriel phthalimide synthesis§ 9.1 →
phthalimide $\xrightarrow{\text{KOH}}$ K-phthalimide $\xrightarrow{\mathrm{RX}}$ $N$-alkylphthalimide $\xrightarrow{\mathrm{NaOH(aq)}}$ $\mathrm{RNH_{2}}$ (pure 1°; not for arylamines)
Hoffmann bromamide degradation (one C fewer)§ 9.1 →
$\mathrm{RCONH_{2}+Br_{2}+4NaOH\rightarrow RNH_{2}+Na_{2}CO_{3}+2NaBr+2H_{2}O}$
Boiling points (similar $M$)§ 9.1 →
alcohol $\gt$ 1° amine $\gt$ 2° amine $\gt$ 3° amine $\approx$ alkane
Basic strength§ 9.2 →
$K_{b}=\tfrac{[\mathrm{RNH_{3}^{+}}][\mathrm{OH^{-}}]}{[\mathrm{RNH_{2}}]}$, $\ \mathrm{p}K_{b}=-\log K_{b}$, $\ \mathrm{p}K_{a}+\mathrm{p}K_{b}=14.00$ (298 K); smaller $\mathrm{p}K_{b}$ = stronger base
Basicity orders§ 9.2 →
water: $\mathrm{(CH_{3})_{2}NH\gt CH_{3}NH_{2}\gt(CH_{3})_{3}N\gt NH_{3}}$; $\ \mathrm{(C_{2}H_{5})_{2}NH\gt(C_{2}H_{5})_{3}N\gt C_{2}H_{5}NH_{2}\gt NH_{3}}$; gas: 3° $\gt$ 2° $\gt$ 1° $\gt\mathrm{NH_{3}}$; $\mathrm{NH_{3}\gt C_{6}H_{5}NH_{2}}$
Carbylamine test (1° only)§ 9.2 →
$\mathrm{RNH_{2}+CHCl_{3}+3KOH\xrightarrow{\Delta}RNC+3KCl+3H_{2}O}$
Hinsberg's reagent $\mathrm{C_{6}H_{5}SO_{2}Cl}$§ 9.2 →
1°: sulphonamide soluble in KOH · 2°: insoluble in KOH · 3°: no reaction
Nitrous acid with 1° amines§ 9.2 →
aliphatic: $\mathrm{RNH_{2}+HNO_{2}\rightarrow ROH+N_{2}\uparrow+H_{2}O}$; aromatic, 273–278 K: $\mathrm{ArN_{2}^{+}Cl^{-}}$
Ring reactions of aniline§ 9.2 →
$\mathrm{Br_{2}(aq)}$ → 2,4,6-tribromoaniline; protect as acetanilide → 4-substituted product; direct nitration ≈ 51% p, 47% m, 2% o; conc. $\mathrm{H_{2}SO_{4}}$, 453–473 K → sulphanilic acid; no Friedel–Crafts
Diazotisation (273–278 K)§ 9.3 →
$\mathrm{C_{6}H_{5}NH_{2}+NaNO_{2}+2HCl\rightarrow C_{6}H_{5}N_{2}^{+}Cl^{-}+NaCl+2H_{2}O}$
Sandmeyer / Gattermann§ 9.3 →
$\mathrm{ArN_{2}^{+}\xrightarrow{Cu_{2}X_{2}/HX}ArX}$ (Sandmeyer); $\ \mathrm{\xrightarrow{Cu/HX}ArX}$ (Gattermann); $\ \mathrm{\xrightarrow{CuCN/KCN}ArCN}$
Iodo- and fluoroarenes§ 9.3 →
$\mathrm{ArN_{2}^{+}\xrightarrow{KI}ArI}$; $\ \mathrm{ArN_{2}^{+}\xrightarrow{HBF_{4}}ArN_{2}^{+}BF_{4}^{-}\xrightarrow{\Delta}ArF+BF_{3}+N_{2}}$
–H, –OH, –NO₂ from $\mathrm{ArN_{2}^{+}}$§ 9.3 →
$\mathrm{\xrightarrow{H_{3}PO_{2}\ or\ C_{2}H_{5}OH}ArH}$; $\ \mathrm{\xrightarrow{H_{2}O,\ warm}ArOH}$; $\ \mathrm{ArN_{2}^{+}BF_{4}^{-}\xrightarrow{NaNO_{2},\ Cu}ArNO_{2}}$
Coupling (N₂ kept)§ 9.3 →
$\mathrm{ArN_{2}^{+}}$ + phenol ($\mathrm{OH^{-}}$, mild) → 4-hydroxyazobenzene (orange); + aniline ($\mathrm{H^{+}}$, mild) → 4-aminoazobenzene (yellow); attack para to $\mathrm{{-}OH}$/$\mathrm{{-}NH_{2}}$
Chapter 10 · Biomolecules
Glucose: open-chain evidence§ 10.1 →
HI → hexane (straight chain) · $\mathrm{NH_{2}OH}$, HCN (C=O) · $\mathrm{Br_{2}}$ water → gluconic acid (CHO) · $\mathrm{(CH_{3}CO)_{2}O}$ → pentaacetate (5 OH) · $\mathrm{HNO_{3}}$ → saccharic acid ($\mathrm{CH_{2}OH}$)
Anomers and D/L§ 10.1 →
α/β differ only at the anomeric C (C1 aldose, C2 ketose); Haworth (D sugar): α OH down, β OH up · D/L: OH on the lowest stereocentre right (D) or left (L) in Fischer; (+)/(−) is the sign of rotation
Disaccharides§ 10.1 →
sucrose: α-glucose C1–C2 β-fructose, non-reducing · maltose: α(1→4) glucose–glucose, reducing · lactose: β-galactose C1–C4 glucose, reducing · invert sugar: $+66.5^{\circ}\rightarrow$ glucose $(+52.5^{\circ})$ + fructose $(-92.4^{\circ})$
Molar mass of a sugar chain§ 10.1 →
$n$ hexose units: $M=180.16\,n-18.02\,(n-1)$; disaccharide $342.30\ \mathrm{g\,mol^{-1}}$
Polysaccharides§ 10.1 →
amylose: α(1→4), unbranched, soluble (15–20%) · amylopectin: α(1→4) + α(1→6) branches (80–85%) · cellulose: β(1→4), straight · glycogen: like amylopectin, more branched
Amino acid in solution§ 10.2 →
acid: $\mathrm{H_{3}\overset{+}{N}CHRCOOH}$ ⇌ zwitterion $\mathrm{H_{3}\overset{+}{N}CHRCOO^{-}}$ ⇌ base: $\mathrm{H_{2}NCHRCOO^{-}}$; net charge 0 at the isoelectric point
Peptide arithmetic§ 10.2 →
$n$ residues: $n-1$ peptide bonds, $n-1$ $\mathrm{H_{2}O}$ lost · $M=\sum M_{i}-18.02\,(n-1)\ \mathrm{g\,mol^{-1}}$ · sequences: $k^{n}$ ($k$ amino acids, repeats allowed), $n!$ (all different, each once)
Levels of protein structure§ 10.2 →
1° sequence (peptide bonds) · 2° α-helix, β-sheet (H-bonds) · 3° whole-chain fold (H-bonds, S–S, ionic, van der Waals) · 4° subunits · denaturation destroys 2°/3°, keeps 1°
Enzyme rate enhancement§ 10.2 →
same $A$: $\dfrac{k_{\text{enz}}}{k}=e^{\Delta E_{a}/RT}$, $\Delta E_{a}$ = lowering of $E_{a}$
Isoelectric point (JEE)§ 10.2 →
no ionisable side chain: $\mathrm{pI}=\tfrac{1}{2}(\mathrm{p}K_{a1}+\mathrm{p}K_{a2})$
Vitamins and deficiency diseases§ 10.3 →
fat-soluble: A (night blindness), D (rickets), E (fragile RBCs), K (slow clotting) · water-soluble: B₁ (beri-beri), B₂ (cheilosis), B₆ (convulsions), B₁₂ (pernicious anaemia), C (scurvy)
Nucleoside and nucleotide§ 10.3 →
nucleoside = base + pentose − H₂O (base on C1′) · nucleotide = nucleoside + $\mathrm{H_{3}PO_{4}}$ − H₂O (phosphate on C5′)
Base pairing and Chargaff's rules§ 10.3 →
A–T: 2 H-bonds · G–C: 3 H-bonds · double-stranded DNA: A = T, G = C, purines = pyrimidines · H-bonds $=2n_{\mathrm{AT}}+3n_{\mathrm{GC}}$
DNA vs RNA§ 10.3 →
DNA: 2-deoxyribose, A G C T, double helix · RNA: ribose, A G C U, single strand (m-, r-, t-RNA)
Hormones (elementary)§ 10.3 →
steroids (testosterone, oestrogens) · polypeptides (insulin, glucagon) · amino acid derivatives (adrenaline, thyroxine)