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General Chemistry Formula Sheet

Complete chemistry formula sheet: stoichiometry, electronic structure, bonds, redox, thermochemistry, equilibria, electrochemistry. All formulas in PDF.

Elements, Substances, and Stoichiometric CalculationsTheory
Structure of the Atom and Nucleus
A=Z+NA = Z + N
ZAX^{A}_{Z}\mathrm{X}
N(t)=N0 e−λt,t1/2=ln⁡2λN(t) = N_0\,e^{-\lambda t},\quad t_{1/2} = \dfrac{\ln 2}{\lambda}
Atomic Mass, Molecular Mass, and Formulas
Mr=∑ini Ar,iM_r = \sum_i n_i\,A_{r,i}
Molecular formula=k×empirical formula\text{Molecular formula} = k\times\text{empirical formula}
1 u=1.6605×10−27 kg1\,\mathrm{u} = 1.6605\times10^{-27}\,\mathrm{kg}
The Mole and Avogadro's Constant
NA=6.022×1023 mol−1N_A = 6.022\times10^{23}\,\mathrm{mol^{-1}}
n=mMn = \dfrac{m}{M}
N=n NAN = n\,N_A
Stoichiometric Equations and Limiting Reagent
aA+bB→cC+dDaA + bB \to cC + dD
nAa  vs  nBb  ⇒  minimum = limiting\dfrac{n_A}{a} \;\text{vs}\; \dfrac{n_B}{b}\;\Rightarrow\;\text{minimum = limiting}
η%=mactualmtheor×100\eta\% = \dfrac{m_{actual}}{m_{theor}}\times100
Electronic Structure and the Periodic TableTheory
Bohr Model and Atomic Spectra
E=hν=hc/λE = h\nu = hc/\lambda
En=−13.6/n2 eVE_n = -13.6/n^2\,\mathrm{eV}
1λ=RH ⁣(1nf2−1ni2)\dfrac{1}{\lambda} = R_H\!\left(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2}\right)
Wave Mechanics: Orbitals and Quantum Numbers
Δx Δp≥ℏ/2\Delta x\,\Delta p \geq \hbar/2
H^ψ=Eψ\hat{H}\psi = E\psi
ℓ=0,1,…,n−1;mℓ=−ℓ,…,+ℓ\ell = 0,1,\ldots,n-1;\quad m_\ell = -\ell,\ldots,+\ell
Electron Configuration
1s 2s 2p 3s 3p 4s 3d 4p…1s\,2s\,2p\,3s\,3p\,4s\,3d\,4p\ldots
max 2ℓ+1 orbitals,  2(2ℓ+1) e−\text{max } 2\ell+1 \text{ orbitals},\; 2(2\ell+1)\,e^-
Periodic Properties
X(g)+Ei→X+(g)+e−\mathrm{X(g)} + E_i \to \mathrm{X^+(g)} + e^-
X(g)+e−→X−(g)+Ae\mathrm{X(g)} + e^- \to \mathrm{X^-(g)} + A_e
Chemical Bonds and Molecular GeometryTheory
Covalent Bond and Electronegativity
μ=q⋅d\mu = q\cdot d
Δχ→0: covalent;  Δχ large: ionic\Delta\chi \to 0:\,\text{covalent};\;\Delta\chi\,\text{large}:\,\text{ionic}
Ebond=−Emin,MorseE_{bond} = -E_{min,Morse}
Ionic Bond and Ionic Compounds
Ulat=−NAMz+z−e24πε0r0(1−1n)U_{lat} = -\dfrac{N_A M z^+ z^- e^2}{4\pi\varepsilon_0 r_0}\left(1-\dfrac{1}{n}\right)
F∝z+z−r2F \propto \dfrac{z^+ z^-}{r^2}
Molecular Geometry: Hybridization and VSEPR
sp:180°,  sp2:120°,  sp3:109.5°sp:180°,\; sp^2:120°,\; sp^3:109.5°
n. domains⇒VSEPR geometry\text{n. domains} \Rightarrow \text{VSEPR geometry}
Metallic Bond and Intermolecular Forces
London<dipole-dipole<H bond≪covalent\text{London} < \text{dipole-dipole} < \text{H bond} \ll \text{covalent}
Oxidation States and Redox ReactionsTheory
Oxidation State
∑NO=0  (compound);  =charge  (ion)\sum \text{NO} = 0\;(\text{compound});\; = \text{charge}\;(\text{ion})
Oxidation and Reduction
Red: Ox+ne−→Red\text{Red: } \mathrm{Ox} + ne^- \to \mathrm{Red}
Ox: Red→Ox+ne−\text{Ox: } \mathrm{Red} \to \mathrm{Ox} + ne^-
Balancing Redox Reactions
Acid: O+2H++2e−→H2O\text{Acid: } \mathrm{O} + 2\mathrm{H^+} + 2e^- \to \mathrm{H_2O}
Basic: O+H2O+2e−→2OH−\text{Basic: } \mathrm{O} + \mathrm{H_2O} + 2e^- \to 2\mathrm{OH^-}
Redox and the Periodic Table
Ecell∘=Ecathode∘−Eanode∘E^\circ_{\mathrm{cell}} = E^\circ_{\mathrm{cathode}} - E^\circ_{\mathrm{anode}}
ΔG∘=−nFE∘\Delta G^\circ = -nFE^\circ
States of Aggregation of MatterTheory
Solid State
nλ=2dsin⁡θ  (Bragg)n\lambda = 2d\sin\theta\;\text{(Bragg)}
ρ=Z⋅MNA⋅a3\rho = \dfrac{Z\cdot M}{N_A\cdot a^3}
Liquid State
γ=FL\gamma = \dfrac{F}{L}
η∝eEa/RT\eta \propto e^{E_a/RT}
Ideal Gas Law and Dalton's Law
PV=nRTPV = nRT
Ptot=∑iPiP_{tot} = \sum_i P_i
χi=ni/ntot\chi_i = n_i/n_{tot}
Real Gases and Van der Waals Equation
(P+an2V2)(V−nb)=nRT\left(P + \dfrac{an^2}{V^2}\right)(V - nb) = nRT
Pideal=Preal+an2V2P_{ideal} = P_{real} + \dfrac{an^2}{V^2}
Chemical ThermodynamicsTheory
System, Surroundings, and Energy
ΔU=Q−W\Delta U = Q - W
1 cal=4.184 J1\,\mathrm{cal} = 4.184\,\mathrm{J}
First Law: Internal Energy and Enthalpy
ΔH=ΔU+Δ(PV)\Delta H = \Delta U + \Delta(PV)
ΔHrxn∘=∑νiΔHf,i∘\Delta H^\circ_{rxn} = \sum \nu_i \Delta H_{f,i}^\circ
Hess's Law
ΔHrxn∘=∑νiΔHf∘(prod)−∑νiΔHf∘(reag)\Delta H^\circ_{rxn} = \sum \nu_i \Delta H_{f}^\circ(\text{prod}) - \sum \nu_i \Delta H_f^\circ(\text{reag})
Second Law and Entropy
ΔSuniv=ΔSsys+ΔSsurr≥0\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr} \geq 0
S∘(0 K)=0S^\circ(0\,\mathrm{K}) = 0
ΔS∘=∑νiS∘(prod)−∑νiS∘(reag)\Delta S^\circ = \sum \nu_i S^\circ(\text{prod}) - \sum \nu_i S^\circ(\text{reag})
Gibbs Free Energy and Spontaneity
ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S
ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln K
Ttrans=ΔH/ΔST_{trans} = \Delta H / \Delta S
Phase EquilibriaTheory
Phase Transitions and the Clapeyron Equation
dPdT=ΔHTΔV\dfrac{dP}{dT} = \dfrac{\Delta H}{T\Delta V}
ln⁡ ⁣(P2P1)=−ΔHvapR(1T2−1T1)\ln\!\left(\dfrac{P_2}{P_1}\right) = -\dfrac{\Delta H_{vap}}{R}\left(\dfrac{1}{T_2} - \dfrac{1}{T_1}\right)
One-Component Phase Diagrams
Triple point: S⇌L⇌G\text{Triple point: } S \rightleftharpoons L \rightleftharpoons G
Critical point: Tc, Pc\text{Critical point: } T_c,\,P_c
Raoult's Law and Deviations
Pi=χiPi∘P_i = \chi_i P_i^\circ
Ptot=∑iχiPi∘P_{tot} = \sum_i \chi_i P_i^\circ
Colligative Properties
ΔTb=Kbm\Delta T_b = K_b m
ΔTf=Kfm\Delta T_f = K_f m
Π=iMRT\Pi = iMRT
Gaseous Reaction Equilibria and pHTheory
Chemical Equilibrium Constant
Kc=∏[prod]ν∏[reag]νK_c = \dfrac{\prod [\text{prod}]^{\nu}}{\prod [\text{reag}]^{\nu}}
Kp=Kc(RT)ΔnK_p = K_c(RT)^{\Delta n}
ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln K
Kw and pH of Strong Acids and Bases
Kw=[H3O+][OH−]=10−14K_w = [H_3O^+][OH^-] = 10^{-14}
pH=−log⁡[H3O+]\mathrm{pH} = -\log[H_3O^+]
pH+pOH=14\mathrm{pH + pOH = 14}
Weak Acids and Bases: Ka/Kb and pH Calculation
Ka=[H3O+][A−][HA]K_a = \dfrac{[H_3O^+][A^-]}{[HA]}
Ka⋅Kb=KwK_a\cdot K_b = K_w
[H3O+]≈KaC[H_3O^+] \approx \sqrt{K_a C}
Degree of Dissociation, Inductive Effect, Leveling Effect
α=[H3O+]C=KaC\alpha = \dfrac{[H_3O^+]}{C} = \sqrt{\dfrac{K_a}{C}}
Ka(CCl3COOH)>Ka(CH3COOH)K_a(\mathrm{CCl_3COOH}) > K_a(\mathrm{CH_3COOH})
Buffer Solutions (Introduction)
pH=pKa+log⁡ ⁣([A−][HA])\mathrm{pH} = \mathrm{p}K_a + \log\!\left(\dfrac{[A^-]}{[HA]}\right)
Buffer range: pKa±1\text{Buffer range: } \mathrm{p}K_a \pm 1
ElectrochemistryTheory
Redox Balancing (Ionic-Electronic Method)
Ox: Red→Ox+ne−\text{Ox: } \mathrm{Red \to Ox + ne^-}
Red: Ox+ne−→Red\text{Red: } \mathrm{Ox + ne^- \to Red}
Galvanic Cells, E°, and the Nernst Equation
Ecell∘=Ecat∘−Ean∘E^\circ_{cell} = E^\circ_{cat} - E^\circ_{an}
ΔG∘=−nFE∘\Delta G^\circ = -nFE^\circ
E=E∘−0.0592nlog⁡QE = E^\circ - \dfrac{0.0592}{n}\log Q
Batteries
Concentration: E=−0.0592nlog⁡CdilCconc\text{Concentration: } E = -\dfrac{0.0592}{n}\log\dfrac{C_{dil}}{C_{conc}}
Corrosion
Fe→Fe2++2e−(E∘=−0.44 V)\mathrm{Fe \to Fe^{2+} + 2e^-} (E^\circ = -0.44\,\mathrm{V})
O2+2H2O+4e−→4OH−(E∘=+0.40 V)\mathrm{O_2 + 2H_2O + 4e^- \to 4OH^-} (E^\circ = +0.40\,\mathrm{V})
Electrolysis and Faraday's Laws
m=I⋅t⋅Mn⋅Fm = \dfrac{I\cdot t\cdot M}{n\cdot F}
F=96485 C⋅mol−1F = 96485\,\mathrm{C\cdot mol^{-1}}
Q=I⋅tQ = I\cdot t
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