Open-book tables

Reference

The periodic table and equation sheet are provided on exams — print them. Everything else here you should know cold or fit onto your handwritten note sheet.

Periodic table

1.008

4.0026

6.94

9.0122

10.81

12.011

14.007

15.999

18.998

20.180

22.990

24.305

26.982

28.085

30.974

32.06

35.45

39.95

39.098

40.078

44.956

47.867

50.942

51.996

54.938

55.845

58.933

58.693

63.546

65.38

69.723

72.630

74.922

78.971

79.904

83.798

85.468

87.62

88.906

91.224

92.906

95.95

101.07

102.91

106.42

107.87

112.41

114.82

118.71

121.76

127.60

126.90

131.29

132.91

137.33

138.91

140.12

140.91

144.24

145

150.36

151.96

157.25

158.93

162.50

164.93

167.26

168.93

173.05

174.97

178.49

180.95

183.84

186.21

190.23

192.22

195.08

196.97

200.59

204.38

207.2

208.98

209

210

222

223

226

227

232.04

231.04

238.03

237

244

243

247

251

252

100

257

101

258

102

259

103

266

104

267

105

268

106

269

107

270

108

269

109

278

110

281

111

282

112

285

113

286

114

289

115

290

116

293

117

294

118

294

Constants

Avogadro's number6.022 × 10²³ mol⁻¹

Gas constant0.08206 L·atm·mol⁻¹·K⁻¹ = 8.314 J·mol⁻¹·K⁻¹

Planck's constant6.626 × 10⁻³⁴ J·s

Speed of light2.998 × 10⁸ m/s

Rydberg constant (energy)2.179 × 10⁻¹⁸ J

Specific heat of water4.184 J·g⁻¹·°C⁻¹

Standard pressure760 torr = 760 mmHg = 101.325 kPa = 1.01325 bar

Standard molar volume (STP)22.414 L/mol at 0 °C and 1 atm

Elementary charge1.602 × 10⁻¹⁹ C

Mass of electron9.109 × 10⁻³¹ kg (0.00055 amu)

0 °C in Kelvin273.15 K

Equation sheet

Measurement & Matter

Densityd = m / V
Celsius ↔ KelvinK = °C + 273.15
Fahrenheit ↔ Celsius°F = (9/5)°C + 32
Percent error% error = |exp − acc| / acc × 100%

Atoms & Moles

Average atomic massΣ (isotope mass × fractional abundance)
Moles from massn = m / M
Particles from molesN = n × 6.022 × 10²³
Mass percent of element% = (n × atomic mass) / molar mass × 100%
Percent yield% yield = (actual / theoretical) × 100%

Solutions & Acids/Bases

MolarityM = mol solute / L solution
DilutionM₁V₁ = M₂V₂
Water autoionizationK_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C
pH / pOHpH = −log[H₃O⁺]; pOH = −log[OH⁻]; pH + pOH = 14.00
From pH back to concentration[H₃O⁺] = 10^(−pH)

Light & Quantum

Wave relationc = λν
Photon energyE = hν = hc / λ
Bohr energy levelEₙ = −2.179 × 10⁻¹⁸ J / n²
Transition energyΔE = −2.179 × 10⁻¹⁸ J (1/n_f² − 1/n_i²)
de Broglie wavelengthλ = h / (mv)
Photoelectric effectKE = hν − Φ

Bonding

Formal chargeFC = valence e⁻ − nonbonding e⁻ − ½(bonding e⁻)
Bond order (MO)BO = ½(bonding e⁻ − antibonding e⁻)
ΔH from bond energiesΔH ≈ Σ BE(bonds broken) − Σ BE(bonds formed)

Gases

Ideal gas lawPV = nRT
Combined gas lawP₁V₁/T₁ = P₂V₂/T₂
Boyle / Charles / AvogadroP₁V₁ = P₂V₂ ; V₁/T₁ = V₂/T₂ ; V₁/n₁ = V₂/n₂
Density of a gasd = PM / RT
Molar mass from gas dataM = dRT / P = mRT / PV
Dalton's lawP_total = ΣP_i ; P_i = χ_i P_total
Gas over waterP_gas = P_total − P_H₂O
RMS speedu_rms = √(3RT / M) (M in kg/mol, R = 8.314)
Graham's lawrate₁/rate₂ = √(M₂/M₁)
van der Waals(P + an²/V²)(V − nb) = nRT

Thermochemistry

Heat with temperature changeq = mCΔT
Heat of phase changeq = n ΔH_fus or n ΔH_vap
First lawΔE = q + w
Pressure–volume workw = −PΔV
Calorimetry balanceq_rxn = −(q_water + q_calorimeter)
Hess's lawΔH_rxn = Σ ΔH_steps
Standard enthalpies of formationΔH°_rxn = Σ n ΔH°f(products) − Σ n ΔH°f(reactants)

Polyatomic ions

AmmoniumNH₄⁺

HydroniumH₃O⁺

AcetateC₂H₃O₂⁻ (CH₃COO⁻)

CyanideCN⁻

HydroxideOH⁻

NitrateNO₃⁻

NitriteNO₂⁻

PermanganateMnO₄⁻

Hydrogen carbonate (bicarbonate)HCO₃⁻

Hydrogen sulfate (bisulfate)HSO₄⁻

Dihydrogen phosphateH₂PO₄⁻

HypochloriteClO⁻

ChloriteClO₂⁻

ChlorateClO₃⁻

PerchlorateClO₄⁻

CarbonateCO₃²⁻

SulfateSO₄²⁻

SulfiteSO₃²⁻

ChromateCrO₄²⁻

DichromateCr₂O₇²⁻

PeroxideO₂²⁻

OxalateC₂O₄²⁻

Hydrogen phosphateHPO₄²⁻

PhosphatePO₄³⁻

PhosphitePO₃³⁻

Solubility rules

SOLUBLE — Group 1 cations (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺) and NH₄⁺

Exceptions: None.

SOLUBLE — Nitrate NO₃⁻, acetate C₂H₃O₂⁻, chlorate ClO₃⁻, perchlorate ClO₄⁻

Exceptions: None.

SOLUBLE — Halides Cl⁻, Br⁻, I⁻

Exceptions: Ag⁺, Pb²⁺, Hg₂²⁺ are insoluble.

SOLUBLE — Sulfate SO₄²⁻

Exceptions: Ca²⁺, Sr²⁺, Ba²⁺, Pb²⁺, Ag⁺, Hg₂²⁺ are insoluble.

INSOLUBLE — Hydroxide OH⁻

Exceptions: Group 1 and NH₄⁺ soluble; Ca²⁺, Sr²⁺, Ba²⁺ slightly soluble.

INSOLUBLE — Sulfide S²⁻

Exceptions: Group 1, Group 2, and NH₄⁺ are soluble.

INSOLUBLE — Carbonate CO₃²⁻, phosphate PO₄³⁻, chromate CrO₄²⁻

Exceptions: Group 1 and NH₄⁺ are soluble.

VSEPR geometries

Notation	Domains	Electron geometry	Molecular geometry	Angle	Hybrid	Polarity
AX₂	2	Linear	Linear	180°	sp	Nonpolar (identical X)
AX₃	3	Trigonal planar	Trigonal planar	120°	sp²	Nonpolar (identical X)
AX₂E	3	Trigonal planar	Bent	<120°	sp²	Polar
AX₄	4	Tetrahedral	Tetrahedral	109.5°	sp³	Nonpolar (identical X)
AX₃E	4	Tetrahedral	Trigonal pyramidal	<109.5°	sp³	Polar
AX₂E₂	4	Tetrahedral	Bent	<109.5°	sp³	Polar
AX₅	5	Trigonal bipyramidal	Trigonal bipyramidal	120°/90°	sp³d	Nonpolar (identical X)
AX₄E	5	Trigonal bipyramidal	Seesaw	<120°/<90°	sp³d	Polar
AX₃E₂	5	Trigonal bipyramidal	T-shaped	<90°	sp³d	Polar
AX₂E₃	5	Trigonal bipyramidal	Linear	180°	sp³d	Nonpolar
AX₆	6	Octahedral	Octahedral	90°	sp³d²	Nonpolar (identical X)
AX₅E	6	Octahedral	Square pyramidal	<90°	sp³d²	Polar
AX₄E₂	6	Octahedral	Square planar	90°	sp³d²	Nonpolar

Strong acids

HCl · HBr · HI · HNO₃ · H₂SO₄ · HClO₄ · HClO₃

Strong bases

LiOH · NaOH · KOH · RbOH · CsOH · Ca(OH)₂ · Sr(OH)₂ · Ba(OH)₂

Anything not on these lists is weak.

Oxidation number rules

• Free elements have oxidation number 0 (including O₂, P₄, S₈, and metals).
• Monatomic ions equal their charge (Na⁺ = +1, S²⁻ = −2).
• Fluorine is always −1; other halogens are −1 except when bonded to oxygen or a lighter halogen.
• Oxygen is usually −2; −1 in peroxides, +2 in OF₂.
• Hydrogen is +1 with nonmetals, −1 with metals (metal hydrides).
• The sum of oxidation numbers equals the overall charge of the species.

Significant figures

• All nonzero digits are significant.
• Zeros between nonzero digits are significant (1002 has 4).
• Leading zeros are never significant (0.0034 has 2).
• Trailing zeros count only if a decimal point is present (2.50 has 3; 250 is ambiguous, 2.50 × 10² is not).
• Multiplication/division: the answer takes the FEWEST significant figures.
• Addition/subtraction: the answer takes the FEWEST decimal places.
• Logs: the number of decimal places in the log equals the sig figs in the original number (pH of 1.0 × 10⁻³ M is 3.00).
• Exact numbers (counted items, defined conversions) have infinite significant figures.