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General Chemistry Reference Sheet This reference sheet addresses some of the more peculiar pieces of information that need to be memorized in a general chemistry course. It also contains a simple set of essential formulas in chemistry with cautions, explanations, and general tips. This sheet is meant to be as concise as possible, and many information in the textbook is left out in favor of cautions and tips. This sheet is, therefore, best used as a supplement to, not a replacement of, the textbook.

Soluble NO3 − CH3 COO− Cl− Br− I− SO4 2− Insoluble S2− 2−

SI Fundamental Units Mass Length Time Temperature Amount of substance Electric current Luminous intensity

Kilogram (kg) Meter (m) Second (s) Kelvin (K) Mole (mol) Ampere (A) Candela (cd)

Atomic Experiments and Models

Discovered e− ; Cathode ray Plum pudding model R. A. Millikan Measured charge of e− ; Oil drop H. Becquerel/M. Curie Discovered radioactivity E. Rutherford Discovered α, β, and γ rays Discovered nucleus; Gold foil experiment J. Chadwick Discovered neutrons N. Bohr Bohr model (electron orbits) Quantum mechanicists Quantum model J. J. Thomson

Polyatomic Ions +

−

CO3 PO4 3− OH−

Exceptions None None Ag+ , Hg2 2+ , Pb2+ Ag+ , Hg2 2+ , Pb2+ Ag+ , Hg2 2+ , Pb2+ Sr2+ , Ba2+ , Hg2 2+ , Pb2+ Exceptions NH4 + , alkali metal cations, Ca2+ , Sr2+ , Ba2+ NH4 + , alkali metal cations NH4 + , alkali metal cations NH4 + , alkali metal cations, Ca2+ , Sr2+ , Ba2+

Strong acids and bases dissociate in water completely. Strong Acids HCl HBr HI HClO3

HClO4 HNO3 H2 SO4 Ba(OH)2

Strong Bases Alkali metal hydroxides Ca(OH)2 Sr(OH)2

Activity Series

Metals below H+ cannot react with acids to form H2 . More active metals are better reducing agents. From most active to least active: Li+ , K+ , Ba2+ , Ca2+ , Na+ , Mg2+ , Al3+ , Mn2+ , Zn2+ , Cr3+ , Fe2+ , Co2+ , Ni2+ , Sn2+ , Pb2+ , H+ , Cu2+ , Ag+ , Hg2+ , Pt2+ , Au3+

OH C2 O4 2− CNO− C2 H3 O2 −

hydroxide oxalate cyanate acetate

SCN− SO3 2− CO3 2− PO4 3− S2 O3 2−

NO3 − ClO4 − ClO3 − ClO− HPO4 2−

CrO4 2− Cr2 O7 2− MnO4 − N3 − C4 H4 O6 2− O2 − PO2 3− SiO3 2−

chromate dichromate permanganate azide tartrate superoxide hypophosphite silicate

H3 O+ PO3 3− Hg2 2− C2 2− S2 2− AsO3 3− AsO4 3− P2 O7 4−

nitrate perchlorate chlorate hypochlorite hydrogen phosphate hydronium phosphite mercury (I) carbide Phase Changes disulfide From solid arsenite To solid arsenate To liquid melting pyrophosphate To gas sublimation

Flame Colors Calcium Copper (I) Copper (II) Potassium Lithium Sodium Strontium Barium Iron (III) Cesium Indium Lead Rubidium

Copper (II) Nickel Permanganate Chromate Dichromate Iron (II) Iron (III)

Blue Green Purple Yellow Orange Light blue Rusty yellow

Thermodynamic Laws First Law: Energy cannot be created nor destroyed. It can only be transferred in the form of either heat or work. Second Law: Any spontaneous reaction increases the entropy of the universe. Third Law: An ideal solid crystal at 0 K has an entropy of 0.

Thermodynamic Formulas

Strong Acids and Bases

ammonium cyanide peroxide hydrogen sulfate thiocyanate sulfite carbonate phosphate thiosulfate

NH4 CN− O2 2− HSO4 −

Solution Colors

Ionic Solubility Chart

Brick red Blue Green or blue-green Lilac Dark red Bright yellow Red Light green Gold Blue–Violet Blue Blue Red–Violet

Standard thermodynamic conditions 298 K; 1 atm; 1 M Kinetic energy K = mv 2 /2 Electrostatic potential energy UE = (kC Q1 Q2 )/d Internal energy ∆E = q + w Enthalpy H = E + PV Specific heat s = q/(m · ∆T ) Entropy in reversible reaction ∆Ssystem = (∆H)/T ∆Ssurrounding = −(∆H)/T Microstate-entropy relationship S = k ln W Gibbs free energy G = H − TS Gibbs free energy change ∆G = ∆H − T ∆S ∆G = ∆G◦ + RT ln Q Hess’s Law ∆Htotal = Σ∆Hi

Constants

Boltzmann’s constant kB = 1.381 × 10−23 m2 kg · s−2 K−1 Coulomb’s constant kC = 1/(4π0 ) = 8.988 × 109 J · m/C2 Avogadro’s number NA = 6.022 × 1023 mol−1 Faraday’s constant F = 9.649 × 104 C/mol Planck’s constant h = 6.626 × 10−34 J·s Ideal gas constants R = 0.0821 (L · atm)/(mol · K) R = 8.314 J/(mol · K) Vacuum permittivity 0 = 1/(µ0 c2 ) = 8.854 × 10−12 F/m Vacuum permeability µ0 = 1.257 × 10−6 N·A−2 Atomic mass 1 amu = 1.661 × 10−24 g Electron charge e = 1.602 × 10−19 C Electronvolt 1 eV = 1.602 × 10−19 J Atmospheric pressure 1 atm = 1.013 × 105 Pa Absolute zero 0 K = -273.15 ◦ C Speed of light in vacuum c = 2.998 × 108 m/s

Quantum Mechanical Formulas From liquid freezing vaporization

From gas deposition condensation -

Energy of a quantum E = hν Wavelength-frequency relationship RRR c=ν·λ Probability distribution PV = |ψ(x, y, z)|2 dxdydz V

Laws of Quantum Mechanics Heisenberg’s Uncertainty Principle

Pauli Exclusion Principle

Hund’s Rule

Atomic size

Corollary: It is impossible to determine both the position and the momentum for a sufficiently small particle like an e− . No two e− in an atom can share the same set of four quantum numbers. Corollary: A suborbital can hold a maximum of 2e− . Energy is the lowest when the number of e− with the same spin is maximized. Corollary: e− will first half-fill all the empty suborbitals, then go back and fill the half suborbitals.

Ionic size

−

Quantum Numbers of e Principal (n) Azimuthal (l) Magnetic (ml ) Spin (ms )

The energy shell of the e− , e.g. 4 in 4d1 . The suborbital shape, with s=0, p=1, d=2, f=3, e.g. 2 in 4d1 . The suborbital, ranging from −l to l, e.g. −2 in 4d1 . The spin of e− . Two e− in the same suborbital has either −1/2 or 1/2.

Molecular Geometry Hybridization sp

Atomic Properties

∆x · ∆p ≥ ¯ h/2

Nonbonding electrons

Geometry

IMFs in Molecular Solids 1 the 2

N-th ionization energy Electron affinity Metallic character

distance between two adjacent nucleii. Cations are smaller than their parent atoms. Anions are larger than their parent atoms. The energy required to remove the n-th electron from a ground state gaseous atom. The energy released by adding an electron to a gaseous atom. The qualities of a metal. Metals are shiny and heat and electricity-conducting; they have malleble solid form, form basic ionic oxides, and tend to form cations in an aqueous solution.

Periodic Properties Property Atomic size Ionization energy Electron affinity Metallic character

Left to Right Decreasing Increasing Large if adding to a previously empty orbital Decreasing

Type IMFs Molecular Van der Waals forces, dipole-dipole interactions, hydrogen bonds Covalent- Covalent bonds network

linear

sp

0 1

trigonal planar bent

Ionic

Electrostatic interactions

sp3

0 1 2

tetrahedral trigonal pyramidal bent

Metallic

Metallic bonds

0 1 2 3

trigonal bipyramidal seesaw T-shaped linear

0 1 2

octahedral square pyramidal square planar

3

sp d

sp3 d2

Increasing

Types of Crystalline Solids

0

2

Top to Bottom Increasing Decreasing No apparent change

Properties Soft, low melting point, poor conduction Very hard, high melting point, poor conduction Hard, high melting point, poor conduction Soft to very hard, low to very high melting point, excellent conduction

Boiling Points of Molecular Compounds The relative boiling points of molecular compounds can be determined by their IMFs. The stronger the IMFs are, the higher the boiling point. (Note that linear compounds like straight-chain hydrocarbons have higher van der Waals forces than non-linear compounds because their molecules have a greater area of contact.)

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London dispersion force (van der Waals forces, induced dipoledipole interactions) Dipole-dipole tions

interac-

Hydrogen bonds

Interactions between dipoles partially charged through the movement of shared electron. Presents in all compounds. Weakest of the three. Interactions between dipoles partially charged through the electronegativity difference of two bonding atoms. A special kind of dipole-dipole interactions present in compounds that have hydrogen and either oxygen or nitrogen. Strongest of the three.

Acid-Base Theories Arrhenius

BrønstedLowry Proton donors Proton acceptors Hydrogen atom

Acids

[H+ ] >[OH− ]

Bases

[OH− ] >[H+ ]

Acids have

H+

Bases have

OH−

Unshared electron pair

Acid + Base →

Salt + H2 O

Conjugate acid + Conjugate base

Lewis Electron acceptors Electron donors Electron accepting atom Unshared electron pair

Kinetic Molecular Theory (KMT) There is a very large number of particles; Particles are in constant random motion and collide constantly with the wall; Collisions of particles with the wall are perfectly elastic; Particles exert no force upon each other.

Properties of Solutions Solvation The uniform dispersion of a solute in a solvent. Hydration Solvation in water. Crystallization The reverse reaction of solvation. Saturated A solution in equilibrium. Unsaturated A solution with less solute than saturation. Supersaturated A solution with more solute than saturation. (Will undergo crystallization if a crystal seed is present.) Miscible Two liquids that dissolve in any proportion. Henry’s Law S ∝ P (S: solubility)

Colligative Properties

Activation Energy

Physical properties of a solution that depends on the concentration of solutes. More solutes will lead to:

Collision model

1. Lower vapor pressure: PA = XA PA◦ (Raoult’s Law) 2. Higher boiling point: Tb = Tb◦ + kb m (Molality) 3. Lower freezing point: Tf = Tf◦ − kf m (Molality) 4. Higher osmotic pressure: π = RT · M (Molarity) Colligative properties also depend on the van ’t Hoff factor (i = number of particles after reaction / number of particles before reaction). The greater i is, the more colligative properties it exerts on the solution.

Reaction Rate The reaction rate r = d[X]/dt can be determined from the reaction by the rate law r = k[A]a [B]b ... Where a, b, etc. are reaction orders for the reactants. Reaction orders can only be determined experimentally, because reactions will in theory go through several steps, the slowest of which is the rate-determining step. Reaction order is determined by the number of atoms participating in the rate-determining step. The sum of these orders is the overall order. Concentration function [X] can be determined as Z

t

rdτ + [X]0

[X]t = 0

Therefore, for first-order reactions, ln[X]t = −kt + ln[X]0 Graphically, t is proportional to ln[X]t with the slope −k. And for second-order reactions, 1 1 = kt + [X]t [X]0 Graphically, t is proportional to 1/[X]t with the slope k.

Reaction Half-time The half-time of a reaction is the amount of time needed to consume half of the reactants. It is denoted t1/2 . For first order reactions, t1/2 ≈ 0.693/k. For second order reactions, t1/2 = 1/(k[X]0 ).

Concentration

Reactions occur as a result of collisions between molecules. Activation energy (Ea ) The minimum energy required for a reaction to occur. Arrhenius equation ln k = ln A − Ea /RT (This means that ln k ∝ 1/T ) Activation energy is lowered when a catalyst is present. Inorganic catalysts usually provide a site on which reactants can adsorb; organic catalysts, or enzymes, bind specific to substrate molecules (“lock-and-key”).

Definition (Moles solute)/(Liters solution) (Moles solute)/(Kilogram solvent) (Moles solute)/(Moles solution) (Mass of solute)/(Mass of solution) (Volume of solute)/(Volume of solution) Caution: It is an extremely common mistake to confuse molarity with molality. Check your R’s and L’s!

Spectrophotometry of Concentration

An equilibrium reaction will spontaneously balance an outside effect added to it. For example, Change in amount of reactants or products: The reaction will consume more of the substance in excess to balance the change; Change in volume or pressure: The reaction will form more gas if volume increases or if pressure decreases, and will form less gas if volume decreases or if pressure increases; Change in temperature: Endothermic reactions will shift left for lower temperatures and shift right for higher temperatures. Exothermic reactions will shift right for lower temperatures and shift left for higher temperatures.

Beer’s law, A = lc, relates concentration and light absorption. Absorbance (A) − log10 (I/I0 ) (liquids) − ln(I/I0 ) (gases) Absorption coefficient () Depends on the solution. Length of path (l) The length of the path travelled by light. Concentration (c) The concentration of the solution. In spectrophotometry, the length of path is fixed. Therefore, when using the same solution, A ∝ c.

Gas Laws STP 273 K; 1 atm Boyle’s Law P ∝ 1/V Charles’s Law P ∝T Avogadro’s Law P ∝n Ideal Gas Equation P V = nRT Law of Partial Pressure pPn = Xn Pt (3RT )/M Effusion Rate u= p Graham’s Law u1 /u2 = M2 /M1 Density Formula d = (P M)/(RT ) Deviation from Ideal Behavior (P V )/(RT ) Van der Waals Equation
P + (n2 a)/V 2 (V − nb) = nRT Clausius-Clapeyron Equation ln P = −∆Hvap /(RT ) + C Caution: When using the effusion rate formula, the R value must be in joules (8.314), and the M value must be converted to kg/mol.

Equilibrium Formulas Ion-product constant of water Kw = [H+ ][OH− ] = 1.0 × 10−14 (278 K) Henderson-Hasselbalch equation pH = pKa + log([base]/[acid]) Van ’t Hoff equation d(ln K)/dT = (∆H ◦ )/(RT 2 ) ln K = −∆H ◦ /(RT ) + ∆S ◦ /R

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Notation Molarity (M) Molality (m) Mole fraction (X) Mass percentage Volume percentage

Le Chˆ atelier’s Principle

Equilibrium Constant For reactions in a solution, the equilibrium constant of a reaction * sS + tT aA + bB ) Is defined as Kc =

[S]s [T ]t [A]a [B]b

When the reaction is in equilibrium. If the reaction is a equilibrium between a solid and its ions in solution, then Kc is its solubility product constant, Ksp . If the reaction is a dissociative reaction of a weak acid, then Kc is its acid dissociation constant, Ka . Polyprotic (having more than one H) acids have multiple Ka , but usually Ka1 determines the pH. For a conjugate acid-base pair, Ka · Kb = Kw . If the reactants are gases, then the equilibrium constant is defined as P sP t Kp = Sa Tb PA PB When the reaction is in equilibrium. The Formulas above, when applied to non-equilibrium situations, gives Q. The reaction forms products if Q < K, reactants if Q > K, and nothing if Q = K (already in equilibrium).

Equilibrium Constant (cont.)

Types of Magnetic Materials (cont.)

Stereoisomerism (cont.)

For all equilibrium reactions, there are more reactants than products if K < 1, more products than reactants if K > 1, and the same amount of reactants and products if K = 1.

Diamagnetic: Can be magnetized to repulse external magnetic fields, but cannot retain magnetism. Diamagnetic materials have a magnetic permeability of less than µ0 . Examples of diamagnets are bismuth and antimony. Ferromagnetic: Can be magnetized and retain magnetism. Ferromagnetism depends both on the chemical composition and the structure of the material (iron is a ferromagnet, while stainless steel is not). Examples of ferromagnets include cobalt and iron.

E/Z isomerism: If the two ends of the bond do not have a common hydrogen atom, then the compound exhibits E/Z isomerism. The Z isomer has the “larger” substituents (defined by the CIP Rules) of both ends on the same side, while the E isomer has the larger substituents on different sides.

Acid Character of Hydrogen Atoms Hydrogen atoms are acidic when they are weakly bonded, and when the molecule/atom they are bonded to forms stable anions. In organic compounds, the hydrogen atoms in carboxyl groups (COOH) are usually the most acidic.

Indicators for Acid-Base Titration Indicator Small pH Methyl violet Yellow Bromophenol Yellow blue Methyl orange Red Methyl red Red Litmus Red Bromothymol Yellow blue Phenolphthalein Colorless

Color change 0.0–1.6 3.0–4.6

Large pH Violet Blue

3.1–4.4 4.4-6.2 5.0–8.0 6.0–7.6

Yellow Yellow Yellow Blue

8.3–10.0

Pink

Oxidation and Reduction Oxidation Loss of electrons Oxidation num. increases Occurs at anode Mnemonic devices:

Reduction Gains electrons Oxidation num. decreases Occurs at cathode

• “OIL RIG” (Oxidation Is Loss, Reduction Is Gain) • “What an ox loses, a red cat gains” (An = anode; ox = oxidation; red = reduction; cat = cathode)

Electrochemical Formulas E = −(∆G)/(nF ) E = E ◦ − (RT /nF ) ln Q E = E ◦ − (0.0592/n) log Q ◦ ◦ ◦ Standard cell potential E = Ered cathode − Ered anode Energy of a charged particle E = qV Faraday’s Law of Electrolysis m = (Q/F )(M/z)

Electromotive force Nernst equation

Types of Magnetic Materials Paramagnetic: Can be magnetized to attract external magnetic fields, but cannot retain magnetism. Paramagnetic materials have a magnetic permeability of more than µ0 . They usually have free electrons, especially d and f electrons. Their magnetization follows Curie’s Law (M = C · B/T ). Examples of paramagnets are tungsten and cesium.

Nuclear Chemistry Alpha particles (α) Helium nuclei (42 He) − Beta particles (β ) Electrons (0−1 e) Positrons (β + ) Antielectrons (01 e) Gamma radiation (γ) High energy radiation (00 γ) Units of radioactivity SI: Becquerel (Bq): 1 nucleus/s (Disintegration per second) Curie (Ci): 3.7 ×1010 nuclei/s Units of absorbed radiation SI: Gray (Gy): 1 J/kg (Energy per kilogram tissue) Rad: 0.01 Gy

Metallurgy Metallurgy is the extraction of minerals from ores. Pyrometallurgy: The use of heat to convert ores to metals. (Example: Production of iron) Hydrometallurgy: The use of chemical processes in a solution to separate a metal from its ore. (Example: Bayer process for producing aluminum) Electrometallurgy: The use of electrochemical processes to separate a metal. (Example: Hall process for producing aluminum)

Hydrocarbons Name Common Formula Hybridization Alkane Cn H2n+2 sp3 Cycloalkane Cn H2n sp3 Alkene Cn H2n sp2 Alkyne Cn H2n−2 sp Aromatic Cn H2n−6 sp2 In a hydrocarbon with n carbons, the number of hydrogens is 2n + 2, minus 2 for each π bond or carbon ring.

Stereoisomerism Stereoisomerism occurs at bonds such as C=C, where both ends have two different substituents, because the rotation of these substituents are restricted. Cis-trans isomerism: If both ends have a hydrogen atom substituent, then the compound exhibits cis-trans isomerism. The cis-isomer has both hydrogen atoms on the same side, and the trans-isomer has the hydrogen atoms on different sides.

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Cahn-Ingold-Prelog Rules The CIP Rules are used to compare two substituent groups in the E/Z and R/S groups of naming isomers. 1. Direct comparison: If the atoms that are directly connected to the stereocenter are different, then the atom with a higher atomic number receives higher priority. 2. Tiebreaker I: If there is a tie, then a list of atoms two bonds away from the stereocenter is compiled for each of the two substituent groups. The atoms with the greatest atomic number from each list are then compared. If they tie, then the second greatest atoms from each list are compared. This process is repeated until the tie is broken. 3. Tiebreaker II: If there is still a tie after consider atoms two bonds away from the center, then atoms three bonds away are considered in the same way in Tiebreaker I. This process is repeated until the tie is broken. 4. Isotopes: If two groups differ only in isotopes (and are otherwise identical), then mass number is used instead of atomic number in the process. 5. Double and triple bonds: If there is a double bond in the substituent group, then the double bond is treated as a bond with “ghost atoms” (e.g. R-A=B-R’ is treated as R-(A-B)-(B-A)-R’). Triple bonds, similarly, have two ghost atoms for each atom. 6. Cycles: To handle a molecule containing one or more cycles, one must first expand it into a tree (called a hierarchical digraph by the authors) by traversing bonds in all possible paths starting at the stereocenter. When the traversal encounters an atom through which the current path has already passed, a ghost atom is generated in order to keep the tree finite.

Criteria of Aromaticity

Functional Groups (cont.)

If a hydrocarbon

Functional Group Name Suffix/Prefix R-CH2 C6 H5 (benzyl, toluene der. benzylBn) R-C5 H4 N (pyridyl) pyridine der. pyridin-x-yl Note: In actual compounds, change all instances of “halo” above to halogen names (fluoro, chloro, bromo, iodo).

1. Is cyclic, i.e. possesses a carbon ring; 2. Is planar, i.e. all carbons on the ring are on the same plane; 3. Has an uninterrupted cloud of π electrons; 4. The number of pairs of π electrons in the cloud is an odd number, i.e. the number of π electrons in the cloud is 4n + 2; then the hydrocarbon is aromatic. Aromatic compounds are highly stable (cannot undergo addition reactions), but can undergo substitution reactions.

Functional Groups Functional Group R-OH (hydroxyl) R-O-R’ (ether) R-X (halo) R-NH2 (amino) R-COH (aldehyde) R-COX (haloformyl) R-CO-R’ (carbonyl) R-COOH (carboxyl) R-COO( carboxylate) R-COO-R’ (ester) R-CONH2 (amide) R-CNH-R’ (ketimine) R-CHNH (aldimine) R-CONCO-R’ (imide) R-N3 (azide) R-N2 -R’ (azo) R-OCN (cyanate) R-NCO (isocyanate) R-CN (nitrile) R-NC (isonitrile) R-NO (nitroso) R-NO2 (nitro) R-ONO (nitrosooxy) R-ONO2 (nitrate) R-SH (sulfhydryl) R-SCN (thiocyanate) R-NCS (isothiocyanate) R-CSH (carbonothioyl) R-PH3 (phosphino) R-C6 H5 (phenyl, Ph)

Name alcohol ether haloalkane amine aldehyde acyl halide ketone carboxylic acid carboxylate ester amide ketimine aldimine imide

Suffix/Prefix -ol ether halo-amine -al -oyl halide -one -oic acid -oate -oate -amide iminoiminoimido-

azide azo cyanate isocyanate nitrile isonitrile nitroso nitro nitrite nitrate thiol thiocyanate isothiocyanate

azidoazocyanatoisocyanatocyanoisocyanonitrosonitronitrosooxynitroxy-thiol thiocyanatoisothiocyanato-

thial phosphine benzene der.

Enantiomerism

Amino Acids Hydrophobic amino acids: Name Code Name Alanine Ala Valine Phenylalanine Phe Methionine Leucine Leu Proline Isoleucine Ile Tryptophane

Code Val Met Pro Trp

Hydrophilic amino acids: Name Code Name Glycine Gly Threonine Serine Ser Cysteine Tyrosine Tyr Asparagine Glutamine Gln Arginine Lysine Lys Histidine Aspartic acid Asp Glutamic acid

Code Thr Cys Asn Arg His Glu

Protein Structure Proteins are large biochemical complexes that contain several polypeptide compounds (amino acid chains). They are organized into four levels of structure: Primary structure: The chain of amino acids that make up the protein; this chain directly controls the other levels of protein structure. Secondary structure: The patterns formed by segments of the polypeptide chain; can be either α-helices or βpleated sheets. Tertiary structure: The folding of the polypeptide to produce a certain shape. Quarternary structure: The geometrical bonding of several polypeptides to form the protein.

Chirality

A molecule possessing a nonsuperimposable mirror image is chiral. Two mirror images of a chiral molecule are enantiomers. A carbon that is bonded to 4 different groups is an asymmetric center. Chiral molecules have at least one asymmetric centers. Chiral molecules rotate polarized light. Two enantiomers -thial rotate polarized light by the same degrees, one clockwise and one counterclockwise. A mixture of two enantiomers -phosphane in 1:1 does not rotate polarized light, and is racemic. phenyl-

c

2009–2011 Zee Zuo. Licensed under CC-BY-SA 3.0, United States.

System Name R/S (+)/(−)

Based On Structure Direction of rotation of polarized light D/L Enantiomer of glyceraldehyde the molecule is derived from R/S notation: Orient the enantiomer so that the smallest (by CIP Rules) substituent points backward (away from the viewer) and the largest substituent points upward. If the larger substituent of the other two points toward the right, then the enantiomer is an R-enantiomer. If the larger substituent points toward the left, then the enantiomer is an L-enantiomer. (+)/(−) notation: An enantiomer that rotates the plane of polarization clockwise is dextrorotary (+). An enantiomer that rotates the plane of polarization counterclockwise is levorotary (−). D/L notation: An enantiomer that is derived from (+)glyceraldehyde is the D-enantiomer. An enantiomer that is derived from (−)-glyceraldehyde is the L-enantiomer. Note that nomenclature in a system cannot be determined by that in another system. Caution: The (+)/(−) system is sometimes written as (d)/(l), which is easily confused with the D, L system. As these two systems sometimes conflict (a D-enantiomer can be an (l)-enantiomer), the (+)/(−) notations are strongly preferred.

Significant Figures Significant figures (“sig figs”) is the number of digits that carry precision in a number. Non-measured Numbers: Non-measured numbers, such as π, integer counts, definition of units, etc. always have infinite sig figs. Other constants, such as NA , have limited sig figs. Non-zero Digits: Nonzero digits are always significant, unless one or more of the other rules are violated. Zeros: Leading zeros are never significant; trailing zeros, however, are significant only if they are part of the measurement. Zeros between non-zero digits are always significant. Reporting Numbers: Reported numbers are only significant to the precision of the equipments with which they are measured. Addition/Subtraction: When adding or subtracting two numbers, the result should have as many decimal places as the number with the smallest sig figs. Multiplication/Division: When multiplying or dividing, the result should have as many sig figs as the number with the smallest sig figs.

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