Cheat Sheet

General Chemistry Reference Sheet

This reference sheet addresses some of the more peculiar pieces of information that need to be memorized in a gen-eral chemistry course. It also contains a simple set of es-sential 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 supple-ment to, not a replacesupple-ment of, the textbook.

SI Fundamental Units

Mass Kilogram (kg)

Length Meter (m)

Time Second (s)

Temperature Kelvin (K)

Amount of substance Mole (mol) Electric current Ampere (A) Luminous intensity Candela (cd)

Atomic Experiments and Models

J. J. Thomson 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

Polyatomic Ions

NH4+ ammonium OH− hydroxide

CN− cyanide C2O42− oxalate

O22− peroxide CNO− cyanate

HSO4− hydrogen

sul-fate

C2H3O2− acetate

SCN− thiocyanate NO3− nitrate

SO32− sulfite ClO4− perchlorate

CO32− carbonate ClO3− chlorate

PO43− phosphate ClO− hypochlorite

S2O32− thiosulfate HPO42− hydrogen

phosphate CrO42− chromate H3O+ hydronium

Cr2O72− dichromate PO33− phosphite

MnO4− permanganate Hg22− mercury (I)

N3− azide C22− carbide

C4H4O62− tartrate S22− disulfide

O2− superoxide AsO33− arsenite

PO23− hypophosphite AsO43− arsenate

SiO32− silicate P2O74− pyrophosphate

Ionic Solubility Chart

Soluble Exceptions NO3− None CH3COO− None Cl− Ag+, Hg22+, Pb2+ Br− Ag+, Hg22+, Pb2+ I− Ag+, Hg22+, Pb2+ SO42− Sr2+, Ba2+, Hg22+, Pb2+ Insoluble Exceptions

S2− NH4+, alkali metal cations, Ca2+,

Sr2+, Ba2+

CO32− NH4+, alkali metal cations

PO43− NH4+, alkali metal cations

OH− NH4+, alkali metal cations, Ca2+,

Sr2+, Ba2+

Strong Acids and Bases

Strong acids and bases dissociate in water completely. Strong Acids Strong Bases

HCl HClO4 Alkali metal hydroxides

HBr HNO3 Ca(OH)2

HI H2SO4 Sr(OH)2

HClO3 Ba(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+_{, Fe}2+_{, Co}2+_{, Ni}2+_{, Sn}2+_{, Pb}2+_{, H}+_{, Cu}2+_{, Ag}+_,

Hg2+_{, Pt}2+_{, Au}3+

Flame Colors

Calcium Brick red

Copper (I) Blue

Copper (II) Green or blue-green

Potassium Lilac

Lithium Dark red

Sodium Bright yellow

Strontium Red

Barium Light green

Iron (III) Gold

Cesium Blue–Violet

Indium Blue

Lead Blue

Rubidium Red–Violet

Phase Changes

From solid From liquid From gas To solid - freezing deposition To liquid melting - condensation To gas sublimation vaporization

-Solution Colors

Copper (II) Blue

Nickel Green

Permanganate Purple

Chromate Yellow

Dichromate Orange

Iron (II) Light blue

Iron (III) 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 en-tropy of the universe.

Third Law: An ideal solid crystal at 0 K has an entropy of 0.

Thermodynamic Formulas

Standard thermodynamic conditions 298 K; 1 atm; 1 M Kinetic energy K = mv2_/2

Electrostatic potential energy UE= (kCQ1Q2)/d

Internal energy ∆E = q + w

Enthalpy H = E + P V

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 − T S 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 × 10−23m2kg · s−2K−1

Coulomb’s constant kC= 1/(4π0) = 8.988 × 109 J · m/C2

Avogadro’s number NA= 6.022 × 1023mol−1

Faraday’s constant F = 9.649 × 104 C/mol Planck’s constant h = 6.626 × 10−34J·s Ideal gas constants R = 0.0821 (L · atm)/(mol · K) R = 8.314 J/(mol · K) Vacuum permittivity 0= 1/(µ0c2) = 8.854 × 10−12F/m

Vacuum permeability µ0= 1.257 × 10−6 N·A−2

Atomic mass 1 amu = 1.661 × 10−24g Electron charge e = 1.602 × 10−19C Electronvolt 1 eV = 1.602 × 10−19J 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

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

Laws of Quantum Mechanics

Heisenberg’s Uncer-tainty Principle

∆x · ∆p ≥ ¯h/2

Corollary: It is impossible to de-termine both the position and the momentum for a sufficiently small particle like an e−. Pauli Exclusion

Prin-ciple

No two e−in an atom can share the same set of four quantum numbers.

Corollary: A suborbital can hold a maximum of 2e−.

Hund’s Rule 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 subor-bitals.

Quantum Numbers of e

Principal (n) The energy shell of the e−, e.g. 4 in 4d1.

Azimuthal (l) The suborbital shape, with s=0, p=1, d=2, f=3, e.g. 2 in 4d1_.

Magnetic (ml) The suborbital, ranging from −l to

l, e.g. −2 in 4d1_.

Spin (ms) The spin of e−. Two e−in the same

suborbital has either −1/2 or 1/2.

Molecular Geometry

Hybridization Nonbonding Geometry electrons sp 0 linear sp2 _{0 trigonal planar} 1 bent sp3 _{0 tetrahedral} 1 trigonal pyramidal 2 bent sp3d 0 trigonal bipyramidal 1 seesaw 2 T-shaped 3 linear sp3d2 0 octahedral 1 square pyramidal 2 square planar

Atomic Properties

2the distance between two

ad-jacent nucleii.

Ionic size Cations are smaller than their parent atoms. Anions are larger than their parent atoms. N-th ionization energy The energy required to re-move the n-th electron from a ground state gaseous atom. Electron affinity The energy released by adding

an electron to a gaseous atom. Metallic character 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 Left to Right Top to Bottom Atomic size Decreasing Increasing Ionization energy Increasing Decreasing Electron affinity Large if adding

to a previously empty orbital

No apparent change

Metallic character Decreasing Increasing

Types of Crystalline Solids

Type IMFs Properties Molecular Van der Waals forces,

dipole-dipole inter-actions, hydrogen bonds

Soft, low melting point, poor conduc-tion

Covalent-network

Covalent bonds Very hard, high melting point, poor conduction

Ionic Electrostatic interac-tions

Hard, high melting point, poor conduc-tion

Metallic Metallic bonds Soft to very hard, low to very high melting point, ex-cellent 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.)

IMFs in Molecular Solids

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

Interactions between dipoles partially charged through the movement of shared electron. Presents in all compounds. Weakest of the three.

Dipole-dipole interac-tions

Interactions between dipoles partially charged through the electronegativity difference of two bonding atoms.

Hydrogen bonds A special kind of dipole-dipole interactions present in com-pounds that have hydrogen and either oxygen or nitrogen. Strongest of the three.

Acid-Base Theories

Arrhenius Brønsted-Lowry

Lewis Acids [H+] >[OH−] Proton

donors

Electron acceptors Bases [OH−] >[H+] Proton

acceptors

Electron donors Acids have H+ Hydrogen

atom

Electron accepting atom Bases have OH− Unshared

electron pair Unshared electron pair Acid + Base → Salt + H2O Conjugate acid + Conjugate base

Kinetic Molecular Theory (KMT)

There is a very large number of particles;

Particles are in constant random motion and collide con-stantly 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

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

1. Lower vapor pressure: PA = XAPA◦ (Raoult’s

Law)

2. Higher boiling point: Tb= Tb◦+ kbm (Molality)

3. Lower freezing point: Tf = Tf◦− kfm (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 parti-cles 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. Re-action orders can only be determined experimentally, be-cause reactions will in theory go through several steps, the slowest of which is the rate-determining step. Reaction or-der 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 [X]t=

Z t 0

rdτ + [X]0

Therefore, for first-order reactions, ln[X]t= −kt + ln[X]0

Graphically, t is proportional to ln[X]twith the slope −k.

And for second-order reactions, 1 [X]t

= kt + 1 [X]0

Graphically, t is proportional to 1/[X]twith 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).

Activation Energy

Collision model 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. In-organic catalysts usually provide a site on which reactants can adsorb; organic catalysts, or enzymes, bind specific to substrate molecules (“lock-and-key”).

Spectrophotometry of Concentration

Beer’s law, A = lc, relates concentration and light absorp-tion.

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. There-fore, 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 Pn= XnPt

Effusion Rate u =p(3RT )/M Graham’s Law u1/u2=pM2/M1

Density Formula d = (P M)/(RT ) Deviation from Ideal Behavior (P V )/(RT ) Van der Waals Equation

P + (n2_a)/V2
_{(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◦)/(RT2) ln K = −∆H◦/(RT ) + ∆S◦/R

Concentration

Notation Definition

Molarity (M) (Moles solute)/(Liters solution) Molality (m) (Moles solute)/(Kilogram solvent) Mole fraction (X) (Moles solute)/(Moles solution) Mass percentage (Mass of solute)/(Mass of solution) Volume percentage (Volume of solute)/(Volume of

solu-tion)

Caution: It is an extremely common mistake to confuse molarity with molality. Check your R’s and L’s!

Le Chˆ

atelier’s Principle

An equilibrium reaction will spontaneously balance an out-side 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 in-creases;

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.

Equilibrium Constant

For reactions in a solution, the equilibrium constant of a reaction aA + bB *) sS + tT 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 Kcis its solubility product constant, Ksp.

If the reaction is a dissociative reaction of a weak acid, then Kcis its acid dissociation constant, Ka. Polyprotic

(hav-ing more than one H) acids have multiple Ka, but usually

Ka1determines the pH.

For a conjugate acid-base pair, Ka· Kb= Kw.

If the reactants are gases, then the equilibrium constant is defined as Kp= Ps SPTt Pa AP b B

When the reaction is in equilibrium.

The Formulas above, when applied to non-equilibrium sit-uations, gives Q. The reaction forms products if Q < K, reactants if Q > K, and nothing if Q = K (already in equilibrium).

Equilibrium Constant (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.

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 Color change Large pH Methyl violet Yellow 0.0–1.6 Violet Bromophenol

blue

Yellow 3.0–4.6 Blue Methyl orange Red 3.1–4.4 Yellow Methyl red Red 4.4-6.2 Yellow Litmus Red 5.0–8.0 Yellow Bromothymol

blue

Yellow 6.0–7.6 Blue Phenolphthalein Colorless 8.3–10.0 Pink

Oxidation and Reduction

Oxidation Reduction

Loss of electrons Gains electrons Oxidation num. increases Oxidation num. decreases Occurs at anode Occurs at cathode Mnemonic devices:

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

Electrochemical Formulas

Electromotive force E = −(∆G)/(nF ) Nernst equation E = E◦− (RT /nF ) ln Q E = E◦− (0.0592/n) log Q Standard cell potential E◦= Ered◦ cathode − E

◦ redanode

Energy of a charged particle E = qV Faraday’s Law of Electrolysis m = (Q/F )(M/z)

Types of Magnetic Materials

Paramagnetic: Can be magnetized to attract external magnetic fields, but cannot retain magnetism. Param-agnetic materials have a mParam-agnetic 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.

Types of Magnetic Materials (cont.)

Diamagnetic: Can be magnetized to repulse external magnetic fields, but cannot retain magnetism. Diamag-netic materials have a magDiamag-netic permeability of less than µ0. Examples of diamagnets are bismuth and antimony.

Ferromagnetic: Can be magnetized and retain mag-netism. Ferromagnetism depends both on the chemical composition and the structure of the material (iron is a ferromagnet, while stainless steel is not). Examples of fer-romagnets include cobalt and iron.

Nuclear Chemistry

Alpha particles (α) Helium nuclei (42He)

Beta particles (β−) Electrons (0 −1e)

Positrons (β+) Antielectrons (01e)

Gamma radiation (γ) High energy radiation (00γ)

Units of radioactivity SI: Becquerel (Bq): 1 nucleus/s (Disintegration per second) Curie (Ci): 3.7 ×1010nuclei/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 met-als. (Example: Production of iron)

Hydrometallurgy: The use of chemical processes in a so-lution 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 CnH2n+2 sp3

Cycloalkane CnH2n sp3

Alkene CnH2n sp2

Alkyne CnH2n−2 sp

Aromatic CnH2n−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.

Stereoisomerism (cont.)

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.

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 di-rectly 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 ble bond in the substituent group, then the dou-ble 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

If a hydrocarbon

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 Name Suffix/Prefix R-OH (hydroxyl) alcohol -ol R-O-R’ (ether) ether ether R-X (halo) haloalkane halo-R-NH2 (amino) amine -amine

R-COH (aldehyde) aldehyde -al R-COX (haloformyl) acyl halide -oyl halide R-CO-R’ (carbonyl) ketone -one R-COOH (carboxyl) carboxylic acid -oic acid R-COO(carboxylate) carboxylate -oate

R-COO-R’ (ester) ester -oate R-CONH2 (amide) amide -amide

R-CNH-R’ (ketimine) ketimine imino-R-CHNH (aldimine) aldimine imino-R-CONCO-R’

(imide)

imide imido-R-N3 (azide) azide

azido-R-N2-R’ (azo) azo

azo-R-OCN (cyanate) cyanate cyanato-R-NCO (isocyanate) isocyanate isocyanato-R-CN (nitrile) nitrile cyano-R-NC (isonitrile) isonitrile isocyano-R-NO (nitroso) nitroso nitroso-R-NO2 (nitro) nitro

nitro-R-ONO (nitrosooxy) nitrite nitrosooxy-R-ONO2(nitrate) nitrate

nitroxy-R-SH (sulfhydryl) thiol -thiol R-SCN (thiocyanate) thiocyanate thiocyanato-R-NCS (isothio-cyanate) isothiocyanate isothiocyanato-R-CSH (carbonoth-ioyl) thial -thial R-PH3(phosphino) phosphine -phosphane

R-C6H5 (phenyl, Ph) benzene der.

phenyl-Functional Groups (cont.)

Functional Group Name Suffix/Prefix R-CH2C6H5 (benzyl,

Bn)

toluene der. benzyl-R-C5H4N (pyridyl) pyridine der. pyridin-x-yl

Note: In actual compounds, change all instances of “halo” above to halogen names (fluoro, chloro, bromo, iodo).

Amino Acids

Hydrophobic amino acids:

Name Code Name Code Alanine Ala Valine Val Phenylalanine Phe Methionine Met Leucine Leu Proline Pro Isoleucine Ile Tryptophane Trp Hydrophilic amino acids:

Name Code Name Code Glycine Gly Threonine Thr Serine Ser Cysteine Cys Tyrosine Tyr Asparagine Asn Glutamine Gln Arginine Arg Lysine Lys Histidine His Aspartic acid Asp Glutamic acid Glu

Protein Structure

Proteins are large biochemical complexes that contain sev-eral 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 β-pleated 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 metric center. Chiral molecules have at least one asym-metric centers.

Chiral molecules rotate polarized light. Two enantiomers rotate polarized light by the same degrees, one clockwise and one counterclockwise. A mixture of two enantiomers in 1:1 does not rotate polarized light, and is racemic.

Enantiomerism

System Name Based On R/S 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 small-est (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 enan-tiomer that rotates the plane of polarization counterclock-wise 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 mea-surement. Zeros between non-zero digits are always signif-icant.

Reporting Numbers: Reported numbers are only signif-icant 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 divid-ing, the result should have as many sig figs as the number with the smallest sig figs.

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