dipole/induced-dipole and dipole/induced-dipole attractions. forces

Halogen derivatives of hydrocarbons:

Bonding system and physical properties. Factors affecting theC-Hlg bond strength of the response relationship skills.Halides with reduced, normal and increased reactivity. Keymechanisms and application of nucleophilic substitution (SN1and SN2). Factors affecting nucleophilic substitution.

Elimination reactions: - and -elimination, basic mechanismof -elimination (E1, E2 and E1cB). Substitution and eliminationshare of influence. Reaction of halogen compounds withmetals. Preparation of aliphatic and aromatic halogencompounds.

Classification of C-Hlg compounds

According to Hlg qualityNumbers of Hlg (di-, tri-, tetra- etc.)

in case of dihalogenids:

Type of carbon chain: • aliphatic (saturated, unsaturated)• aromatic

The order of C (primary, secondary, or tertiary according to the classification of the carbon that bears the functional group)

n 1

Particular importance of the hybrid form of the - and -carbon reactivity

n 2

• trivial names: eg. chloroform, iodoform, fluothane

Nomenclature

• substitution nomenclature (substitutive nomenclature) - halogen name as a prefix only!

• functional group nomenclature (functional class nomenclature): hydrocarbon group + halide (fluoride, chloride, bromide, iodide) Suffix - assuming that no higher priority functional group

The IUPAC rules permit alkyl halides to be named in two different ways, called functional

class nomenclature and substitutive nomenclature.

In functional class nomenclature the alkyl group and the halide ( fluoride, chloride, bromide, or iodide)

are designated as separate words. The alkyl group is named on the basis of its longest continuous

chain beginning at the carbon to which the halogen is attached.

Substitutive nomenclature of alkyl halides treats the halogen as a halo- ( fluoro-, chloro-, bromo-, or

iodo-) substituent on an alkane chain. The carbon chain is numbered in the direction that gives the

substituted carbon the lower locant.

When the carbon chain bears both a halogen and an alkyl substituent, the two substituents are considered

of equal rank, and the chain is numbered so as to give the lower number to the substituent nearer the end

of the chain.

Substitutive names are preferred, but functional class names are sometimes more convenient or more

familiar and are frequently encountered in organic chemistry.

IUPAC NOMENCLATURE OF ALKYL HALIDES

Francis A. Carey: Organic Chemistry (4th Edition), ISBN 0-07-290501-8; The McGraw-Hill Companies, Inc., 2000, p. 127

Substitutive nomenclature of alkyl halides

John McMurry: Organic Chemistry (7th Edition), ISBN-10: 0840054440 ISBN-13: 9780840054449, Brooks/Cole, 2012, p. 333

Bonding system of C-Hlg compounds

Typically EN(Hlg) > EN(C) polarized hetero nuclear -bond, partial positive charge on carbon atom(-I effect)

BUT! If the pillar C is a sp2 or sp hybridized +M effect also occurs. Result: shorter, stronger bonds

Carbon–halogen bonds are polar covalent bonds, and carbon bears a partial positive charge in alkyl halides. The presence of this polar bond makes alkyl halides polar molecules.

Electronegativity (EN): A measure of the ability of an atom to attract the electrons in a covalent bond toward itself. Fluorine is the most electronegative element.

Inductive effect: An electronic effect transmitted by successive polarization of the bonds within a molecule or an ion. OR The electron-donating or electron-withdrawing effect of a group that is transmitted through bonds is called an inductive effect.

Electronic effect: An effect on structure or reactivity that is attributed to the change in electron distribution that a substituent causes in a molecule.

Mesomeric effect: The effect is used in a qualitative way and describes the electron withdrawing orreleasing properties of substituents based on relevant resonance structures and is symbolized by theletter M. The mesomeric effect is a permanent effect and operates in compounds containing at leastone double bond and another double bond or a lone pair separated by a single bond. Themesomeric effect is negative (–M) when the substituent is an electron-withdrawing group and theeffect is positive (+M) when based on resonance and the substituent is an electron releasing group.

–M effect of a carbonyl group in acrolein

Electronegativity is a chemical property that describes the tendency of an atom to attract electrons in a covalent bond towards itself.

Average C-Hlg bond energy (kJ/mol)C-F 488C-Cl 326C-Br 278C-I 210 (est.)Reason: weaker overlapping,

smaller charge separation

C-Hlg dissociation energy (kJ/mól)

homolytic heterolytic

F Br F Br

MeCH2-Hlg 448 282 920 770

PhCH2Hlg 403 229 820 657

CH2=CH-Hlg 497 320 1004 837

C-Hlg bond energy depends on: the quality of halogen, carbon hybrid status

Halogens increase in size going down the periodic table, so the lengths of the corresponding carbon-halogen bonds increase accordingly. In addition, C―X bond strengths decrease going down the periodictable.

C-Hlg bond energy

C-Hlg bond distance depends on: the quality of halogen, carbon hybrid status

C-Hlg bond distance

dC-Hlg (nm)

F Cl Br I

0.139 0.178 0.195 0.214

0.133 0.172 0.188 0.210

Longer bonds

Sho

rte

rb

on

ds

Tendencies:1. aryl/vinyl halides: stronger bonds (+M effect)2. allyl/benzyl halides: weaker bonds - greater stability of the formed radical/cation

has a lower energy3. homolytic bond cleavage requires less energy

BUT!! This is true in gas phase, in solution the solvation energy can overwrite it

Bonding system of C-Hlg compounds 2.

Expected results

• aryl/vinyl halides are less reactive than simple alkyl halides

• allyl/benzyl halides are more reactive than alkyl halides

C-Hlg dissociation energy (kJ/mól)

homolytic heterolytic

F Br F Br

MeCH2-Hlg 448 282 920 770

PhCH2Hlg 403 229 820 657

CH2=CH-Hlg 497 320 1004 837

benzyl

alkyl

vinyl

Due to the ground state polarization: dipole moment appears

Me-F: 1.81 D Me-Cl: 1.87 D Me-Br: 1.80 D

The presence of the polar bonds makes alkyl halides polar molecules.

Electrostatic potential maps ofchloromethane.The most positivelycharged regions are blue, the mostnegatively charged ones red. Theelectrostatic potential is mostnegative near chlorine inchloromethane.

Distribution of electron density in chloromethane:

The polarization of the bonds to chlorine, as well as its unshared electron pairs, contribute to the concentration of negative charge on chlorine atoms.Relatively simple notions of attractive forces between opposite charges are sufficient to account for many of the properties of chemical substances. You will find it helpful to keep the polarity of carbon–oxygen and carbon–halogen bonds in mind as we develop the properties of alcohols and alkyl halides in later sections.

Halogens are more electronegative than carbon. The C-X bond is therefore polar, withthe carbon atom bearing a slight positive and the halogen a slight negative charge.

Dipole moment

The effective dipole moment is formed by two factors: the value of charge separation (EN difference) and the bond length.

CH3-Br CH3CH2-Br CH3CH2CH2-Br

[D] 1.80 1.88 1.92

Cause: Charge separation runs through the chain.Important lessons for the future: electron-withdrawing groups are not the only carbon but also decreasing around the carbon and reduce the electron density of the carbon!!!

BUT! due to the nature of elementary dipole moments the resultant vector may be zero!

Bromine is less electronegative than chlorine, yet methyl bromide and methyl chloride have very similar dipole moments. Why?Dipole moment is the product of charge and distance. Although the electron distribution in the carbon–chlorine bond is more polarized than that in the carbon–bromine bond, this effect is counterbalanced by the longer carbon–bromine bond distance.

= 0

Halogens are more electronegative than carbon. The C-X bond is therefore polar, with thecarbon atom bearing a slight positive and the halogen a slight negative charge. This polarity results in a substantial dipole moment for all the halomethanes and impliesthat the alkyl halide C-X carbon atom should behave as an electrophile in polar reactions. We’ll see that much of the chemistry of alkyl halides is indeed dominated by theirelectrophilic behavior.

Don’t forget!

Physical properties of C-Hlg compounds

The forces of attraction between neutral molecules are of three types listed here. The first two of these involve induced dipoles and are often referred to as dispersion forces, or London forces.1. Induced-dipole/induced-dipole forces2. Dipole/induced-dipole forces3. Dipole–dipole forces

Induced-dipole/induced-dipole forces are the only intermolecular attractive forcesavailable to nonpolar molecules such as alkanes. In addition to these forces, polar moleculesengage in dipole–dipole and dipole/induced-dipole attractions.

The dipole–dipole attractive force is easiest to visualize. Two molecules of a polar substance experience a mutual attraction between the positively polarized region of one molecule and the negatively polarized region of the other. Two molecules of a polar substance are

oriented so that the positively polarizedregion of one and the negatively polarizedregion of the otherattract each other.

As its name implies, the dipole/induced-dipole force combines features of both the induced-dipole/induced dipole and dipole–dipole attractive forces. A polar region of one molecule alters the electron distribution in a nonpolar region of another in a direction that produces an attractive forcebetween them.

Francis A. Carey: Organic Chemistry (4th Edition), ISBN 0-07-290501-8; The McGraw-Hill Companies, Inc., 2000, p. 130.

Physical properties of C-Hlg compounds 2.

With respect to the halogen in a group of alkyl halides, the boiling point increases as one descends the periodic table; alkyl fluorides have the lowest boiling points, alkyl iodides the highest. This trend matches the order of increasing polarizability of the halogens.Polarizability is the ease with which the electron distribution around an atom is distorted by a nearby electric field and is a significant factor in determining the strength of induced-dipole/induced-dipole and dipole/induced-dipole attractions. Forces that depend on induced dipoles are strongest when the halogen is a highly polarizable iodine, and weakest when the halogen is a nonpolarizable fluorine.

When comparing the boiling points of related compounds as a function of the alkyl group, we find that the boiling point increases with the number of carbon atoms, as it does with alkanes.


The boiling points of the chlorinated derivatives of methane increase with the number of chlorine atoms because of an increase in the induced-dipole/induced-dipole attractive forces.


The reason for this behavior has to do with the very low polarizability of fluorine and a decrease in induced-dipole/induced-dipole forces that accompanies the incorporation of fluorine substituents into a molecule. Their weak intermolecular attractive forces give fluorinatedhydrocarbons (fluorocarbons) certain desirable physical properties such as that found in the “no stick” Teflon coating of frying pans.(Teflon is a polymer made up of long chains of -CF2CF2-units.)

Fluorine is unique among the halogens in that increasing the number of fluorines does not produce higher and higher boiling points.


Melting point (Mp) and boiling point (bp) – forces: dipole-dipole interactionMp and bp greater than in case of the alkanes, alkenes with the same number of C’s.

R-Hlg boiling point (oC) R-H (oC)

Hlg F Cl Br

Me-Hlg -78 -24 4 -162

Et-Hlg -32 12 38 -89

Bu-Hlg 32 79 102 -1

Bp is increasing: • changes in the quality of halogen (F I)• increase in the number of carbon atoms• increase in the number of Hlg-s (except fluorides)


Conlusion

Solubility

Properties: low water solubility (all alkyl halides are insoluble in water, H bridges are stronger than dipole-dipole interactions). Highly dissolves the less polar organic substances, fats.

good extraction agents good cleanersmodification of biological lipid-lipid systems, high narcotic effect (e.g. fluothane:

CHClBr-CF3)

Density – increasing F I, and with the number of Hlg-s, BUT decreasing with the size of the carbon chain

d(Me-F) = 0.877 g/cm3, d(Pr-F) = 0.779 g/cm3

d(Me-F) = 0.877 g/cm3, d(Me-Br) = 1.732 g/cm3

d(Me-Cl) = 0.991 g/cm3, d(CHCl3) = 1.489 g/cm3 (but! d(CHBr3) = 2.890 g/cm3


Because alkyl halides are insoluble in water, a mixture of an alkyl halide and waterseparates into two layers. When the alkyl halide is a fluoride or chloride, it is the upperlayer and water is the lower. The situation is reversed when the alkyl halide is a bromide oran iodide. In these cases the alkyl halide is the lower layer. Polyhalogenation increases thedensity. The compounds CH2Cl2, CHCl3, and CCl4, for example, are all more dense thanwater.

Preparation of C-Hlg compounds1. Synthesis of alkyl halides

1.1. Halogenation of alkanes

It involves substitution of a halogen atom for one of the alkane’s hydrogens.

The alkane is said to undergo fluorination, chlorination, bromination, or iodination according towhether X2 is F2, Cl2, Br2, or I2, respectively. The general term is halogenation. Chlorination andbromination are the most widely used.The reactivity of the halogens decreases in the order F2 > Cl2 > Br2 > I2.Fluorine is an extremely aggressive oxidizing agent, and its reaction with alkanes is stronglyexothermic and difficult to control. Direct fluorination of alkanes requires special equipment andtechniques, is not a reaction of general applicability.Chlorination of alkanes is less exothermic than fluorination, and bromination less exothermic thanchlorination.Iodine is unique among the halogens in that its reaction with alkanes is endothermic and alkyliodides are never prepared by iodination of alkanes.

Disadvantages: mixture, no control! (Hlg = Cl, Br)

CHLORINATION OF METHANE

The gas-phase chlorination of methane is a reaction of industrial importance and leads to a mixture of chloromethane (CH3Cl), dichloromethane (CH2Cl2), trichloromethane (CHCl3), and tetrachloromethane(CCl4) by sequential substitution of hydrogens.

The intermediates in the chlorination of methane and other alkanes are quite different; they are neutral (“nonpolar”) species called free radicals.

Simple alkyl radicals, for example, require special procedures for their isolation and study. We will encounter them here only as reactive intermediates, formed in one step of a reaction mechanism and consumed in the next. Alkyl radicals are classified as primary, secondary, or tertiary according to the number of carbon atoms directly attached to the carbon that bears the unpaired electron.

alkyl substituents stabilize free radicals

Some of the evidence indicating that alkyl substituents stabilize free radicals comesfrom bond energies. The strength of a bond is measured by the energy required to breakit. A covalent bond can be broken in two ways.

In a homolytic cleavage a bond between two atomsis broken so that each of them retains one of the electrons in the bond.The more stable the radical, the lower the energy required to generate it by C-H bond homolysis.The energy required for homolytic bond cleavage is called the bond dissociationenergy (BDE).

In contrast, in a heterolytic cleavage one fragment retains both electrons.

Alkyl radicals


As the table indicates, C-H bonddissociation energies in alkanes areapproximately 375 to 435 kJ/mol (90–105kcal/mol). Homolysis of the H-CH3 bond inmethane gives methyl radical and requires435 kJ/mol (104 kcal/mol). Thedissociation energy of the H-CH2CH3 bondin ethane, which gives a primary radical, issomewhat less (410 kJ/mol, or 98kcal/mol) and is consistent with thenotion that ethyl radical (primary) is morestable than methyl.

The dissociation energy of the terminal C-H bond in propane is exactly the same as that of ethane. The resulting free radical is primary in both cases.

Note, however, that Table 4.3 includes two entries for propane.The second entry corresponds to the cleavage of a bond to one ofthe hydrogens of the methylene (CH2) group. It requires slightlyless energy to break a C±H bond in the methylene group than inthe methyl group.

Since the starting material (propane) and one of the products (H) are the same in both processes, the difference inbond dissociation energies is equal to the energy difference between an n-propyl radical (primary) and an isopropylradical (secondary). The secondary radical is 13 kJ/mol (3 kcal/mol) more stable than the primary radical.

Alkyl radicals 2.

Francis A. Carey: Organic Chemistry (4th Edition), ISBN 0-07-290501-8; The McGraw-Hill Companies, Inc., 2000, p. 151-152.

The reaction itself is strongly exothermic,but energy must be put into the systemin order to get it going. This energy goesinto breaking the weakest bond in thesystem, which we see from the bonddissociation energy data in Table 4.3, isthe Cl-Cl bond with a bond dissociationenergy of 242 kJ/mol (58 kcal/mol). Thestep in which Cl-Cl bond homolysisoccurs is called the initiation step.

Each chlorine atom formed in theinitiation step has seven valenceelectrons and is very reactive. Onceformed, a chlorine atom abstracts ahydrogen atom from methane as shownin step 2. Hydrogen chloride, one of theisolated products from the overallreaction, is formed in this step.A methyl radical is also formed, whichthen attacks a molecule of Cl2 in step 3.Attack of methyl radical on Cl2 giveschloromethane, the other product of theoverall reaction, along with a chlorineatom which then cycles back to step 2,repeating the process.

Steps 2 and 3 are called the propagation steps of the reaction and, when added together, give the overall equation forthe reaction. Since one initiation step can result in a great many propagation cycles, the overall process is called afree-radical chain reaction.

MECHANISM OF METHANE CHLORINATION


The chain sequence is interrupted whenever two odd-electron species combine to give an even-electron product. Reactions of this type are called chain-terminating steps.Some commonly observed chain-terminating steps in the chlorination of methane are shown in the following equations.

Combination of a methyl radical with a chlorine atom:

Combination of two methyl radicals:

Combination of two chlorine atoms:


MECHANISM OF METHANE CHLORINATION 2.

1.2. Addition of Hlg2 or HHlg to alkenes, alkynes (radical or electrophile addition mechanism)

Problems with regioselectivity

Reactivity depends on the quality of the HHlg: HI > HBr > HCl >> HF

1.2.1. ELECTROPHILIC ADDITION OF HYDROGEN HALIDES TO ALKENES

In many addition reactions the attacking reagent is a polar molecule. Hydrogen halides are among the simplest examples of polar substances that add to alkenes.

The reactivity of the hydrogen halides reflects their ability to donate a proton. Hydrogen iodide is the strongest acid of the hydrogen halides and reacts with alkenes at the fastest rate.

An alkene can accept a proton from a hydrogen halide to form a carbocation.

Carbocations, when generated in the presence of halide anions, react with them to form alkyl halides.

This reaction is called electrophilic addition because the reaction is triggered by the attack of an electrophile(an acid) on the p electrons of the double bond. Using the two p electrons to form a bond to an electrophile generates a carbocation as a reactive intermediate; normally this is the rate-determining step.

GENERAL MECHANISM

REGIOSELECTIVITY OF HYDROGEN HALIDE ADDITION: MARKOVNIKOV’S RULE

In principle a hydrogen halide can add to an unsymmetrical alkene (an alkene in which the two carbons of the double bond are not equivalently substituted) in either of two directions. In practice, addition is so highly regioselective as to be considered regiospecific.

In 1870, Vladimir Markovnikov, a colleague of Alexander Zaitsev, noticed a pattern in the hydrogen halide addition toalkenes and assembled his observations into a simple statement. Markovnikov’s rule states that when anunsymmetrically substituted alkene reacts with a hydrogen halide, the hydrogen adds to the carbon that has thegreater number of hydrogen substituents, and the halogen adds to the carbon having fewer hydrogen substituents.The preceding general equations illustrate regioselective addition according to Markovnikov’s rule, and theequations that follow provide some examples.

When a hydrogen halide adds toan alkene, protonation of thedouble bond occurs in thedirection that gives the morestable carbocation.

The way we usually phrase it now:

Markovnikov’s rule

MECHANISTIC BASIS FOR MARKOVNIKOV’S RULE

Compare the carbocation intermediates foraddition of a hydrogen halide (HX) to anunsymmetrical alkene!

The activation energy for formation of the more stable carbocation (secondary) is less than that for formation of the less stable (primary) one. Both carbocations are rapidly captured by X- to give an alkyl halide, with the major product derived from the carbocation that is formed faster. The energy difference between a primary carbocation and a secondary carbocation is so great and their rates of formation are so different that essentially all the product is derived from the secondary carbocation.

Structure of methyl cation CH3+. Carbon is sp2-hybridized.

Each hydrogen is attached to carbon by a bond formedbyoverlap of a hydrogen 1s orbital with an sp2 hybridorbital of carbon. All four atoms lie in the same plane. Theunhybridized 2p orbital of carbon is unoccupied, and itsaxis is perpendicular to the plane of the atoms.

The properties of carbocations are intimately related to their structure, and so let’s think about the bonding in methyl cation, CH3

+ .The positively charged carbon contributes three valence electrons, and each hydrogen contributes one for a total of six electrons, which are used to form three C-H bonds. Carbon is sp2-hybridized when it is bonded to three atoms or groups. Carbon forms bonds to three hydrogens by overlap of its sp2 orbitals with hydrogen 1s orbitals. The three bonds are coplanar. Remaining on carbon is an unhybridized 2p orbital that contains no electrons.The axis of this empty p orbital is perpendicular to the plane defined by the three bonds.

STRUCTURE OF METHYL CATION

STRUCTURE, BONDING, AND STABILITY OF CARBOCATIONS


Carbocations are classified as primary, secondary, or tertiary according to the number of carbons that are directlyattached to the positively charged carbon. They are named by appending “cation” as a separate word after the IUPACname of the appropriate alkyl group. The chain is numbered beginning with the positively charged carbon (thepositive charge is always at C-1).

Alkyl groups directly attached to the positively charged carbon stabilize a carbocation. Thus, the observed order of carbocation stability is

Because alkyl groups stabilize carbocations, we conclude that they release electrons to the positively charged carbon, dispersing the positive charge. They do this through a combination of effects.

One involves polarization of the bonds to the positively charged carbon.Electrons in a C-C bond are more polarizable than those in a C-H bond, so replacing hydrogens by alkyl groups reduces the net charge on the sp2-hybridized carbon. The electron-donating or electron-withdrawing effect of a group that is transmitted Through bonds is called an inductive effect.

The charge in ethyl cation is stabilized by polarization of the electron distribution in the bonds to the positivelycharged carbon atom. Alkyl groups release electrons betterthan hydrogen

A second effect, called hyperconjugation, is also important.

According to hyperconjugation, electrons in the C-H bond of a +C-C-H unit are more stabilizing than +C-H electrons. Thus, successive replacement of the hydrogens attached to CH3 by alkyl groups increases the opportunities forhyperconjugation, which is consistent with the observed order of increasing carbocation stability: methyl primary secondary tertiary. Finally, although we have developed this picture for hyperconjugation of a +C-C-H unit, it also applies to +C-C-C as well as many others.

Ethyl cation is stabilized by delocalization of

the electrons in the C-H bonds of the methylgroup into the vacant 2p orbital of thepositively charged carbon.

1.2.2. FREE-RADICAL ADDITION OF HYDROGEN BROMIDE TO ALKENES

When the addition ofhydrogen bromide toalkenes was performedin the presence of anadded peroxide, only1-bromobutane wasformed.

Peroxides are initiators;they are notincorporated into theproduct but act as asource of radicalsnecessary to get thechain reaction started.


Don’t forget!

anti-Markovnikov addition

Markovnikov addition

The regioselectivity of addition of hydrogen bromide to alkenes under normal (ionic addition) conditions is controlled by the tendency of a proton to add to the double bond so as to produce the more stable carbocation.

ionic addition

Under free-radical conditions the regioselectivity is governed by addition of a bromine atom to give the more stable alkyl radical.

free-radical addition

Free-radical addition of hydrogen bromide to the double bond can also be initiated photochemically,either with or without added peroxides.

1.2.3. ADDITION OF HALOGENS TO ALKENES

Halogens react with alkenes by electrophilic addition.

The products of these reactions are called vicinal dihalides. Two substituents, in this case the halogens, are vicinal if they are attached to adjacent carbons. The word is derived from the Latin vicinalis, which means “neighboring.” The halogen is either chlorine (Cl2) or bromine (Br2), and addition takes place rapidly at room temperature and below in avariety of solvents, including acetic acid, carbon tetrachloride, chloroform, and dichloromethane.

Mechanism of electrophilicaddition of bromine toethylene.


The reaction of chlorine and bromine with cycloalkenes illustrates an important stereochemical feature of halogen addition: Anti addition is observed; the two bromine atoms of Br2 or the two chlorines of Cl2 add to opposite faces of the double bond.

STEREOCHEMISTRY OF HALOGEN ADDITION

Anti addition!

1.2.4. ADDITION OF HYDROGEN HALIDES TO ALKYNES

Hydrogen halides, for example, add to alkynes to form alkenyl halides.

The regioselectivity of addition follows Markovnikov’s rule. A proton adds to the carbon that has the greater number of hydrogens, and halide adds to the carbon with the fewer hydrogens.

In the presence of excess hydrogen halide, geminal dihalides are formed by sequential addition of two molecules of hydrogen halide to the carbon–carbon triple bond.

The hydrogen halide adds to the initially formed alkenyl halide in accordance with Markovnikov’s rule. Overall, both protons become bonded to the same carbon and both halogens to the adjacent carbon.


1.2.5. ADDITION OF HALOGENS TO ALKYNES

Alkynes react with chlorine and bromine to yield tetrahaloalkanes. Two molecules of the halogen add to the triple bond.

A dihaloalkene is an intermediate and is the isolated product when the alkyne and the halogen are present in equimolar amounts. The stereochemistry of addition is anti.


dipole/induced-dipole and dipole/induced-dipole attractions. forces

Documents