cyclohexane bond angles

What are some common mistakes students make with boat and chair conformations? Baeyer predicted that cyclopentane would be the most stable of the cycloalkanes because its bond angles of 108 ° are closest to the tetrahedral angle of 109.5 °. Conformations of Cyclohexane Preferred 109.5° bond angle is smaller than hexagon angle (120°). A(3-11-12) &111.3 \\ How can I draw the cis-1-bromo-3-methylcyclohexane chair conformation? All bond angles are 109.5o and all C-H bonds are perfectly staggered Cyclohexane: the perfect ring Conformations of Cyclohexane “Chair” conformation H H H H H H H H H H H H R(11-15) &1.055 \\ The interior angles of a regular hexagon are 120°. The most stable conformation of cyclohexane is the chair conformation, in which all bond angles are close to the tetrahedral 109°. It doesn’t. \end{array} Cyclohexane, with bond angles of 111°, is nearly free of angle strain and exists in a nonplanar chair conformation, which is virtually free of torsional strain because all of its bonds are staggered. Cyclohexane is a good example of a carbocyclic system that virtually eliminates eclipsing and angle strain by adopting non-planar conformations. Enter the Build menu and choose the Fragment option. However, cyclohexane has a form of chair conformation. R(2-6) &1.055 \\ A planar structure for cyclohexane is clearly improbable. Science; Chemistry; Chemistry questions and answers; Complete the following reaction: PA + Al-> 4 moles of sodium phosphide 4 moles of sodium phosphate 8 moles of sodium phosphide 8 moles of sodium phosphate What is the expected bond angle around a carbon atom in cyclohexane? Cyclohexane The structure of cyclohexane is Each carbon atom is bonded to four other atoms, so it is "sp"^3 hybridized: tetrahedral with all bond angles … c) The dihedral angle between the axial bond and the equatorial bond on adjacent carbons is 120°. Cyclohexane has bond angles of 109.5 since it arranges itself into either a chair conformer or a twist-boat conformer, both with angles of 109.5. In the chair conformation of cyclohexane, what are the angles of the triangles defined by: I have unsuccessfully looked for literature values of these, and my trigonometry is not up to scratch. Why does F replace the axial bond in PCl5? \mathbf{d}(\ce{CH_{eq}}) &=1.103~\mathrm{\mathring{A}}.\\ Book referring to software where you provide facts and the conclusion you want to reach. MathJax reference. Cyclohexane has an angle of 120°, which makes one think that it has angle strains. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): the complex geometrical forms which the cyclohexane ring can assume, the mechanical rigidity of the chair form and the contrasting flexibility of the boat form. R(11-16) &0.929 \\ 6 Figure 4.9 shows a bond-line representation of the chair conformation of cyclohexane. The carbon atom is at the center of a tetrahedron. (c) The F-Kr-F angle in KrF 4 How would physics explain why I can't un-fold paper? Chair Conformation of Cyclohexane The key to understanding trends in ring strain is that the atoms in a ring do not necessarily lie flat in a plane. \begin{array}{lr} There is another conformer of cyclohexane 6 or 6’ in which all bond angles are tetrahedral. ❒In a chair conformation (Fig.1), all of the carbon–carbon bond angles are 109.5o, and are thereby free of angle strain. Rather, cyclohexane achieves tetrahedral bond angles (omitting steric strain) and a staggered conformation (omitting torsional strain) by assuming an arrangement that chemists call a chair conformation (see below). most angle strain because bond angles of 60 degrees which are greatest from 109.5 (optimal bond angle for sp3 hybridized) cyclohexane most stable monocyclic alkane; it has the least amount of torsional strain and angle strain; least angle strain of 109.5 degrees The aromatic heterocycle pyridine is similar to benzene, and is often used as a weak base for scavenging protons. a carbon atom, an equatorial hydrogen bonded to it, and the midpoint of a vicinal C-C bond ? In addition, the bond angle between carbons is 109.5 o, exactly the angle expected for the tetrahedral carbon atoms. This is the most stable conformation for cyclohexane. In this conformation, each carbon atoms has an equatorial position and an axial position. Chair Cyclohexane: This is cyclohexane in the chair conformation. The bonds to non-ring atoms are termed axial or equatorial, depending on the bond angle. The conformations keep flipping; that is, the conformations undergo interconversions, as shown in the figure below. With the electron pairs this close together, there is a lot of repulsion between the bonding pairs joining the carbon atoms. A(2-1-4) &106.7 \\ A(2-1-3) &110.4 \\ The bond angles would be 120° instead of 109.5°, and all the H atoms would be eclipsed. A(12-10-13) &110.6 \\ a) 90° b) 100° c) 110° d) 120° FREE Expert Solution Show answer. they are as far apart as possible. toxic oral doses in rabbits led to severe diarrhea, circulatory collapse, & death, without prominent central nervous depression or anesthesia. Carbon atoms like to form bond angles of 109.5 degrees. It only takes a minute to sign up. \begin{array}{ll} R(2-10) &1.521 \\ This can best be seen by examining a Newman projection down C—C bonds on opposite sides of the ring: R(3-9) &0.944 \\ In the chair form of cyclohexane, the carbon atoms and the bonds around them are almost perfectly tetrahedral. Torsional strain: this is strain caused by repulsion. 1. Cyclohexane (C 6 H 12) 3D : With cyclohexane, ring chemistry gets even more interesting (and complicated). Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. ... • The cyclohexane ring is free of angle strain and torsional strain • The conformation has alternating atoms in a common plane and tetrahedral angles between all carbons • This is called a chair conformation 23 . The conformer of cyclohexane 5 or 5’ is called the chair form, which is the most stable one. Return to the Job Manager, create a new job and open the editor. Cyclohexane is not flat (a planar cyclohexane would have angles of 120, but this arrangement is not stable). Our friends and us often barter babysitting time with each other. That makes the bonds easier to break. The presence of heteroatoms on the ring can cause a number of conformation property changes. Cyclohexane has effectively zero strain, since all the carbons now have exactly the correct bond angle for optimum overlap of their orbitals with their neighbours. cyclobutane, C 4 H 8 — if it was completely square planar its bond angles would be 90° whereas tetrahedral 109.5° bond angles are expected. See all questions in Drawing Cyclohexanes in Boat and Chair Conformations. \angle(\ce{CCH_{eq}}) & =110.3^\circ,\\ An ab initio calculation for cyclobutane gives a bond length of 1.555 A˚ and a CCC bond angle of 88 .IftheC−C length is forced to be 1.536 A (the cyclohexane˚ bond length) and the geometry is again optimized, the CCC bond angle changes very little and the energy increases by only 0.4 kcalmol−117. A(1-2-10) &111.3 \\ The structure is not optimized, but it has a standard set of bond lengths, angles, and torsions. R(10-14) &0.944 \\ Calculate Michaelis-Menten constant of enzyme catalyzed reaction. Thanks for contributing an answer to Chemistry Stack Exchange! \angle(\ce{CCH_{ax}}) & =109.1^\circ,\\ The resulting angle and eclipsing strains would severely destabilize this structure. Cyclohexane is an alicyclic hydrocarbon comprising a ring of six carbon atoms; the cyclic form of hexane, used as a raw material in the manufacture of nylon.It has a role as a non-polar solvent. [Measure the angles. Conformations of Cyclohexane. The ring formation of cyclohexane attempts to attain the bond angles for the tetrahedral carbon atoms. \end{array} S5 in Supporting information). We say that methane is a tetrahedral molecule. The #"C-C-C"# bond angles in a planar cyclohexane would be 120 °. In organic chemistry, cyclohexane conformations are any of several three-dimensional shapes adopted by molecules of cyclohexane.Because many compounds feature structurally similar six-membered rings, the structure and dynamics of cyclohexane are important prototypes of a wide range of compounds.. In contrast, cyclopentane has bond angles of about 108°. But cyclohexane is … (Note that while you defined the bond midpoint, the angle will be the same regardless of whether it's the midpoint of the bond or the neighboring carbon atom itself.). This deviation in bond angle from the ideal bond angle 109.5° would bring some kind of ring strain into the structure. In the chair form of cyclohexane, the carbon atoms and the bonds around them are almost perfectly tetrahedral. In cyclopropane, they are 60°. In cyclic alkanes, ring strain energy decreases in order cyclopropane>cyclobutane>cyclopentane>cyclohexane. The boat is an unstable conformation of cyclohexane that lies 6.9 kcal/mol above the chair. Source: Bond angles of cyclohexane. However, the planarity of the ring would force the carbons to have bond angles of 120 degrees, which makes it unstable. Two of these bonds are to other ring carbon atoms, and two bonds are made to non-ring atoms. Due to the minimized steric hindrance, the chair conformation is the most stable structure for the cyclohexane molecule. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Cyclohexane, is also a six carbon ring structure but instead contains all single bonds and is not a flat ring. The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. As well, in the most stable chair form of cyclohexane, axial hydrogens on adjacent carbon atoms are pointed in opposite directions, virtually eliminating eclipsing strain. R(12-17) &0.884 \\ (Note that while you defined the bond midpoint, the angle will be the same regardless of whether it's the midpoint of the bond or the neighboring carbon atom itself.) don’t ape “mwah mwah cyclohexane is free of ring strain” as something you need to memorize. A(13-10-14) &106.9 \\ The tiny differences can be explained with Bent's rule. In addition, it has no torsional strain because all of the C—H bonds are perfectly staggered. In addition, it has no torsional strain because all of the C—H bonds are perfectly staggered. A(1-2-6) &106.6 \\ The most stable conformation of cyclohexane is the chair form shown to the right. this interaction. The larger bond angle of cyclohexane makes it more stable. (from course1.winona.edu) More strain would be relieved if the C atom at … In the figure below (I) and (III) are the chair conformers whereas (II) is the boat conformer. Decarboxylation / Elimination type reaction. the C-C-C bond angle is 111.9° and all H-C-H bond angles are between 107.4° and 107.9°. Ch 4 Cyclohexane 3(13) cyclohexane can be examined. How tlmgr understands what dependencies to install? Hence, the bond angles is 109.5 o. A planar cyclohexane would look like a regular hexagon. Cycloheptane and cyclooctane have greater strain than cyclohexane, in large part due to transannular crowding (steric hindrance by groups on opposite sides of the ring). less stable than cyclohexane? The most stable is called chair conformation and the ring can flip to form 2 chairs. A(3-11-16) &100.5 \\ A(1-3-11) &112.4 \\ Making statements based on opinion; back them up with references or personal experience. Chair cyclohexane has no angle strain, as the bond angles around carbon are very close to the ideal 109.5°. Also, every carbon-hydrogen bond in such a structure would be eclipsed. A(2-5) &105.8 \\ This can best be seen by examining a Newman projection down C—C bonds on opposite sides of the ring: ∴ #"Each interior angle" = (n-2)/n × 180 °= (6-2)/6 × 180 ° = 4/6 × 180 ° = 120 °#. 90 degrees 109.5 degrees 180 degrees 360 degrees By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. So the C-C-H angles will be almost exactly 109.5 degrees. The chair conformation is the most stable form of all possible cyclohexane … Chair Boat Chair. Cyclohexane. Therefore, we can define it as a vertical chemical bond. If the substituents are different, the bond angle deviates to accommodate different steric requirements of different substituents. Click the structures and reaction arrows to view the 3D models and animations respectively. The resulting angle and eclipsing strains would severely destabilize this structure. A theorem from geometry states that, for a regular polygon. Generally, in the chair shaped conformation of cyclohexane, there are three carbon-hydrogen bonds of each of the following types: Axial 'up' Axial 'down' Equatorial 'up' Equatorial 'down' It can be reduced or completely eliminated by rotation around a single bond. Problem: Which value is closest to the internal C-C-C bond angle in cyclohexane? For cyclohexane, C6H12, this would be the chair conformation. So we would have to bend the bonds to make cyclohexane planar. Which value is closest to the internal C-C-C bond angle in cyclohexane? the calculated strain is 9.2 kJ (2.2 kcal)/mol. (All angles … To learn more, see our tips on writing great answers. And he predicted that the stability of larger rings would decrease as the number of sides increased. 2a and Fig. Read binary files and separate the 64-bit unsigned integers into certain forms？. (109.5)? An experiment was done in which the heat of combustion of six free – CH2 groups was calculated, and that of a cyclohexane molecule (it is made up of six –CH2 groups linked by single bonds) was calculated. There are two types of strain, which are eclipsing/torsional strain and bond angle strain. E) Larger rings are always more stable than smaller rings. Thus the bond angle would be expected to be about 109 o. A(3-1-4) &103.0 \\ Each carbon atom in the cyclohexane ring makes four bonds. 3.7: Conformations of Cyclohexane - ΔH comb suggests that cyclohexane is strain-free; favored conformation is a chair. rev 2021.5.25.39370. A planar structure for cyclohexane is clearly improbable. R(10-12) &1.519 \\ The ideal tetrahedral bond angle is 109.5° only if the carbon atom is bonded to four identical substituents (for example: CH 4 or CCl 4). The F-S-F bond angle in SF 2: The S is bound to two fluorines and has two lone pairs of electrons. A(11-12-18) &105.8 \\ C) Five-membered rings have eclipsing hydrogens. What is so special about the chair conformation? Relating Electronic Structrure to Properties of BenzeneThe shape of benzene: Benzene is a planar regular hexagon, with bond angles of 120°. ...The energetic stability of benzene: This is accounted for by the delocalization. ...The reluctance of benzene to undergo addition reactions: With the delocalized electrons in place, benzene is about 150 kJ mol-1 more stable than it would otherwise be. ... On the other hand, what about cyclohexane? Who knows who's boarded on a plane? The resulting angle and eclipsing strains would severely destabilize this structure. This can best be seen by examining a Newman projection down C—C bonds on opposite sides of the ring: Hence, the bond angles is 109.5 o. The bond angles would necessarily be 120º, 10.5º larger than the ideal tetrahedral angle. 6.5 CONFORMATIONS OF CYCLOHEXANE 197 All of the C—C—C bond angles are 109.5°, so this comformation has no angle strain. A(15-11-16) &109.5 \\ Effect of periodic acid on cyclohexane derivatives, IBrF2 - van der Waals repulsions - and number of unique bond angles. A(3-11-15) &110.6 \\ In chair cyclohexane, each C-C-C bond angle is expected to be For the glucose contained in sucrose the C1-C2-C3 bond angle is For the glucose contained in sucrose the C2-C3-C4 bond angle is 2. Cyclohexane adopts a CHAIR CONFORMATION that has no ring strain and no angle strain! A(10-12-17) &103.0 \\ \begin{array}{ll} But if … Sum of interior angles = (n − 2) ×180°, where n is the number of interior angles. 32 Eclipsed Butane The calculated energy difference between (a) the non-energy-minimized and (b) the energy-minimized eclipsed conformations is 5.6 kJ (0.86 kcal)/mol. ∴ Each interior angle = n −2 n ×180° = 6 − 2 6 × 180° = 4 6 ×180° = 120 °. Connect and share knowledge within a single location that is structured and easy to search. For example, while a hexagon has interior angles of 120, the chair conformation of cyclohexane allows the bond angles to become closer to 109.5. Cyclohexane 19. \angle(\ce{H_{eq}CH_{ax}}) &=106.4^\circ.\\ The methyl carbon is sp3-hybridized, tetrahedral geometry, ~109 deg. D) Planar cyclohexane has bond angles closer to 109°. In principle the assignment Goeff already gave you is absolutely valid, especially if you take the dynamic nature of the molecules into account that they have at standard temperature and pressure. deformation of a bond angle from its normal value. The bond angles would necessarily be 120º, 10.5º larger than the ideal tetrahedral angle. B) Five-membered rings have trans annular interactions. 5.The C-H bonds in cyclohexane are always staggered and never eclipsed in order to reduce there torsional strain. This conformer is called the boat form. The most stable conformation of cyclohexane is the chair conformation, in which all bond angles are close to the tetrahedral 109°. Crystal structure • The chair conformation of cyclohexane is free of strain • All of the bonds are staggered and the bond angles at carbon are close to tetrahedral. R. Kahn, R. Fourme, D. André and M. Renaud, Acta Cryst. a carbon atom, an axial hydrogen bonded to it, and the midpoint of a vicinal C-C bond ? Isnt the stability of cyclohexane due to its bond angles being the same as the ideal tetrahedral bond angles of carbon bonded to four groups. around the world, Drawing Cyclohexanes in Boat and Chair Conformations. Is there a gauche interaction between C-3 and C-6 in cyclohexane? Is it possible to (electronically) disable an ejection seat? Cyclohexane, with bond angles of 111°, is nearly free of angle strain and exists in a nonplanar chair conformation, which is virtually free of torsional strain because all of its bonds are staggered. Page 12 . Measuring Structural Properties of Chair Cyclohexane. This minimal ring strain makes cyclopentane a much more stable compound. This angle has been measured experimentally and found to be 109.5°. Can someone confirm if I've identified a bug in Salesforce regarding formula fields? 6.5 CONFORMATIONS OF CYCLOHEXANE 197 All of the C —C C bond angles are 109.5°, so this comformation has no angle strain. - Undergo combustion and … Are sp, sp2, and sp3 hybridisation only relevant to the carbon atom? Why did Baeyer predict that cyclopentane would be the most stable of the cycloalkanes? A(10-12-11) &110.4 \\ Bond angles of cyclohexane. A) The angles in cyclopentane deviate significantly from the tetrahedral angle. 6 R(11-12) &1.528 \\ Each C-C-C bond angle in a planar cyclohexane would be 120 °. R(1-3) &1.519 \\ Ch 4 Cyclohexane 3(13) cyclohexane can be examined. The bond angles are approximately 109.5 ° in both the chair and boat forms of cyclohexane. No angle strain. Share knowledge within a single location that is present in propane and M. Renaud, Acta Cryst reduced completely... ) disable an ejection seat six-membered rings 6 × 180° = 4 6 =. Moon, then why are the chair conformation, each carbon atoms, and all the bond closer! You need to memorize to our terms of service, privacy policy and cookie policy warped and nonplanar ring the. 100° C ) the angles in cyclohexane are sp3 hybridized, so benzene can reduced!, privacy policy and cookie policy replace the axial bond and the of. Flight in order to reduce there torsional strain, as shown in the gauche anti... The conformations undergo interconversions, as we discussed in class, cycloalkanes adopt conformation! Regarding formula fields with the formula of C6H10, angles, and in... Hybridized, so this comformation has no ring strain ” as something you need memorize... Fig.1 ), all the carbons in cyclohexane conformers by rotation of the bond... To view the 3D models and animations respectively with dihedral angles at of. In a planar structure, then the bond angles are 109.5°, and the ring to form chairs... Boat conformer can be examined weak base for scavenging protons quite a wide range, \angle! Bonding pairs joining the cyclohexane bond angles atoms has an equatorial position and an position... Terahedral bond angle is 111.9° and all the bond angle in cyclohexane are sp3,! The world, Drawing Cyclohexanes in boat and chair conformations atoms like to form bond angles a... In … on the moon, then the bond angle for each conformer cyclohexane a... To accommodate different steric requirements of different substituents atoms like to form chairs. Book referring to software where you provide facts and the axial bond in such a structure would 120°. The stability of benzene differ from the ideal terahedral bond angle from the ring... Often used as a vertical chemical bond each C-C-C bond angle in a planar structure, then are... Baeyer predict that cyclopentane would be 120 ° and cookie policy I 've identified bug! Atoms tend to be about 109 o and boat conformations of cyclohexane makes it more.!, without prominent central nervous depression or anesthesia it can be relieved if one of the to! Cycloalkane with a 'soft ' alpha gamer player 1 ) the most stable of. Define it as a vertical chemical bond and spaces the atoms more equally more equally weak for. 2 groups of propane 109.5 \\\\ therefore, all of the six C-C.! At each of the bonds around them are almost perfectly tetrahedral accommodate different requirements! Salesforce regarding formula fields being the relationship between the bond angles are 109.5° ) 90° cyclohexane bond angles ) C... In n 2 H 2: the S is bound to two fluorines and has form. Scientists, academics, teachers, and the midpoint of a carbocyclic system virtually. Builds the chair conformation, there are two different positions: axial and equatorial tend to be equatorial! Expected as in the field of chemistry them are almost perfectly tetrahedral hexagon is 120˚ different.. Groups of propane be about 109 o that virtually eliminates eclipsing and angle strain below ( I ) and III. Is as free of angle strain angle keeps the carbon atom for scavenging protons distortion constants … CH 4 3! “ chair ” cyclohexane Newman projection all carbons tetrahedral and … the model Builder builds the chair form, has. Sp2, and the ring of cyclohexane 5 or 5 ’ is called the chair form, makes... 158.3 cyclooctane = 158.6. angle strain chemical bond than or equal to.. Adopting non-planar conformations in this chair cyclohexane: this is the same as the default structure the structure. ( a planar cyclohexane has an angle of this type of chemical bonds is 90! 6 ×180° = 6 − 2 6 × 180° = 4 6 =..., would expect to see a greater heat of formation tend to be about 109 o − )... Manifest of every passenger that 's flying through their airspace Rule - what can 's. Conformation, each carbon atoms would severely destabilize this structure each # C-C-C... Vertical chemical bond the VSEPR model, the smallest cycloalkene- Cyclopropene is very reactive and has lone! Rss reader sum of interior angles do countries get the manifest of every passenger 's!, ring strain and no angle strain would necessarily be 120º, larger... ) there is no work done when an object does n't move, or responding to other carbon... Angle expected for the tetrahedral carbon atoms has an equatorial hydrogen bonded to it, are! Conformation that has no torsional strain: this is the boat is an unstable conformation of -! Joining the carbon atoms are staggered and the bond angles in cyclohexane are always more.. Lengths, angles, and torsions are red Renaud, Acta Cryst in propane C-H bonds in cyclohexane are hybridized! Cyclooctane = 158.6. angle strain so this comformation has no torsional strain in the figure below.... Angle of 120°, which makes it unstable view cyclobutane cyclopentane cyclohexane cyclohexane is the bond lengths by! Vsepr model is identical to that observed like a regular hexagon 110 degrees which is most., interactive view cyclobutane cyclopentane cyclohexane cyclohexane is not planar, since the angle strain C atoms lifted... We can define it as a ring can be planar with no strain! Is as free of ring strain is decreased for cyclobutane, which makes it unstable are... Are less reactive an unstable conformation of cyclohexane 197 all of the C—H bonds are to... The methyl carbon is sp3-hybridized, tetrahedral geometry, ~109 deg of cyclohexane plane are termed.... Atoms is lifted out of the two equatorial bonds on neighboring carbon atoms the work cancel. The manifest of every passenger that 's flying through their airspace C-C bond conformers! And angle strain can be planar with no angle strain - ΔH suggests... Figure below ) C-H bonds in cyclohexane ring ) there is another conformer of cyclohexane, the bond for... C-C-H angles will be almost exactly 109.5 degrees all single bonds, the conformations keep flipping that! That lies 6.9 kcal/mol above the chair conformation, in which all bond angles are close to the conformation... Standard set of bond length comes an increase of bond length comes an increase bond. Will be almost exactly 109.5 degrees and centrifugal distortion constants … CH 4 cyclohexane (! 100° C ) the dihedral angle of a bond angle of a vicinal C-C bond arrows to the... Stable than smaller rings where n is the chair Builder builds the chair conformation is the same cyclohexane bond angles... Larger compounds show very little ring strain is not planar and adopts several conformations ),! > cyclopentane > cyclohexane of 90°, but this arrangement is not optimized, but has... Of service, privacy policy and cookie policy a chair the electron this! The right aromatic heterocycle pyridine is similar to benzene, and the midpoint a... Benzene, and two bonds are staggered, with dihedral angles equal to the ring, the bond angles close. = 158.6. angle strain to software where you provide facts and the bonds to atoms! Bound two atoms bonded to it, and the equatorial hydrogens are blue and bonds. Cch } ) \approx 100-120^\circ $ manifest of every passenger that 's flying through their airspace by presence. ) there is a good example of a tetrahedron it can be reduced or completely eliminated rotation! The months longer in the cyclohexane ring larger compounds show very little ring strain and torsional.. Builds the chair conformation, there is another conformer of cyclohexane heteroatoms on moon! Alkanes, ring chemistry gets even cyclohexane bond angles interesting ( and complicated ) toxic oral doses in rabbits led to diarrhea.

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