Who Needs Lewis Structures To Get VSEPR Geometries? - Journal of

In the Classroom

Who Needs Lewis Structures To Get VSEPR Geometries? Alan F. Lindmark Department of Chemistry, Indiana University Northwest, Gary, Indiana 46408 [email protected]

Current first-year textbooks (1a-1u, 2a-2i) teach the VSEPR (valence shell electron-pair repulsion) model (3) more or less in a similar manner (varying only in the level of the course). The student is taught to (i) draw a Lewis (electron-dot) structure, (ii) count the number of “electron clouds” in the Lewis structure, and (iii) relate that number to the standard VSEPR table of structures and geometries, which can be found in any firstyear textbook. Drawing the Lewis structures first often introduces unnecessary complexity into the process and results in confusion, especially in cases where the octet rule may be violated.1 VSEPR can be taught without using Lewis structures more simply and effectively via the following methodology utilizing one or two (75 min) lecture periods as deemed appropriate for the level of the course. A simple statement that could be easily understood by many students is to multiply the number of noncentral atoms, x (ignoring the H atoms), times eight, subtract that number from the number of valence electrons (n) in the compound, and put the leftover electrons on the central atom as electron pairs, where e is the number of lone electron pairs. Then the students simply count the number of groups (a lone electron counts as a group) on the central atom to give the coordination number, CN. No Lewis structures are needed and hydrogens are simply added later to compete the structure. Some may prefer using this method. I will continue using the following mathematical manifestation of this statement for the remainder of this article. CN ¼ x þ e ¼ x þ ðn - 8xÞ=2 ¼ ðn=2Þ - 3x

ð1Þ

where (n - 8x)/2 is equivalent to the number of lone electron pairs, e. Care must be taken to round up the result to a whole number for free radicals. There are two ways interpreting this equation, both of which will help students better understand VSEPR. (i) Eight electrons are associated with the noncentral atom, X, which will always satisfy the octet rule in simple structures. Any leftover electrons belong to the central atom, A, as lone pairs, E. (ii) n/2 is the number of electron pairs in the molecule, either in bonds or as lone pairs. Each X has 3 electron pairs not involved in σ bonding to A that do not contribute to the stereochemistry (hence, -3x in eq 1). The remainders of the electron pairs belong to A and along with the σ bonds determine the stereochemistry.

In both these analyses, the nature of the “electron cloud” does not impact the VSEPR geometry: single, double, and triple bonds, a lone pair, or a lone electron all count as one “cloud”.

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Another aspect of this method is that the hydrogen atoms have no impact on coordination number. The hydrogen valence electrons are counted, but whether the hydrogens are included in the structure or where they are placed is irrelevant. The hydrogen is added later as a proton. For example, H3PO4, H2PO4-, HPO42-, and PO43- all give the same (tetrahedral) structure; H3PO3 gives tetrahedral geometry whether the third H is bonded to the P (correct) or to the O. These concepts are emphasized to the students during lecture to promote understanding. Examples of these concepts are shown in Figures 1 and 2. This method enables the student to do any calculations quickly, and the formula is foolproof for any compound with one central atom. One could go over a list of compounds and quickly establish their coordination number by inspection with this method and then obtain the specific geometry from a VSEPR table. The Lewis structure may be drawn subsequently, if desired.1 I use a simple framework molecular model (FMM) kit (4) to demonstrate in lecture. The central atom is merely the metal component useful for coordination numbers 2 through 6 and different colored tubing represent different noncentral atoms or lone pairs. The students will likely not have the kit available in a large lecture. I prefer to leave the “hands-on” segment to a lab setting in preference to a computer-type lab (see the supporting material). Sample Lecture Although the following lecture is aimed at first-year science majors course and shows how to apply this methodology to each VSEPR geometry, it can easily be adapted to nonscience majors chemistry course or an advanced inorganic chemistry course. A summary of virtually any possible structure (real or hypothetical) or electron configuration one might use in any class (5-8) is found in Tables 1-4 in the supporting material. Many of the more whimsical structures may be better left to an advanced inorganic chemistry class, especially if one wants to discuss hypothetical molecules and perform correlations with molecular orbital theory. To begin the lecture, it is first mentioned to the students that in simple structures, the less electronegative central is listed first (except with H in acids or to show structure, e.g., HClO or OCN-). The overall VSEPR structure is calculated, and then refinements are made using the standard repulsions strengths between electron pairs, E-E > E-BP > BP-BP > E-L > BP-L > L-L, where E is nonbonding electron pair, BP is bonding electron pair, and L is free radical. It is emphasized that

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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 5 May 2010 10.1021/ed800145e Published on Web 04/13/2010

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Journal of Chemical Education

487

In the Classroom Table 1. VSEPR Structure Using eq 1 n

x

-

10

1

2

AX

CN

þ

11

1

3

AXL

12

1

3

AXE2

O2-

13

1

4

AXE2L

O22-

14

1

4

AXE3

“XeF”

15

1

5

AXE3L

“XeF-”

16

1

5

AXE4

CO2

16

2

2

AX2

NO2

17

2

3

AX2L

O3

18

2

3

AX2E

ClO2a

19

2

4

AX2EL

OF2b

20

2

4

AX2E2

“ClF2”

21

2

5

AX2E2L

I3-

22

2

5, “linear”

AX2E3

“XeF2-”

23

2

6

AX2E3L

“XeF22-”

24

2

6

AX2E4

BF3

24

3

3

AX3

“ClO3”

25

3

4

AX3L

the VSEPR geometries are determined by nonbonding electron pairs (E) and noncentral atoms (X) getting as far away from each other as possible to minimize electron repulsions. Hybridization is simply mentioned here and given some meaning in the lecture directly after VSEPR. Calculations are simple via eq 1 and take the students very little time. A derivation and explanation of this equation is amplified again in lecture. CN 2, Linear This structure is simple as a starting point and needs little discussion. CO2 (AX2) is a good first example: CN ¼ ðn=2Þ - 3x ¼ ð16=2Þ - ð3Þð2Þ ¼ 8 - 6 ¼ 2 ð2Þ Other useful examples are OCN- or NO2þ. It is worth discussing with these compounds that the same geometry around the central atom is obtained regardless of which of the three Lewis structures is considered for each (two double bonds or one single and one triple).2 A discussion of dipole moment is relevant here: CO2 and NO2þ have none whereas OCN - does. It should also be pointed out here that “linear” molecules such as I3- and XeF2 from VSEPR Table 1 (expanded version is available in the supporting material) are really trigonal bipyramidal based, although the molecular geometry will be shown later to be “linear”.

2-

26

3

4

AX3E

“BrF3þ”

27

3

5

AX3EL

BrF3

28

3

5, bent- T

AX3E2

“XeF3”

29

3

6

AX3E2L

SO3 Figure 2. Four possible Lewis structures for PO33- (or H3PO3 with protons removed). Note that all structures give the coordination number 4. The positioning of the three H's is irrelevant.

“XeF3-”

30

3

6

AX3E3

CF4

32

4

4

AX4

“SF3O”

33

4

5

AX4L

SF4

34

4

5, seesaw

AX4E

“BrF4”

35

4

6

AX4EL

XeF4

36

4

6, “square planar”

AX4E2

PF5

40

5

5

AX5

a

117.6° (ref 5, p 989). b 103° (ref 5, p 749).

It is shown here that whether or not boron violates the octet rule, the geometry is trigonal planar, which reinforces previous arguments. (2) Two noncentral atoms, one lone-pair (AX2E), for example, O3 CN ¼ ð18=2Þ - 6 ¼ 3

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ð4Þ

It is mentioned here that the structure is technically “bent”. One could also introduce electron-pair repulsions to explain that the angle is not 120°, but 117°, or revisit this again soon after to reinforce learning (as I prefer). The existence of a dipole is mentioned here. (3) One noncentral atom and two lone pairs (AXE2), for example, O2 CN ¼ ð12=2Þ - 3 ¼ 3

CN 3, Trigonal Planar Four types of structures are considered here: (1) Three noncentral atoms (AX3), for example, BF3 CN ¼ ð24=2Þ - 9 ¼ 3 ð3Þ

structure

O2

O2

Figure 1. Four possible Lewis structures for CO32- (or H2CO3 with protons removed). Note that all structures, including the “invalid” one (bottom right), give the coordination number 3. The positioning of the two H's is irrelevant.

CN = (n/2) - 3x

molecule

ð5Þ

This example may seem trivial. However, if one introduces hemoglobin here, this can be used as a possible explanation as to why the oxygen bond to iron is bent (MO theory can be introduced in more advanced courses).

pubs.acs.org/jchemeduc

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r 2010 American Chemical Society and Division of Chemical Education, Inc.

In the Classroom

(4) A compound such as formaldehyde, H2CO (AXH2), provides a good introduction to an organic molecule. Recall that the H are treated as protons and are not counted in the CN. CN ¼ ð12=2Þ - 3 ¼ 3 ð6Þ A discussion here of the geometries of carbon is appropriate and that there are always four bonds to carbon (with no nonbonding pairs) in any neutral organic structure. The Lewis structure is drawn here to emphasize this. Optical and geometrical isomers can also be discussed (obviously, no optical isomers exist here) in lecture and lab to prepare the student for what is to come in organic chemistry. CN 4: Tetrahedral Excellent representative compounds of the formula AHn to use are (i) CH4 (AH4), (ii) NH3 (AH3E), and (iii) H2O (AH2E2). All give tetrahedral-based structures: CN ¼ ð8=2Þ - 0 ¼ 4 ðfor allÞ

ð7Þ

ð1Þ CH4 ; perfect tetrahedral; 109° ð2Þ NH3 ; tetrahedral-based; “trigonal pyramidal”; 107° ð3Þ H2 O; tetrahedral-based; “bent”; 104° A discussion of electron-pair repulsions is discussed here, using the standard arguments previously mentioned. This also presents an opportunity in lab and lecture to introduce optical and geometrical (none) isomers by using a series of molecules CH4, CH3X, CH2XY, and CHXYZ; in lecture this can be done with the tetrahedral model with different color sticks (making the mirror image) or with overheads (which do not seem to work very well here). Students can work with models in the laboratory. It is possible to introduce optical activity of amino acids by analogy to the CHXYZ structure and talk about as much biochemistry as one feels appropriate at this level. For variety, compounds such as CF4 or SO42- (AX4) are shown to be tetrahedral: CN ¼ ð32=2Þ - 12 ¼ 4 ðfor bothÞ ð8Þ

be discussed to obtain the structures by standard arguments. This has unfortunately been deleted from many first-year textbooks. It is again emphasized, via the usual arguments, that the axial-equatorial (90°) repulsions control the structure. Relevant examples are (i) PF5 (AX5) CN ¼ ð40=2Þ - 15 ¼ 5 ð9Þ (ii) SF4 (AX4E) CN ¼ ð34=2Þ - 12 ¼ 5

The seesaw is shown to be the most stable of the two possibilities by the above arguments. (iii) ClF3 (AX3E2) CN ¼ ð28=2Þ - 9 ¼ 5 ð11Þ The T-shaped structure (bent-T) is shown to be the most stable of the three possibilities by the above arguments. (iv) I3-, as I I2-, (AX2E3) CN ¼ ð22=2Þ - 6 ¼ 5 ð12Þ The “linear” structure is shown to be the most stable of the three possible structures by the above arguments. It is also mentioned here the possibilities of geometrical and optical isomers where all five groups are atoms, but because of rapid rearrangement of the system (introduce fluctionality versus nonfluctionality, if desired) isolation is not possible. It is also noted that the three possible arrangements for the seesaw, T-shaped, and “linear” are really the same “geometrical isomers” with the atoms and electron pairs merely changing positions. The discussion of more complex geometrical isomers is best left to octahedral geometry. It is also shown that only a small quantity of energy is required to convert from square pyramidal to trigonal bipyramidal geometry (turnstile mechanism). One can now go back and talk about electron-pair repulsions in three- and four-coordinate geometries and how it controls bond angles. CN 6: Octahedral A relevant example is XeF4 (AX4E2) CN ¼ ð36=2Þ - 12 ¼ 6

CN 4: Square Planar This geometry is worth mentioning if one wants to introduce geometrical isomers and transition-metal complexes. It should be noted that only a few transition-metal complexes adopt the geometry (XeF4 is only square planar as an “accident of geometry” and is actually octahedral based), primarily group 10: Ni, Pd, and Pt. Geometrical and optical (none) for PtX4, PtX3Y, PtX2Y2, PtWXYZ, and so forth can be covered here, if desired. A good example is cis-platin, a chemotherapeutic agent by virtue of its ability to intercalate into DNA. CN 5: Trigonal Bipyramidal After discussing the differences in the equatorial and axial positions, two modes of teaching are useful: First, the simpler technique is to mention that the lone pairs need more space and prefer the equatorial plane and use VSEPR Table 1 (expanded version is available in the supporting material): AX5 is trigonal bipyramidal; AX4E is seesaw; AX3E2 is T-shaped; and AX2E3 is “linear”. Second, E-E > BP-E > BP-BP repulsions can again


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ð10Þ

ð13Þ

The “square planar” geometry is shown to be the most stable of the two possible geometries by the standard arguments. This is shown to be analogous to cis- and trans-isomers of a transition-metal complex, AX4Y2. One can now introduce geometric and optical isomers for octahedral metal complexes, although from experience this may be better left to the lab part of the course. Suggested compounds might be ðiÞ AX3 Y3 ; two geometrical isomers; no optical isomers ðiiÞ AX2 Y2 Z2 ; five geometrical isomers; ðone of which is optically activeÞ Another example is SF5- (AX5E) CN ¼ ð42=2Þ - 15 ¼ 6

ð14Þ

which is octahedral, “square pyramidal”.


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Vol. 87 No. 5 May 2010

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489

In the Classroom

CN 7 and 8 (Optional)

not agree with VSEPR, but these are not relevant to most courses. Some examples of exceptions are

An example of seven coordination is IF7 (AX7) CN ¼ ð56=2Þ - 21 ¼ 7

(i) SeBr62-; It is predicted to have a coordination number of ð15Þ

The common geometries are (one would have to make up models here or use graphics) pentagonal bipyramid (pentagonal planar), capped trigonal prism, or capped octahedron for CN 7 and cube, square antiprism, or dodecahedron for CN 8. Additional Comparisons

(iii)

(iv)

If time permits, some additional comparisons can be made to compare similar compounds.3,4 For example, a comparison of NO2, NO2þ, and NO2- is interesting and instructive. (1) NO2 (AX2L) CN ¼ ð17=2Þ - 6 ¼ 2:5 f 3

ð16Þ

trigonal planar ð135°Þ

(v)

5. A computer program (11) is available for calculation of VSEPR. This provides little aid for a lecture-type setting but may be useful as a companion for a hands-on type lab.

Literature Cited

(2) NO2þ (AX2) CN ¼ ð16=2Þ - 6 ¼ 2

ð17Þ

linear ð180°Þ (3) NO2- (AX2E) CN ¼ ð18=2Þ - 6 ¼ 3

ð18Þ

trigonal planar ð115°Þ This is especially important in showing how a free radical opens up the structure and how a subtle change of one electron can have huge ramifications for structure and chemical reactivity. The next topic in lecture is ideally a discussion of what hybridization means in relation to geometries.5 Notes 1. I have not tried teaching VSEPR before Lewis structures, but in theory this is quite possible and may be even preferred when dealing with simple structures with one central atom (i.e., not N2O5). This would be especially true when the octet rule is exceeded. For example, SF4: four bonds to F, one lone pair [CN = (34/2) - 12 =5]. The lone pair is placed on the equatorial plane (seesaw). Another example is OCN-: CN = (16/20) - 6 = 2, linear, no lone pairs on carbon. 2. I find the technique (9) of S = N - A (authors notations) very effective as a companion tool in teaching Lewis structures where the octet rule is not exceeded. For the previous example, OCN-, S = 24 -16 = 8, 4 bonds, hence three possible resonance structures. S is the number of electrons in bonds; N is the number of atoms x 8 (excluding H); A is the number valence electrons; and or (N - A)/2 is the number of bonds. 3. VSEPR is an appropriate place to introduce symmetry if one were going to teach it in an advanced course. 4. This method is foolproof for any compound one might introduce at the first-year level. A few exceptions do occur where experimental evidence or molecular orbital theory does

490

(ii)

seven, but it is a perfect octahedron (lone pair stereochemically inert) (5). N(SiH3)3; It is predicted to be tetrahedral, but it is actually trigonal planar (5). CH3; It is predicted to be tetrahedral, but it is actually trigonal planar (This is a good example to compare to molecular orbital theory in advanced classes) (6). Hypothetical molecules where there are not enough electrons to go around, i.e., SF6þ. XeO64-; It is predicted to be octahedral, but it is a distorted octahedron in solution (10).


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Vol. 87 No. 5 May 2010

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1. Science majors textbooks surveyed: (a) McMurry, J.; Fay, R. C. Chemistry, 5th ed.; Prentice- Hall: Upper Saddle River, NJ, 2008; pp 242-250 (currently in use at Indiana University Northwest). (b) Atkins, P.; Jones, L. Chemical Principles: The Quest for Insight, 4th ed.; Freeman: New York, 2008; pp 95-103. (c) Zumdahl S. S.; Zumdahl, S. A. Chemistry, 7th ed.; Houghton Mifflin: New York, 2007; pp 367-379. (d) Ebbing D. D.; Gammon S. D.; Ragsdale, R. O. Essentials of General Chemistry, 2nd ed.; Houghton Mifflin: New York, 2006; pp 287-297. (e) Kelter, P.; Mosher, M.; Scott, A. Chemistry, the Practical Science, 1st ed.; Houghton Mifflin: New York, 2008; pp 335-343. (f) Goldberg, D. E. Fundamentals of Chemistry, 5th ed.; Mc Graw Hill: New York, 2007; pp 361-365. (g) Chang, R. Chemistry, 9th ed.; Mc Graw Hill, 2007, pp 400-409. (h) Silberberg, M. S. Principles of General Chemistry, 1st ed., Mc Graw Hill: New York, 2007; pp 306-315. (i) Silberberg, M. S. Chemistry, The Molecular Nature of Matter and Change, 4th ed.; McGraw Hill: New York, 2006; pp 375-385. (j) Chang, R. General Chemistry: the Essential Concepts, 5th ed.; McGraw Hill: New York, 2008; pp 312-322. (k) Kotz, J. C.; Treichel, P. M.; Townsend, J. R. Chemistry and Chemical Reactivity, 7th ed.; ThomsonBrooks/Cole: Belmont, CA, 2009; pp 367-375. (l) Moore, J. W.; Stanitski, C. L.; Jurs, P. C. Chemistry: The Molecular Science, 3rd ed.; Thomson Brooks/ Cole: Belmont, CA, 2008; pp 381-393. (m) Whitten, K. W.; Davis, R. E.; Peck, L. M.; Stanley, G. G. Chemistry, 8th ed.; Thomson Brooks/Cole: Belmont, CA, 2007; pp 289-321. (n) Masterton, W. L.; Hurley, C. N. Chemistry: Principles and Reactions, 6th ed.; Thomson Brooks/Cole: Belmont, CA, 2009; pp 175-182. (o) Oxtoby, D. W.; Gillis, H. P.; Campion, A. Principles of Modern Chemistry, 6th ed.; Thomson/Brooks/Cole: Belmont, CA, 2008; pp 92-97. (p) Tro, N. Chemistry: A Molecular Approach, 1st ed.; Pearson/Prentice Hall: Lebanon, IN, 2008; pp 406-418. (q) Ebbing, D. D.; Gammon, S. D. General Chemistry, 9th ed.; Houghton Mifflin: New York, 2009; pp 375-383. (r) Brown, T. L.; Lemay, H., Jr.; Bursten, B. E. Chemistry: The Central Science, 10th ed.; Pearson/Prentice Hall ; Upper Saddle River, NJ, 2006; pp 348-357. (s) Averill, B.; Eldredge, P. Chemistry: Principles, Patterns, and Applications, 1st ed.; Pearson/Benjamin Cummings: New York, 2007;


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In the Classroom

pp 382-399. (t) Zumdahl, S. S. Chemical Principles, 6th ed.; Houghton Mifflin: New York, 2009; pp 636-650. (u) Gilbert, T. R.; Kriss, R. V.; Foster, N.; Davies, G. Chemistry, 2nd ed.; Norton: New York, 2009; pp 408-419. 2. Nonscience majors textbooks surveyed: (a) Hill J. W.; Kolb, D. K. Chemistry for Changing Times, 11th ed.; Prentice Hall: Upper Saddle River, NJ, 2007; pp136-140. (b) Zumdahl, S. S.; Decoste, D. J. Introductory Chemistry, 6th ed.; Houghton Mifflin: New York, 2008; pp 364-373, plus study card. (c) Gilbert, T. R.; Kirss, R. V.; Davies G. Chemistry, The Science in Context, 1st ed.; Norton: New York, 2004; pp 354-362. (d) Malone, L. G. Basic Concepts of Chemistry, 7th ed.; Wiley: New York, 2004; pp 172-174. (e) Kelter, P. B.; Carr, J. D.; Scott, A. Chemistry, A World of Choices, 2nd ed.; McGraw Hill: New York, 2003; pp 208-212. (f) Seager, S. L.; Slabaugh, M. R. Introductory Chemistry for Today, 6th ed.; Thomson Brooks/Cole: Belmont, CA, 2008; pp 112-116. (g) Cracolice, M. S.: Peters, E. I. Basics of Introductory Chemistry, 1st ed.; Thomson Brooks/Cole: Belmont, CA, 2007; pp 368-375. (h) Bauer, R. C.; Birk, J. P.; Marks, P. S. A Conceptual Introduction to Chemistry, 1st ed.; McGraw Hill: New York, 2007; pp 302-308. (i) Timberlake, K. General, Organic and Biological Chemistry, 2nd ed.; Prentice Hall: Upper Saddle River, NJ, 2007; pp 161-165.


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3. Gillispie, R. J.; Hargittai, I. The VSEPR Model of Molecular Geometry; Allyn and Bacon: Englewood Cliffs, NJ, 1991. The authors use e for a lone electron, but this would cause confusion in later calculations, hence the use of L in this article. 4. Molecular Framework Models; Prentice-Hall: Upper Saddle River, NJ, 1998. 5. Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon Press: Oxford, 1984. 6. An Introduction to Molecular Orbitals; Jean, I., Volatron, F., Burdett, J., Eds.; Oxford University Press: Oxford, 1993. 7. Christe, K. O.; Curtis, E. C.; Dixon, D. A.; Mercier, H. P.; Sanders, J. C. P.; Schrobilgen, G. J. J. Am. Chem. Soc. 1991, 113, 3351–3361. 8. Nabiev, Sh. Sh. Russ. Chem. Bull. 1997, 47, 535–559. 9. Lever, A. B. P. J. Chem. Educ. 1972, 49, 819–822. 10. Forgeron, M. A. M.; Wasylislen, R. E.; Gerhen, M.; Schrobilgen, G. J. Inorg. Chem. 2007, 46, 3585–3592. 11. Winter, M. J. Chemical Bonding, Online VSEPR Calculator; Oxford University Press: Oxford, 1994.

Supporting Information Available VSEPR Tables 1-4; student lab handout including questions and a data sheet. This material is available via the Internet at http://pubs.acs.org.


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Who Needs Lewis Structures To Get VSEPR Geometries? - Journal of

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