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exam question exchange Halomethanes: Combinatorial Analysis in Chemistry I. Novak
JOHN J. ALEXANDER University of Cincinnati Cincinnati,OH 45221
Literature Cited 1.Nambi.P. J. Cham. Edue. 1887,84,678.
Deceptively Simple Competitive Reactions
National University of Singapore Singapore 0511
Rooer S. Macornber ~nirersityof Cincinnati Cincinnati. OH 45221 ~~
Halomethanes have considerable technological (refrigerants, propellants) and ecological ("destroyers of the ozone layer") importance. They also provide a convenient teaching example for group theory and symmetry i n chemistry a s well a s combinatorics. Question (1) Using W, X, Y,and Z to represent the four atoms attached to carbon, draw generic structures for all possible mono-. di-. tri- and tetra-halomethanes. Then s ~ e c i"f vthe point &up (symmetry) of each. (2) Considering only halogens F, C1, Br, and I, calculate the number of possible halomethanes belonging to each of the above point groups a s well a s the total number of possible halomethanes. Don't forget that many halomethanes possess 1to 3 hydrogens. (3) Which of the above halomethanes will exhibit pure rotational spectra and which will be chiral?
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The multi-part question below will serve not onlv to ren e w some aspects of chemical kinetics for stude& who have been through that section of physical chemistrv, but also i t will alert them to a c o m m o ~ m ~ s t a k eimpression. n Question
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Hints The number of different combinations ( C )and permutations ( P )of n things taken p a t a time a r e given by (C(n,p)=n!b!(n -p)!l
(1) In diagram (i) there are two equivalent ways to fmd the
and P(n,p)= n(n - l)(n - 2). . Sn -p
Consider the two kinetic schemes above. All reactions are simple firsborder and irreversible, and the initial concentration of B and C are zero.
+ 1)
Acceptable Solution (1)
(2) For Td symmetry C (5,1)=5except that this includes CH4 which is not a halomethane; thus, there are 4 tetrahedral combinations (CF4,CCI,, CBq, and C4. For C, symmetry, P(5,2)=20.For Cz,, C(5,2)=10.For C. symmetry we must divide P(5,3) by 2 to avoid double counting superimposable mirmr images; 6012 = 30. Finally, for C1, C (5,4)=5. Thus, the total number of halomethanes is
value of k. One can either monitor the disappearance of A, or the appearance of B. Give the integrated rate expressions for bath experiments, and describe what functions you would plot against time to evaluate k. (2) Now focusing on diagram (ii), what is the slope of a plot of In([Al&Al)versus time? (3) Assuming kinetic control of the reaction, what relationship exists between the ratios k$kc and [B], /[C].. ? (4) What is the slope of a plot of hl[CII([CI.. - [CI)t versus time? (Hint: It is not kc!) (5) Haw would you determine the value of kc? Acceptable Solution (1) From the stoichiometryof the reaction, [Bl- = [Ale and [BI = CAIo- [Al. The rate law gives, upon integration from [Alo to IAl, the equation In([Al&Al) = kt The rate law
(3) All molecules except those with Tdsymmetry will exhibit pure rotational spectra. Only those five structures belonging to C1 are chiral. All the rest have at least one plane of symmetry and are, therefore, achiral. The total number ofhalumethanes has becn recorded prevluuvly ( I and rt was wrongly stated as 70 In fact, if one mriudcs all phvn~callvand chaml~allvdlstmct enanttomcrs (of CI svmmetrv) the totalhumher becomes 74.
548
Journal of Chemical Education
d[Blldt = k[Al= k([BI..- [BI) gives, upon integration from 0 to [Bl, the equation Inl[BlI(d([Bl_- [Bill =kt Plotting either in([Ald[Al) or lnl[BlJ(d([Bi..- [BI)1 versus time will give a straight line of slope k. (2) The rate law
gives, upon integration from CAIo to [Al, the equation In([Ald[Al) = ( k +~kc)t Therefore, the indicated plot will have slope kB +kc. (3) Since these two competitive reaction are irreversible, the product ratio a t any t ~ m eLS a kinetically mntrolled mnstant. The means that [BY[CI = (d[Blldt)l(d[Clldt) = k$kc Thus, Awill be partitioned between B and C such that the fraction of B is k ~ = V(1+ [CY[BI) fe = k ~ l ( +kc) and the fraction of C is fc = k d ( k ~+ k c ) = 141+ [BIr'ICI)
(4) At this juncture, one must be careful. Almost by inspection, or based on the result in art (1). most students will assume that the s l o ~ will e e a u h kn: But that is incorrect. --u because the stoichiornetry in part (a)no longer holds. Now [CI, = fc[Alo and [CI = fc([Alo- [A]).Thus, the term
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can be rewritten fc[Aloif~l[Alo- ([Alo - [A111 which reduces to [AlJAI. Therefore, the indicated plot will give the same result as part (21, a slope of kg +kc. ( 5 ) Since we have both the sum ( k +~kc) from parts (2) or (4), and the ratio from part (31, the individual values ofkc and kBare available by simply multiplying (kB+kc) by fc and fB, respectively.
Volume 70 Number 7 July 1993
549
