J. A. YOUNG Wilker-Borre, Pennrylvonio
chemical queries
J. G. MALlK 'Son Dieoo 5tote Colleoe
. . . especially
for
introductory chemistry teachers
Queslion
The statement is often made that the rate of a reaction approximately doubles for n ten degree temperature rise. However, there seem i o be exceptions to this rule. When is it valid? Answer
by J . E. House, Jr., Department of Chemistry, Illinois State University, Normal, Illinois
It is true, for example, that many decomposition reactions proceed slowly a t one temperature; but when the temperature is increased only a few degrees, some decompcsition reactions proceed very rapidly, perhaps explosively. Also, many enzyme-catalyzed biochemical reactions actually become slower with an increase in temperature, due to deactivation of the enzyme, a protcin material. These systems do not follow the Arrhenius equat,ion and we shall not consider them. But let's consider the many systems that do follow the Arrhenius equation; these are more consonant with the question asked. The Arrhenius equation may be written,
similarly fork, and T,. I t is seen that E, the activation energy, is a linear function of in(l;z/kl) for given values of TI and T2. Thus if the activation energy is very small, approaching zero, In(k,/lcl) approaches zero and kz approaches lc,. For given valoes of TI and TI, the rate is affected to a smaller extent the smaller the activation energy. This result is shown graphically in Figure 1 for TI = 300°K and Tz = 310°R. The 10" rise results in a doubling of the rate only i f E = 12.8 keal/mole and the initial temperature is 300°1i. From Figure 1, the relation between E and the ratio of the rate constants at two temperatures can be estimated for the 10" rise from 300' to 310°K (or for other intervals if a similar graph is constructed). To complete our discussion, it will help to examine eqn. (1) in a rearranged form.
For any fixed value of E we select, and for any values of T, and Tz we choose (subject to the condition imposed by the question, that the difference between TI and Tz is 10") the terms on each side of the eouation are constant. For example
where k1 is the rate constant a t temperature TI; and
'b/ MI Figure 1.
The relationship between the activation energy, E, and the relative rote, kzlkr, for an increment of 10' between 300' and 310DK.
674 / lournol of Chemical Education
Figure 2. The relationship between ks/h and the averoge temperotura of o 10- interval, i, for constant values of the octivdion energy. Tho activation energies ore (1 1, 10; 121, 15; and (31. 20 kcd/mole.
So, if we plot T,T, versus ln(lse/kJ we will obtain a hyperbola. For different fixed values of E, we would. obtain different hyperbolas; in such a set of hyperbolas, one would be nested inside another, and those two inside another, and so on. However, the point we are after in this discussion is easier to see if we use k2/kl instead of the natural logarithm of this ratio, and if we use the square root (approximately) of the product T2T1. Figure 2 shows a set of three "warped" hyperbolas, obtained for three different values of E, when we plot I~p/k~ versus T , the average temperature of the 10' interval. This figure is particularly revealing. It shows that the ratio k,/ks is equal to 2 a t markedly different temperatures for different values of the activation energy. It also shows that a t a given temperature, for example 270°K, a reaction with an activation energy of 10 kcal/mole will have its rate doubled by a 10' increase in temperature (from 265°K to 275'K) while one with an activation energy of 20 kcal/mole would have its rate increased fourfold. Even this difference is a function of temperature, as can be seen in Figure 2; the curves are much closer to each other as T increases. At temperatures near 500°1i, and higher, an increase of 10" affects the rates of all reactions in an almost identical manner; all the rates increase by a factor slightly less than 2, when the temperature is raised from T - 5' to T 5". Thus, whether or not the rate of a reaction is doubled by an increase of 10' depends upon the activation energy of the reaction and upon the range of temperature where the 10" interval falls.
+
Question
The colors of transition metal complexes are ascribed to the absorption of photons of visible light which have certain energies, while the remainder, unabsorbed, generate a color sensation when thw strike the eve. But.. how can a hoto on be absorbed bv an hIOm if there arc 1111 nearby, sliphtlg bi~lter,cn,pt~.energy level+ to which art rlectrm ran be prornlwd when x phoron is ulwrbcd'! Fur exmqrlc, concider n il%pl (\m~pIexwith x d l rorrtigurntim; how can photons be absorbed (and color generated) by d-d transitions since the&, and dzn-Y=orbitals are used in bonding and are filled with paired electrons from the ligands?
Answer
The question alludes to the valence bond theory description of complex ions. Consider the complex ion, Cr(H20)6a+; i t is a d2sp3 octahedral complex according to this theory. One writes the electronic configuration of the central ion and from this predicts the presence of three unpaired electrons in three of the five 3d orbitals; thus ~ r + "is2
2s' 2pB35' 3P6 3d3 4s' 4p0, etc,
The remaining two 3d, the 4s, and the three 4p orbitals are considered to be used for the ligand attachments for six electron pairs, one from each ligand. Note that the next highest unfilled orbital is a 4d orbital; electron transitions to this orbital are inconsistent with the
absorption of visible light. (The energy difference between a 3d and a 4d orbital is large; 3d to 4d transitions correspond to absorption of photons in the ultra-violet region of the spectrum.) This picture may be refined by using crystal field concepts and recognizing that the 3d orbitals are not degenerate (of equal energy or in the same energy state) in this case. They are degenerate in the simple metal ion or in a field of spherical symmetry; but in an octahedral field, as in the Cr(H20)63+complex, the d,. and the d,.-,> orbitals on the axis find their electron clouds pointing directly a t the ligand electron clouds and therefore are electrostatically repulsed to a greater extent than the d,,, d,, and d,, orbitals. Thus the degeneracy among all five 3d orbitals is not retained. The energy separation is represented by A and has a definite value for a particular complex.
d,.
d,,.,z
f f 1->
; c
w
4, d,, Simple Metal Ion
4,
Octahedral Field
Now, electronic transitions from the lower three to the higher two are possible and consistent with the absorption of visible light. However, we have not yet answered the question fully; we have considered only the expected bond configuration of the central ion. After the respective electron cloud distributions of this ion in appropriate energy levels have been defined, the ligands do not just attach with no further consequences. That is, we have not yet recognized what occurs when the ligands attach, particularly in relation to the alteration in energy of the orbitals of both the central ion and of the ligands. To see this, we shall use the molecular orbital approach. The electrons of the central ion and of the ligaud molecules are both considered in this complete description. What then is the MO picture for Cr(H20),3+? First, the orbitals of chromium up to and including the 3p"Ar) level and those in each water molecule except the one pair involved in bonding are omitted, since they are not involved in the bonding picture. This leaves five (34, one (4s), and three (4p) orbitals for the Cr3+ ion and six orbitals, one each, from the six water molecules. These fifteen molecular orbitals must be accounted for in the complex ion environment. Study of the references cited below will provide more detailed insight about the determination of the proper MO energy distributions. For our purposes here we shall simply state that three of the five 3d orbitals of Cr3+ each with one electron in it, are of the non-bonding variety. (Recall, these three electrons are the electrons which undergo the d-d transitions, and "account" for the color.) The hybrid is d2sp3,thus six orbitals are bonding for the ligands. Therefore, six antihonding orbitals (higher energy level) must exist and this, happily, happens to account for all fifteen of the orbitals. (Six for ligand bonding, six antibonding, and three (half-filled) non-bonding). A description with an approximate energy scale is shown in the figure. The less energetic, more stable, Volume 46, Number 10, October 1969
/ 675
bonding molecular orbitals contain the six pairs of ligand electrons. Three unpaired electrons residue in the non-bonding d level, and above this are the higher
This question refen to Chem Study Experiment No. 25 which is su electrolysis experiment. The first electrolytic cell consists of copper electrodes in a solution of copper sulfrtte. According to the directions, 50 ml of cone. H.SO,is added to each liter of CuSO, solution. It is also stated that if the solution is to be reused the next year, 15 ml of 6 M H2S04should be added before use. Why is the acid necessary and why:is additional acid added to asolution if it is reused a. year later?
Answer
by Dr. J . A. Campbell, Harvey M u d d College, Claremont, California energy, less favorable, anti-bonding, orbitals. The A sign represents the same energy difference as shown in the previous diagram and accounts for the d-d transitions which result in photon absorption by, and color of, the complex. The energy needed for such transitions corresponds to the energy of the photons of visible light which are absorbed. The 110 diagram completes the picture for us; it has some relation to the valence bond concept which did not account for color. Note that two of the pairs of electrons are present in the bonding orbitals of d,. and d,.-,. symmetry (the higher two of the six bonding levels of the complex ion). This leaves the antibonding set empty; so d-d transitions can take place between the half filled d,,, d,,, and d , non-bonding orbitals and the empty, antibonding, d,,, dz2-,. orbitals (the lowest two of those six). For a more complete answer, other factors would be considered. We have not indicated that the three electrons jn the non-bonding orbitals interact with one another. When this interaction is included, the detailed calculations show that those three non-bonding orbitals are not quite degenerate; their relative energies differ somewhat, one from the other. The same is true for the two lowest anti-bonding orbitals. So, photons of slightly different energies could he absorbed; as is true, factually. Our simpler explanation predicts that only photons of a single energy would be absorbed. The simpler explanation and the more sophisticated details both predict that the energy difference, A, is small and consistent with the energies of photons in the visible portion of the spectrum. References
COMPANION, A. L., "Chemical Bondinp," . McGraw-Hill Book Company, 1964, Chapter 6. GRAY,H. B.. AND HAIGHT. G . P.. "Basic Prineide~of Chemis. try;" W. A. Benjamin, I&., 19&, Chapten l2and 16. L. E., J. CHEM.EDUC.,37,498 (1960). SUTPON, LIEHE,A. D., J. CHEM. EDUC.,39,135 (1962). EDUC.,41, 2 (1964). GRAY,H. B., J. CHEM.
676 / Journal o f Chemical Education
The desired crll reuction is the frnn;fer of coppw from thc anode to rhc rnthodr. TIE Ilolf-equations ,Ire anode cathode
Cu(c)
-+
Cu'+(aq)
Cua+(aq)
2e-
+ 2e-
+ Cu(c)
An acid solution is used to minimize hydrolysis of CuZ+ to CuOH+ and CU(OH)~(C). Cus+(aq)
+ HzO(1)
+
+ CuOHYaq) H+(aq); HIO(L)+ Cu(0H)dc) CuOH+(aq)
+
+ Ht(rtq)
The formation of Cu(OH),(c) would effectively stop cell operation by coating the electrodes as well as preventing the transfer of Cu2+through solution. At low current densities and in well-stirred solutions the transfer of copper takes place at low voltage with minimum side reactions. However, a t larger current densities and in the absence of stirring, copper ion is depleted in the vicinity of the cathode. When the depletion makes the copper ion concentration low enough, the electrolysis begins. This uses up H+ and requires the replacement of acid each year. One might note on p. 447 of the "Chem Study Teacher's Guide" that 0.63 * 0.02 g of copper dissolves a t the anode while 0.60 + 0.02 g of copper precipitates at the cathode. These numbers, of course, agree with one another within experimental uncertainty but they may also indicate hydrogen formation a t the cathode. Many student results show an even wider discrepancy. With adjustable power supplies, it is easy to increase the voltage and observe copious amounts of gas evolution, but i t is difficult for beginning students to controllably reduce the voltage, still have a good rate of copper deposition, and be certain there is no hydrogen gas evolution. On the "average," the added 15 ml of 6 M HSOd approximates the expected loss of hydrogen ion through the undesired, but nevertheless likely to occur, electrolysis.
