NOTES
118
theory which can, however, only be solved by successive approximations. Welsh4 uses Lippincott and Schroeder's expression though with a different parameter. Due to the incertitude of the experimental results it is difficult to favor one curve over the other. The curve calculated according t o equation 3 has, however, the following advantages. (1) It fits the results without using any free parameter obtained from hydrogen bond data. ( 2 ) It is based on a simple mathematical expression. (3) It is a smooth curve and does not show the discontinuity of Lippincott's and of Welsh's curves a t LO-H = '/zLo. -0. Conversely the good fit of the curve with the experimental results shows that the inverse cube law (1) holds also for the 0-H and H. .O bonds. The above treatment can, of course, be extended to other straight hydrogen bonds. For the C-H. .O system, for instance E +E"
kW k = LC-Ea + ( L C . . O - LC-E)*
(4)
where E and k are given above, and the energy of the C-H bond E" = 3 kcal./mole2 and according t o b" = 128.2 A.Skcal./mole. Unfortunately there are no data t o check expression (4) with experiment.
Vol. 62
tion solution a time r before the regular reaction mixture is initiated, one has the equation for this solution Lt+r
- m~[A]o=
BYDAVID M. GRANTAND RANDALL E. HAMIM Department of Chemiatry, University of Utah, Salt Lake City, Utah Received J u l g 23, 1967
The specific conductivity a t time t of a solution in which the reaction A -+ B is occurring is given by the equation Lt = LA
+ LB = m ~ [ A l tf m ~ [ B ] t
(1)
where Lt is the specific conductance at time t, LA and LB are the specific conductance of the individual species A and B, mA and mB are the molar conductances of A and B each divided by 1,000, and [A], and [Bit are the molar concentrations at time t. If the rate law for this change is d[A]/dt = -klA], use of the conservation of mass expression, [Bit = [AI0 - [AIt, yields an equation which expresses the dependence of L on t Lt
- rn~[A]o= [AID(
m ~ mB)e-kr
(2)
Thus, a plot of the natpral logarithm of the quantity on the left side of the equation versus time will give a straight line with a slope of - k . This method requires a knowledge of the quantities [AIoand mB. I n a modification of the method suggested by Guggenheiml, King2 showed that first-order rate constants may be obtained directly on the spectrophotometer. In a similar manner a conductometric modification, of the above method yields first-order rate constants without a knowledge of either [Ala or mB. By starting an equivalent reacE. A. Guggenheim, Phil. Mag.. 171 8, 538 (1926). (2) E. L. King, J . Am. Chem. Soo., 74, 563 (1952). (1)
"?Zg)e-k(t+T)
(3)
Lt - Lt+r = [A]o(m~- m ~ ) ( 1 e+")e+' (4) A plot of logarithm (Lt - LL+,)vs. t will now yield a straight line of slope -k . The circuit proposed as a means of obtaining the quantity (Lt - Lt+.) directly is a conductance bridge which has been altered by placing a potentiometer, Rg, between the ratio arms Rs and R4, with the variable point on the potentiometer connected t o the detector. For the purpose of the following discussion Rgohms of Rsplus Ra is the left ratio arm and Rsohms of R8 plus Rq is the right ratio arm. The other two arms of the bridge are two conductance cells of identical construction, having cell constants of n1 and n2 for the left and right cells, respectively. By means of a three position single throw switch, a variable resistance, R7,is in position t o be connected to shunt either cell 1 or cell 2, or be left unconnected. As an initial step the earlier-mixed solution is introduced into both cells 1 and 2 making it possible to write
L1
CONDUCTOMETRIC DETERMINATIONS O F THE RATE CONSTANT O F FIRSTORDER REACTIONS
[A]o(m~-
Subtracting equation 3 from equation 2, equation 4 is obtained
= Lz = Lt+.
(5)
from which follows n1 ( 1 / R A = nz (1/Rz)
(6)
where Li,l/Ri, and ni are the specific conductance, actual conductance, and cell constant, respectively, for the ith cell. With the switch in position SO that R7 is not in the circuit, the bridge is balanced with the variable resistance Rg. The circuit has now been adjusted t o compensate for any differences between the two cell constants, and R8 is then left unchanged as long as the other circuit components are not altered. The equation for circuit balance is
+ R's)/(Re+ R4) = Ri/R2 which upon combining with equation 6 yields (R5 + &)/(Re + R I ) = ndna (Rs
(7) (8)
Equation 8 is now valid even though different solutions are placed in cells I and 2. Cell 1 is then emptied and filled with the second reaction mixture started r seconds after the solution used to sthndardize the bridge. As LI and Lz will no longer be equal, R7 must be introduced into one of the lower branches of the bridge depending upon the relative values of mA and mB. If mB is greater than mA then the specific conductance of the first reaction mixture would be greater than that of the second requiring that R7 be placed across cell 1. This is necessary to compensate for the proportionately higher resistance noted for cell 1 as compared t o cell 2. For mA greater than mB, the case where the specific conductance of the solution decreases as A goes to B, R7is placed in parallel with cell 2. For the argument which follows, the latter case is assumed t o be valid for the postulated reaction. One can now write the following expression as the condition for a balanced bridge where R, is in parallel with cell 2
5
NOTES
Jan., 1958
+
+
+
RI(1/R2 1/&) = (Rs %)/(Re Rd = n h z (9) By rearranging and making the substitutions, Lt = L - nl/R1and L ~ += , L~ = n2/R2,equation 10 is obtained Lt - Lt+, = nz/RT for mA > mB (lo) Had it been assumed that ?%B is greater than ?%A with the above derivation carried through in the same manner, equation 11would have resulted
119
same differences observed when comparing the spectrum of the red Potassium (Or sodium) salt of phenolphthalein with the spectrum of white phenolphthalein.s Specifically, several samples of the red material each showed a decrease in the relative intensity of the 1740 cm.-l band which in phenolphthalein is due t o the lactone structure3
Lt - Li+7 = -nl/R7 for mB > mA If either equation 10 or 11 is now equation 4 the following is obtained 1/R,= e-kt [ [A]o(m~- mB)(1 - e - k r ) / n z } for mA > mB
-
(12)
and 1/Rr = e+$( [ A ] o ( ~ B - V Z A )( ~e - k r ) / n l } for mB
0
> mA (13)
Thus, by plotting the natural logarithm of 1/R, vs. t for a reaction treated in this manner a straight line with a Of - k is Obtained. Data obtained in this manner, exhibiting the success of the method, are now being prepared for publication. This work was assisted by a research grant (REHI and a predoctoral fellowshiP (DMG) received from the National Science Foundation.
WHITE
Fig. 1.-Proposed
RED
reaction responsible for color change.
and which is absent in the potassium (or sodium) salt The red material produced by &ear did not sho&, however, infrared bands at 1572 cm,-l and a t 1154 cm.-l where the red salt of phenolphthalein shows infrared bands which do not appear in white phenolphthalein. 3 Examination of the visible spectrum of the sheared material, again using the potassium bromide pellet technique, showed no well-defined absorption maxima. The pellet examined contained a sample loading of 400 y-cm.-2 and PLASTIC DEFORMATION OF showed an optical density of 0.3 at 553 mp, the PHENOLPHTHALEIN AT 50,000 wave length of the absorption maximum reported ATMOSPHERES for the red form of phenolphthalein in a solution of pH 10LL4 Based upon the extinction coefficient of BY H. A. LARSENAND H. G. DRICKAMER Talalay, et ~ l . only , ~ about 4 y-cm.-2 of red phenolDepartment of Chemzstry a d Chemical Engineerang, Unzuerszty of phthalein would be required t o give an optical denIllznoaa, Urbana, Illznoas sity of 0.3 a t this wave length. No direct chemical Recezved August 19,1967 studies were attempted as the red material prowhite phenolphthalein has been found to duced by shear at high pressure became colorless turn red when plastically deformed in shear at pres- upon dissolving in ethanol methanol and sures from 20,000 to 50,000 atm. The experimental Evidently the color ,,hanke persists in the technique was the same as that reported in detail state only. in an earlier communication.2 I n essence the high lntermolecular hydrogen bonding must Play an pressure experiment involves first the compression of a thin layer of powder between flat pistons. The important Part in the crystalline structure of phesample is then deformed plastically in nolphthalein as shown by the broadness of the infrashear by forcing the pistons to rotate with respect red absorption band at 3430 cm.-l which is due to the oxygen-hydrogen vibration. It seems reasont o one another about the common axis. Based upon evidence cited below it is postulated able to suppose that the severe plastic deformation that a small percentage of white, crystalline phenol- of high Pressure shear has a strong effectupon these phthalein when disordered by plastic deformation a t hydrogen bonds as the relative orientation of the high pressure undergoes the chemical change shown molecules is changed. Once the crystal is disin Fig. 1 and that this change is responsible for the ordered by high pressure shear restoration of order red coloration observed. It will be noted that this will be Slow due to the restricted nature Of mOleCUchange is analogous to the change induced by the h' motion in the solid State. Solutions obtained reaction of sodium hydroxide with phenolphthalein; from the ordered white material and from the dishere, however, protons take the place of the sodium ordered red material should be the same, however, as they appear t o be. ions. The yellowish color of vitreous phenolphthalein The infrared spectrum of the material produced by one minute of shear at 50,000 atm. was com- which has been prepared by rapid cooling from a pared with the spectrum of the original white phe- melt has been ascribed to a slight decomposition.6 nolphthalein. This examination, which was made It may be that this color is also due t o solid state using potassium bromide pellets of the solid Sam- disorder induced by the quenching. ples, showed inconclusive evidence for some of the (1) This work was aupported in part by the A.E.C. (2) H. A. Larsen and H. G. Drickamer, THIEJOURNAL, 61, 1249 (1957).
(3) M. Daviea and R. L. Jones, J . Cfiena.Soo., 120 (1954). (4) P. Talalay, W. H. Fishman and C. Huggins, J . Biol. Chsm., 166,
757 (1946). (5) E. Rencker, Compt. rend., 208, 179 (1939).
