J. N. Spencer Lebanon Valley College Annville, Pennsylvania 17003
Spectrophotometric Determination of an Equilibrium Constant
T h i s experiment h a s been a d a p t e d from t h e original work of Motoyama a n d Jarboe,' a n d is intended t o introduce t h e s t u d e n t to a spectral s t u d y of t h e hydrogen hond. T h e equilibrium constant for t h e formation of t h e hydrogen bonded methanol-ether complex i n carbon tetrachloride solvent is determined by application of Beer's law a n d through temperature studies of t h e equilibrium, t h e enthalpy a n d entropy changes accompanying t h e hydrogen hond formation are calculated.
Experimental Procedure. A series of dilute solutions of methanol in carbon tetrachloride in the range O.M)5-0.015 M are first prepared. Solutions more concentrated than about 0.015 M lead to self-association of the methanol. The methanal may be added volume-wise from micropipets and the density of methanol at the temperature of delivery used to calculate the concentration of methanol. The spectra of methanol in these solutions are recorded aver the range 2650-2850 mu, carbon tetrachloride serves as the reference. From Beer's law and the peak absorbance of each solution the molar absorptivity, e, of the hydroxyl stretch of methanol is calculated. Because the molar absorptivity of methanal in carbon tetrachloride solution decreases with increasing temperatureI2these spectra must be recorded as a function of temperature. A correction for the change in concentration with temperature should be made prior to calculating the molar absorptivities at different temperatures. Next, solutions of about 0.2 M diethyl ether and 0.005-0.015 M methanol in carbon tetrachloride are prepared and the spectra recorded over the spectral range 2650-2950 mp as a function of temperature. The solutions should be freshly made because of the evaporation of ether and methanol. Because ether absorbs in the spectral range of interest, it is necessary to use an ether-carbon tetrachloride mixture as the reference solution. The ether concentration in the reference solution should be the same as that in the sample solution. This situation is most easily realized by preparing a 0.2 M ether in carbon tetrachloride solution and dividing the solution, using part as the reference solution. To the other part of the solution, appropriate quantities of methanol are added. The volume of methanol added is sufficiently small so as not to significantly change the ether concentration. Corrections for the changes in concentration with temperature should be made. General. The temperature studies may be carried out by equilibration of the various solutions at the desired temperature for about 15 min in a water bath. The solutions should be kept tightly stoppered. The changes in concentration of the solutions with temperature may be taken into account by assuming in all cases that the density of the solution is the same as that of the solvent, carbon tetrachloride. Multiplication of the concentration of the species of interest by the ratio of the density of carbon tetrachloride at the temperature of the solution to the density of carbon tetrachloride at the temperature at which the solution was prepared gives the concentration corrected for temperature. Temperature studies should not exceed about 40°C due to the volatility of the ether. The preparation of solutions may be done on the
open laboratory bench without regard for the absorption of water vapor by the solution$. Minor precautions should be taken, however; to insure that the reaeents are reasonablv. drv . .orior to making the solutions. Baker grade anhydruus ether ma! he used uith. out funher purificatiun. The rnrhon trtrachloridc should he da. tilled. Dirtillatton of methanol ontu a drymg agent is suiticient tu prepare quite dry methanol. Spectra recorded in the presence of water added to solutions prepared from dry reagents showed that the added water produced no significant change in the peak absorbance. If water is present, two small absorption peaks at about 2670 and 2750 mu will readily be apparent.
Discussion I n t h e most elementary view, t h e formation of t h e hydrogen bond between methanol a n d ether m a y he viewed a s an electrostatic interaction between t h e relatively positive hydrogen . . of t h e methanol hydroxy . group - . a n d t h e relatively negative oxygen of t h e ether. ,C,H, (C,HJ,O = CH,-0-H--0, CHaOH C,H,
+
Formation of t h e hydrogen bond causes a lengthening of t h e 0-H hond distance of t h e methanol a n d a weakening of t h e 0-H bond. T h e weakened hond absorbs at a lower hydroxyl stretching frequency a n d t h e spectrum of a solution of methanol-ether in C C 4 shows two absorption h a n d s as seen in Figure 1. T h e shorter wavelength b a n d is d u e t o t h e "free" or monomeric methanol while t h e longer wavelength h a n d corresponds to.the absorption of t h e weakened 0-H hond i n t h e ether complex. T h u s a determination of t h e concentration of t h e "free" methanol may be m a d e b y application of Beer's law t o t h e absorbance of
2.7
'Matoyama, Izumi, and Jarboe, Charles H.. J. Phys Chem.. 71,2723(1967). 2Hoover. G. P., Robinson, E. A., McQuate, R. S., Sehreiber, H. D., and Spencer, J . N.. J. Phys C h e m . , 73,4027(1969). 3Motoyama. Izumi, and Jarboe, Charles H., J Phys. Chem.. 70,3226(1966). 298
/ Journal of Chemical Education
2.8
2.9
WAVELENGTH ( p ) Figure 1 . Spectra of 0.0100 M methanol-0.200 M ether in carbon tetrachloride solution as a function of temperature. The "free" peak absorbance decreases with temperature due to the temperature dependence of the molar absorptivity. Spectra recorded on the Beckmann DK-2A spectrophotometer.
the shorter wavelength peak. Subtraction of the equilihrium methanol concentration from the initial methanol concentration gives directly the complex concentration and hence all necessary information for the calculation of the equilihrium constant. Consider for example the calculation of the equilibrium constant a t 20°C for a solution originally 0.206 M in ether and 0.0119 M in methanol. The absorbance of the "free" methanol peak at 2745 mfi was found to be 0.627. From Beer's law and the molar absorptivity previously found a t 20°C and listed in the table, the equilibrium concentration of methanol is found for a I-cm path length to he A = tlc
By assuming that the complex is one to one and subtracting the equilibrium methanol concentration from 0.0119 the equilibrium complex concentration is found to be 0.0025 M. The equilihrium constant a t 25°C is then 4 3.1
3.2
3.3
3.4
3.5
3.6
+x103
Similarly K may be found a t other temperatures for which data are available. Standard plots of log K versus 1/T may then he used to find AH" and from
Figure 2. Plot of log K versus 1I T for the data given in the table.
Representative Student Data for the Methanol-Ether Complex
T, "C
AS" may he found. Typical student results are given in the table and Figure 2.
K c (lem-'mole-') AH" (keal mole-') AS" Ical deerlmole-')
10 1.7 71.7 -3.0 -9.6
20 1.4 67.0
30 1.2 62.7
40 1.0 58.7
Volume 50, Number 4, April 1973
/
299
