edited by ROBERT REEVES Marlborough School 250 S. Rossmore Avenue LOS Angeles. CA 90004
Polarized Light and Rates of Chemical Reactions John J. Weir Millburn Senior High School, Millburn, NJ 07041 Advanced placement chemistry teachers recognize the fact that maintaining a rigid schedule for lectures and lahoratory experiments-is vjtal for student success in their courses. Any presentation that can unify concepts and combine teachine strateeies would he a welcome addition to their curricula. One such lahorntory experiment inv~~lves chanees of rotation of the olane of polarized light in a study of t h i rate of a chemical reaction ikvolving o&ically active molecules. This lahoratory experiment could also he performed by some honors and biochemistry classes. Since many high school laboratories may not have a polarimeter for measuring the angle of rotation of the polarized light, i t is suggested that an inexpensive polarimeter could be constructed by following the published directions (1). This experiment provides the opportunity to introduce the nrincinles of reaction kinetics (2).nolarized lieht (3). . . . and the 'chemi$try of optically active cbmpounds (4). The rate of a chemical reaction can be studied in this lahoratory experiment by measuring the rate of hydrolysis of sucrose to glucose and fructose and catalvzed bv hydrochlo-
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The concentration of an aqueous sucrose solution can be determined bv measuring the amount of rotation of the plane of polarizedlight. his rotation varies with time as the reaction proceeds. Sucrose is dextrotatorv (rotates the polarized light to the right or clockwise), while an equimol&ular mixture of glucose and fructose is levorotatory (rotates the polarized light to the left or counterclockwise). The experiment is commonly referred toas the inversionof sucrose. Polarhetry For some reactions the concentrations may he followed by use of a polarimeter, which measures the rotation of plane polarized light. Ordinary white light consists of waves vibrating in all planes perpendicular to the direction in which the wave travels (7). Certain materials, such as a polaroid sheet selectively transmits light waves vibrating in one specific plane. This light that is transmitted is said to be planepolarized. If another polarizing material is put in the path of the plane-polarized light so that its polarizing axis is parallel to the axis of the plane nolarized lieht. then a maximum intensity of light will pass through. ~ o i e v e rif, the axis of the second nolarizine material is ~ e r ~ e n d i c u lto a rthe axis of light &en a minim;m bf polarized light will he the allowed to pass through. The pol&imeter consists of a light source, two polarizing filters, and a cell that contains a solution of an optically
active compound. The filter that is closest to the light source is referred to as the polarizer, while the other filter is called the analvzer. When the axis of the ~olarizerand the analvzer are at right angles toeach other, nb light passes throughand thissituation is knownas theendnoint or null noint. When a solution of an optically active compound is placed in the cell between the filters, the plane of polarized light is rotatedand acertain amount of light can now pass through the analyzing filter. T o compensate for the rotation by the sample the analyzing filter must he rotated, either clockwise or counterclockwise, to produce again minimum transmittance of the light, so that the field of view is dark. Compounds that affect polarized light in this manner are 'said to he optically active and most frequently have one or more chiral carbon atoms. These atoms have four different groups attached to them and are referred to as being asymmetric carbons. The attachments to these chiral carbon atoms interact with the electric field of the light that passes through them and causes the rotation of the light. Solutions made up of these optically active substances produce a rotation proportional to the amount of the active suhstance present. The specific rotation is defined as the rotation caused by the compound a t a given concentration in a sample tube 1dm long. This may he written as an equation, [.I; = wc for any wavelength A, or
[.IDT
= 011~
where [or] is the specific rotation, 0 = measured rotation in angular degrees, 1 = the length of the light path in decirneters, c = concentration in grams per millimeter of solution, D = wavelength of light, usually 589 nm, and T = temperature, usually 25 "C. Specific rotation depends on the temperature and the wavelength of the light source. The most common light source is a sodium vapor lamp, which supplies the characteristic D line, which has a wavelength of 589 nm. Since some teachers mav not have a sodium vapor lamp in their laboratory, i t is suggested that a cell containing 10%solution of potassium dichromate he placed in the beam of white light. This solution transmits a narrow range of wavelengths that are close to the yellow line of sodium. The instructions for the suggested lahoratory experiment for the acid hydrolysis of sucrose are given below. Some adjustments may he necessary in terms of time to complete the experiment in a double lahoratory period.
a
Procedure One hundred milliliters of a 4.0 M solution of HCI ia added to a sucrose solution, which is prepared.by dissolving 20 g of the sucrose Volume 66 Number I2 December 1989
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in 100 mL of a water solution, using a volumetric flask.After thorough miring, the solution is allowed to reach temperature equilibrium and is stored in a 250-mL glass-stoppered bottle. Rinse the polarimeter tube with small amounts of the reaction mixture, and then fill it completely. Turn the analyzing filter of the polarimeter either clockwise or counterclockwise until darkness is restored to the field of view. Place the solution in the polarimeter and measure the number of degrees the analyzing filter must he turned again to restore darkness to the field of view. This angle is called the ohserved rotation. Record the time when the first reading is taken. This readine" will be used as the initial value in determininethe rate. -~~~~ Readings ~houldbe rnken every 10 min during the first'hour and then every 20 min durmg the next allowable rime period Record t h ~ time of the final reading, a.. ~~~~~~~
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Calculatlons The order of the reaction can he determined from which graph gives a linear plot (8).If a reaction is zero order, a plot of concentration versus time is linear. If a reaction is first order, a plot of the log of the concentration versus time is linear. For a second-order reaction, a plot of llconc. versus time is a straieht line. The order l f the reaction should be determined by plotting the following graphs. A plot should he made with time in minutes on the abscissa and the angle of rotation on the ordinate. usine t = 0 as the time of the first readinrr. A second Got should have the log of ( a - a,) as the ordinate and t (min) on the abscissa. Draw the best straight line through the points. Determine the slope of the line. When the slope is multiplied by 2.303, the constant h is obtained. A comparison should he made between the value of k determined eraohicallv and the calculated value. Since the concentration of the sucrose, C, a t time t is proportional to the difference between the anele of rotation a a t time t and a, a t time equal t o m , the co&entration-time relationship can be written: ~~~
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and
Substituteat least five different values into this equation, and calculate the values of k and their averape. Compare the result obtained from this equation and thatbf the graphical method. The experiment was performed, and the data are presented in the table. Calculatlons The numerical value for the slooe of the line for the m a ~ h of log ( a - a,) versus time was fo&d to be -0.0124. ~o"th;ee sienificant fieures the numerical value for h was determined to-he -0.0286. This number was identical with the calculat-
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Journal of Chemical Education
Data Table for the Rotation ot Polarized Llght Time (mi") 0 10 20 30 40 50 60 70 90 110 130 150
01
+5.01 t3.37 t1.96 t0.92 +0.15 -0.44 -0.93 -1.25 -1.73 -2.01 -2.15 -2.23
- a,
log (a- a,)
k(ca1c.)
+7.24 +5.60 t4.19 t3.15 t2.38 +1.79 +1.30 +0.98 +0.50 t0.22 +0.08 0
0.86 0.75 0.62 0.50 0.38 0.25 0.11 -0.01 -0.30 -0.66 -1.09
0 0.013 0.023 0.028 0.028 0.028 0.029 0.029 0.030 0.032 0.034
a
ed slope for 60 and 70 s. The average of the calculated values fork was found to he 0.0274, which was a 4.2% error from the graphical value of k.
Conclusions Since the graphs of concentration versus time and the reciprocal of concentration versus time were not straight lines, the reaction for the acid hydrolysis of sucrose was neither zero or second order. The reaction obtained from the graph of log ( a - a,) vs. time appears to he first order. With increasing time the line on the maoh dimesses from linearitv. Unon deletine the last several experimental points, a good match was obtained resultine in a straieht line. The anale of rotation is affected by temperature chkges, which wokd change the density of the sample. Other changes that might affect the sample could be solvation and molecular attractions and interactions. There was good agreement between the calculated and graphical values of the constant k. The rotation of the plane of polarized light appears to he an effective way to measure the rate of the hydrolysis of the sucrose.
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Acknowledgment Sincere appreciation is extended to James E. Kuder of Hoechst Celanese Cor~orationfor his valuable suaaestions -and guidance in the preparation of this paper.
Literature Clted 1. Walker, J.Sci.Am. 1986,120. 2. T0on.E. R.;Ellis.G.E.Foundotionsa/Ch~miatrr:Holt.RinehartandWinston: 1 9 7 3 ; ~ ""a ,,,*.
3. Heeht, E. Optiea. 2nd ad.; Addison-Wesley: 1987. 4. Barrett,G. C.Applic.fionsofOplieolRolnfian and circv1or Dichrolsm;Teehniq"es of Chemistry: 1972: p 616. 5 , Steinhach,~.F.;Kinp,C.V.E~parim~nUinPhysi~a1Chhhiiff~;AmeriiiBwk:19M, p217 6. Bolkau, R. S.;Edelson, E. Chemical Principles; H w e r and Row: 1985: ~ 6 8 8 . 7. Brown, W . H. lnfmduelion La O r p n i e and Rinrh~mlalry;BrwLsICole: 1987:p 275. 8. Masterton, W. L. Chemicol Pn'ncipl~s;Saunders: 1985;p 491.
