Model Lab Write-up
Introduction:
The purpose of this experiment was to determine the rate law for an iodine clock reaction. The iodine clock reaction possesses a two-step reaction mechanism where,
3I + S2O82- ® I3- + SO42-
I3- + S2O3 ® 3I- + S4O6
starch + I3- ® starch-I3- complex
The first step of this reaction is the rate-determining step. The I3- produced in the first reaction is an intermediate and is immediately used in the second step of the reaction. The thiosulfate ion in the second step of the reaction is treated as a limiting reagent. Once its concentration is depleted the I3- reacts with the starch to form a blue-black complex. It is at this point that the reaction is treated as having been concluded. Because the first step of the reaction mechanism is the rate determining step, the generic rate law for this reaction may be written as: R= k(I)m(S2O82-)n where m & n are the reaction orders and k is the rate proportionality constant.
This investigation utilized a standard experimental design to determine the effects of varying the concentrations of ammonium persulfate (NH4)2S2O8, and potassium iodide (KI) on the rate of the reaction. The concentrations of the iodide ions ranged from 0.1-0.5M in experiment 1. The concentrations of the persulfate ion similarly varied from 0.1-0.5M in experiment 2. The concentrations of the persulfate and the iodide ions were controlled in experiments 1 and 2, respectively. Because the sodium thiosulfate was the limiting reagent, the concentration of the thiosulfate ions was fixed at 0.005 M throughout the experiment. The time required for the color change to occur (as measured with a SensorNet photometric probe, 0-6000 lux, 1 reading/second) was determined from to the point where the lux vs.time plot became parallel to the x- axis
I (M) (a) / S2O8-2 (M) (b) / S2O3-2(M) (c) / time to color change (sec)a1, a1, a1 / b1,b1,b1 / c1,c1,c1
a2, a2, a2 / b1,b1,b1 / c1,c1,c1
. / . / .
.
a8, a8, a8 / b1,b1,b1 / c1,c1,c1
a1, a1, a1 / b2,b2,b2 / c1,c1,c1
.
.
. / .
.
. / .
.
.
a1, a1, a1 / b8,b8,b8 / c1,c1,c1
The times required to complete the reaction for each set of concentrations were measured and repeated three times. The mean and standard deviations for each of the measurements were determined for each of the measurements. A Q-test for removing outliers was conducted for each of the replicated sets where appropriate. Using the technique described by Brown and LeMay (1993), linear regressions of the natural log of concentration vs. time and the inverse concentration vs. time were used to determine the reaction orders for both the I- and the S2O3-2 ions. The instantaneous rates for each of the reactions were determined by determining the slopes of tangent lines drawn against each of the concentration vs. time points along the rate curve. The rate proportionality constant was calculated by comparing the changes observed in conentrations and rates.
Results:
The concentrations used in this experiment ranged from 0.1-0.3 M of I- and 0.1-0.4 M S2O8-2 under controlled conditions. Reaction times were measured by establishing when the lux curve because parallel to the x- axis during the course of each experimental run. The means and standard deviations were calculated for each of the concentration vs. time data sets.
Table 1: Concentration vs. Time Data for both the Persulfate and Iodide Ions
I (M) / S2O8-2 (M) / S2O3-2(M) / time to color change (sec) / Mean ( x ) time (sec) / S.D..1 / .1 / .005 / 30 25 28 / 27.7 / 2.5
.2 / .1 / .005 / 25 20 22 / 22.3 / 2.5
.3 / .1 / .005 / 18 16 17 / 17.0 / 1.0
.1 / .2 / .005 / 27 23 28 / 26.0 / 2.6
.1 / .3 / .005 / 18 15 13 / 15.3 / 2.5
.1 / .4 / .005 / 10 07 11 / 9.3 / 2.1
The above table shows a decrease in reaction times from 27.7 + 2.5 seconds to 17.0 + 1.0 seconds when the concentration of iodide ion was varied from 0.1 to 0.3 M and both the persulfate and thiosulfate ions were maintained at 0.1 and 0.005 M respectively. A change in S2O8-2 concentration of 0.1 – 0.4 M revealed a decrease in reaction times from 27.7 + 2.5 seconds to 9.3 + 2.1 seconds. Graphically, the first set of three concentration vs. time data sets presents as an exponential curve (r = 0.989) The second set of four data appears to be exponential as well (r = -.915)
Discussion:
In order to determine the rate law for this reaction, the reaction orders must first be established. This requires that the researchers conduct a first order and second order test on concentration vs. time data for both the I and the S2O82- experiments. First and second order tests were conducted taking advantage of the y = mx + b nature of the integrated rate laws for first and second order reactions. If the linear regression of time vs. ln[I-] is positive, then the reaction is 1st. If the linear regression of (time vs. 1/[I-] is positive, then the reaction is 2nd order. Comparing the correlation coefficients for the two regressions will establish whether the reactant is first or second order.
An examination of the time data when the iodide was treated as the experimental variable revealed that the first order test (L1 - L3: time vs. ln[I-]) produced a linear regression with a slope (a) of –0.103 (r=-.989). The second order test (L1 - L4: time vs. 1/[I-]) produced a linear regression with a slope (a) of 0.624 (r=0.962). These data suggest that the reaction is 1st order in the iodide (I-) ion.
In experiment 2, the concentrations of the I- and the S2O32- were controlled. The S2O82- was the experimental (independent) variable. A similar evaluation of the data produced in experiment 2 showed that the first order test (L1 - L3: time vs. ln[I-]) produced a linear regression with a slope (a) of –0.062 (r=-.915). The second order test (L1 - L4: time vs. 1/[I-]) produced a linear regression with a slope (a) of 0.031 (r=0.97). These data suggest that the reaction is 2nd order in the persulfate (S2O82-) ion.
The rate proportionality constant was found by finding the slope of the tangents (instantaneous rates) for each of the concentration vs. time data sets and comparing the change in rates to the change in concentrations.
Table 2: Mean, Standard Deviation and Reaction Rates (M/s)
I (M) / S2O8-2 (M) / S2O3-2(M) / Mean ( x )time (sec) / S.D. / Rates (M/s)
.1 / .1 / .005 / 27.7 / 2.5 / .010
.2 / .1 / .005 / 22.3 / 2.5 / .019
.3 / .1 / .005 / 17.0 / 1.0 / .031
.1 / .2 / .005 / 26.0 / 2.6 / .009
.1 / .3 / .005 / 15.3 / 2.5 / .019
.1 / .4 / .005 / 9.3 / 2.1 / .025
The 'k' values were then determined for each of the experiments based upon the assumption that the reaction is first order in the iodide ion and second order in the persulfate ion. The mean rate proportionality constant was determined to be 5.95 + 4.38 1/M2-s.
The purpose of this experiment was to determine the rate law for the iodine clock reaction. Based upon these results the rate law is:
R= k [I-][S2O82-]2 where k = 5.95 + 4.38 1/M2-s at 25 °C
However, it must be pointed out that the magnitude of the standard deviation suggests that one or the other or both reaction orders may not be correct.
An examination of the above table shows that while I- appears to be first order (e.g. R= 0.10 to 0.19 for 0.1 and 0.2 M respectively), a comparison between the change in concentrations of the persulfate ion and the reaction rates does not suggest a second order effect for that ion. Therefore while one may suggest that the final rate law may include a 1st order contribution from the iodide ion, it is less likely that the reaction is second order in the persulfate ion.
Additional data will have to be collected before this issue can be resolved.