Rate of Isomerism of [Co(en)2Cl2]

In the course of this experiment the rate of isomerism for the coordination complex cis[Co(en)2Cl2]Cl was determined using UV/Vis spectrometry. Using a range of wavelengths the optimum spectrometer setting for analysis was identified. The corresponding maximum and minimum absorbance of the cis and trans isomers respectively at 540 nm meant that it was selected as the wavelength to determine the rate of conversion between the isomers. The first order rate constant was calculated to be 0.0092 m-1 which is somewhat similar to the literature value of 0.00845 m-1 (Brasted and Hiriyama 1958). The half-life (t 1/2) was found to be 75.34 minutes.

Introduction:

The compound [Co(en)2Cl2]+ is known as a coordination complex, that is, it consists of a Cobalt atom surrounded by an array of molecules to which it is bound, called ligands (Brown 2010). In this case the ligands are Ethylenediamine which are ‘bidentate’, meaning bound in two locations. These ligands are bonded between the two Nitrogen atoms as seen in figure 1 below. This complex occurs in two geometric isomers, cis-[Co(en)2Cl2] + and trans-[Co(en)2Cl2] +. In this experiment the Chloride salt form of the complexes were used i.e. cis-[Co(en)2Cl2]Cl. Figure 1:

The Trans and Cis isomers of [Co(en)2Cl2]+
Source: Shapter ,J. 2014 Experiment 1: Rate of Isomerism cis[Co(en)2Cl2]Cl, Flinders University, Australia The Cis- isomer form of the complex which is purple in solution reacts to form the Trans- isomer which is green in solution. This experiment uses spectroscopy to quantify the conversion of the Cis into the Trans isomer due to the fact that the concentration of the Cis isomer is proportional to the difference in absorbance of the two complexes in solution. This isomerism of the Cis-form is a first order reaction and its rate is expressed in equation 1 below. Equation 1:

By measuring the optical densities at time 0, t and infinity the rate constant k can be determined with equation 2, a rearranged and substituted form of the formula used above. Equation 2:
a)

Which rearranges to give:
b)

Experimental:
Solutions of 2 × 10-3 M Cis- and Trans-[Co(en)2Cl2]Cl were prepared and placed in volumetric flasks of 100 ml and 10ml volumes respectively. Samples of these solutions were placed in cuvettes and measured in a spectrometer over the range of wavelengths between 350 and 700 nm. The Varian Car 50 UV-Vis spectrometer recorded the absorbance of the two isomers and produced a print out which was used to identify the correct wavelength for further spectroscopy (see Appendix 1). Using the SP – 880 Metertech spectrometer, the absorbance was measured and recorded as seen in Table 1. Next the Cis isomer solution was warmed in a water bath at 40 degrees Celsius and a sample was taken and cooled in an ice bath. The absorbance of the sample was then measured using the wavelength previously selected. This was repeated at ten minute intervals for an hour. Finally a last sample of the cis[Co(en)2Cl2]Cl was analysed with the spectrometer 24 hours after to determine the value.

Results:
Table 1: Absorption of the Two Isomers at Various Wavelengths Wavelength (nm)
Cis
Trans
350
0.468
0.144
360
0.289
0.090
370
0.207
0.087
380
0.180
0.091
390
0.170
0.091
400
0.466
0.397
410
0.123
0.070
420
0.092
0.057
430
0.066
0.049
440
0.049
0.047
450
0.041
0.048
460
0.043
0.048
470
0.049
0.045
480
0.061
0.039
490
0.076
0.031
Wavelength (nm)
Cis
Trans
500
0.093
0.025
510
0.110
0.020
520
0.124
0.017
530
0.134
0.017
540
0.137
0.020
550
0.134
0.025
560
0.129
0.034
570
0.122
0.044
580
0.116
0.055
590
0.065
0.109
600
0.102
0.071
610
0.095
0.075
620
0.085
0.074
630
0.073
0.067
640
0.060
0.055
650
0.049
0.049
660
0.035
0.038
670
0.026
0.028
680
0.018
0.020
690
0.013
0.013
700
0.009
0.008

Figure 1: Absorbance against Wavelength of Cis and Trans Isomers

Table 2: Absorbance of Cis Isomer at 540 nm
Time (min)
Cis Abs
ln[Dt-D∞]
y = -0.01104 X – 2.40936
10
0.117
-2.51331
-2.519758607

20
0.108
-2.63109
-2.630158414

30
0.100
-2.74887
-2.74055822

40
0.093
-2.8647
-2.850958026

50
0.089
-2.93746
-2.961357833

60
0.082
-3.07911
-3.071757639

t ∞
0.036

Figure 2: Natural Logarithm of the Cis Isomer Absorbance against Time

Table 3: Slope, Y intercept and Regression Error Generated by Linest Function -0.01104
-2.40936
0.00036364
0.014162
0.995679
0.015212
921.711268
4
0.21329205
0.000926

Calculations:
Mass of Cis Isomer Required to Make 2 x 10-3 M 100ml
M = Mass/(Volume × Molar Mass)
Mass req. = 2 × 10-3 × ((100/1000) × 285)
= 57mg
Mass of Trans Isomer Required to Make 2 x 10-3 M 10ml
M = Mass/(Volume × Molar Mass)
Mass req. = 2 × 10-3 × ((10/1000) × 285)
= 5.7mg
k
k = (ln[D0-D∞] -ln[Dt-D∞]) / t
k =
0.0092
m-1
ln[Dt-D∞]

ln[D0-D∞]
-3.0718

-2.5198
Half life

t 1/2 =

ln[2/k]
=

75.3422 min

Error Propagation:
Measured weight of isomers
Cis 56.7mg Trans 5.7mg
Resolution of Scales ‘Satorius Extend’: 0.1mg
Volumetric glassware
100ml ± 0.1 ml ‘A’ Class
10ml ± 0.025 ml ‘A’ Class

Discussion:
Methanol was used as a solvent in this experiment to avoid the chemical interactions that may have occurred had water been used in its place (Mahaffy 2011). In the initial solution of the Cis isomer accuracy wasn’t as important as it was being measured to find the optimal wavelength for analysis as seen in Figure 1 and Appendix 1. Preparation of the Cis Isomer solution measured to produce Figure 2 required a mass of the compound as close as possible to the calculated amounts (See Results – Calculations) in order to produce results that allowed for the accurate determination of the rate constant (k) and half-life (t1/2). The relationship between k and t1/2 is that k is a factor in the formula of t1/2 (See Results – Calculations) and determines what unit of time that the half-life is expressed in (in this case minutes-1). Figure 1 plots the absorbance of the two isomers against the various wavelengths from 350nm 700nm. From this graph the wavelength of 540nm was identified as the ideal to be used to determine the reaction rate of the isomers. This was due to the local maxima of the Cis isomer at this point which coincides with the local minima of the Trans isomer. This data is confirmed by the printout of the Varian Car 50 UV-Vis spectrometer which also marked the 540nm point on its plot (see Appendix 1).

This clear difference in absorption of the two isomers at this wavelength meant that the rate of inter-conversion could be determined. The graph of the natural logarithm of the absorbance of the Cis isomer against time can be seen in figure 2. By observing the points on the plot a straight line of decay confirms that this reaction is first order, a logarithm of the measured absorbance values (Christian 2010). Calculations were carried out on the data in table 2 to determine the k and t1/2 (see Results – Calculations). The k value calculated of 0.0092 m-1 roughly matches the figure generated by the linest function 0.01104m-1 (see Table 3, top left) and is also similar to the literature value of 0.00845m-1. With the calculated k value of 0.0092 the t1/2 was determined to be 75.3422 minutes. Slight variations between the k value calculated from the points in figure 2 and that generated by the linest function can be accounted for by the fact that the linest function is a calculated line of best fit and so does not fit the data points collected exactly but is an approximation. The slight difference between the literature value of k 0.00845m-1 and the calculated k of 0.0092m-1 can be accounted for by human error in time, volume and mass measurement. The range of error in this measurement is ±0.00075 which is the difference between the calculated and literature values.

Conclusion:

In this experiment the rate constant (k) was determined to be 0.0092m-1 ±0.00075 and the t1/2 was calculated to be 75.3422 minutes.

References:
Brasted, R. Hirayama C. 1958 The cis-trans Isomeration of Dichlorbis-(ethylenediamine)-cobalt(III) Chloride and Dichlorbis-(propylenediamine)-cobalt(III) Chloride in Alcohols, Journal of Chemistry, Department of Chemistry, University of Minnesota. Vol. 80 pp 788 – 794. Brown, T. LeMay H. Bursten, B. Murphy, C. Langford, S. & Sagatys D. 2010. Chemistry: The Central Science, Pearson, Australia. pp 1196 – 1197. Christian, G. 2010. Analytical Chemistry 6th Ed., John Wiley & Sons, USA. pp 159, 270 – 271. Mahaffy, P. Bucat, B . Tasker, R. Kotz, J. Treichel, P. Weaver, G. & McMurry, J. 2011. Chemistry: Human Activity, Chemical Reactivity, Nelson Education, Canada. pp 99, 115 – 116.

Appendices:
Appendix 1: Figure 3: Absorbance of Cis and Trans Isomers at Various Wavelengths (Varian Car 50 UV-Vis spectrometer)