Full Lab Manual
Introduction & Goals
Chemistry & Background
In Your Write-up
Before coming to lab, complete your prelab, including the objective, reference, three prelab problems, procedure, and sample calculations or analysis flowchart. The latter should include the calculation of the molar extinction coefficient from the Beer's Law plot, the determination of the % Co by mass in your sample, and the % H2O by mass in your sample.
Keep careful records of your observations and any deviations from the prelab procedure. For the Beer's Law test, you should plot absorbance vs. concentration, as you measure it. The extinction coefficient of [Co(SCN)4]-2 at 625 nm should be calculated from the slope of the data. A value of about 1800 M-1 cm-1 should be obtained, using a path length of 1.17 cm for the colorimeter cuvettes. As you record and plot the data, use a ruler to get an approximate slope and extinction coefficient. For your formal report, perform a least squares analysis to determine the molar extinction coefficient more accurately. A typical Beer's Law Plot is shown in Figure 3.
Beer's Law Plot of [Co(SCN)4]2- in aqueous acetone
You will present your results, data and conclusions this week in the form of a formal report. Please prepare a word-processed document including a title page, objective, reference, results, calculations and a discussion. In preparing your formal report, please address the following:
Your Beer's Law plot, completed by determining the slope using a least squares analysis. Use the Least Squares program available on the ChemLab website. Be sure to record the 95% confidence interval in the slope, for your uncertainty analysis.
A calculation of the extinction coefficent of Co(SCN)42- at 625 nm and the concentration of your sample solution, from the Beer's Law calibration plot.
A calculation of the weight percent cobalt in the sample from the result of your analysis and a comparison with the theoretical value calculated from the molecular formula. A direct comparison of these two values will give an indication of the purity of your compound.
An uncertainty analysis, as described below.
The calculation of the percent cobalt by mass is a straight forward application of the principles described in the introduction, but the dilution factors can be tricky. A similar example is worked out below to guide your calculation.
Example. A 40.8 mg sample of [Co(NH3)5 (H2O)][NO3]3 was weighed and subjected to colorimetric cobalt analysis. Unlike the procedure you used, the total volume of the first solutions was 50 mL. Duplicate samples of 4 mL were then taken and treated as described in your procedure, with a final dilution to 50 mL. An absorbance of 0.384 was recorded for the final samples.
1. First calculate the [Co(SCN)4]2- concentration in the solution of absorbance 0.384. An value of 1.82 x 103 M-1 cm-1 was obtained from a least squares fit to the Beer's Law plot.
Although the above calculation was carried through to three significant figures, this practice may exaggerate the precision of the analysis. The 95% confidence interval for your slope can be used to calculate the uncertainty in the extinction coefficient, as in Week 4. The uncertainty in the final weight % result will also have contributions from the volume and mass measurements made in the analysis. Because the calculation of weight percent has several steps, the error propagation becomes correspondingly complex. Rather than performing a complete error propagation, you will compare the relative uncertainty of each measurement and draw conclusions about the contributions to the uncertainty in the final result.
To calculate the percent cobalt, by mass, in your sample, you used the following measurments: the mass of the original complex, volume of the initial solution, the volume of the two aliquots for conversion to the thiocyanate complex, and the volume of the final Co(SCN)4-2 solution. For comparison, calculate the relative uncertainty in each of these measurements. These results would be most clearly displayed in a table of values, absolute uncertainties, and relative uncertainties. Include the extinction coefficient from your Beer's Law plot and its uncertainty, from the 95% confidence interval given by the Least Square program. The value in your table with the largest relative uncertainty will make the greatest contribution to the uncertainty in your final % cobalt result. If all relative uncertainties are comparable, all will contribute in a roughly equal way to the uncertainty in the final result. This comparison will enable you to evaluate the contributions of the different measurements and decide which, if any, limit the uncertainty in your results.
In addition to using the uncertainty in the individual measurements to evaluate the uncertainty of your final results, you can compare the results obtained for your two different cobalt samples. You can take the difference between the two sample's % cobalt, divided by the average % cobalt, as an estimate of the precision of the results actually obtained. Compare this to the relative uncertainties for each measurement, tabulated above. Is the precision of your duplicate analyses smaller or larger than the relative uncertainties in the measurements? If the precision is greater than the relative uncertainties, your experimental values were not both measured to an accuracy consistent with the relative uncertainties you tabulated. In other words, your uncertainties were greater than you estimated from the precision of a pipet, volumetric flask, or balance, because an error was made. If your precision is smaller or close to the largest relative uncertainties you tabulated, you are using the equipment at its precision limits. How could you reduce the uncertainty, in this case?
The Results section for the gravimetric analysis should include the following
The percentage H2O by mass.
A comparison with the theoretical H2O content from the molecular formula.
Calculation of the uncertainty in your % H2O by mass, using error propagation.
Uncertainty Analysis for the Gravimetric Analysis
The calculation of the percent water in your complex is simpler than that of the percent cobalt. We will take advantage of this simplicity to perform a complete error propagation for the uncertainty analysis. In this case, you will estimate the absolute uncertainty for the mass measurements and propagate this error to find the uncertainty in the percent water by mass. To calculate the mass of water lost in the analysis, you subtract two mass measurements, before and after heating. You will use the error propagation rule for addition and subtraction to calculate the uncertainty in the difference of these two measurements. To calculate the percent water, by mass, you divide the mass of water lost by the original mass of the sample. You will determine the uncertainty in the percent water by mass using the error propagation rule for multiplication and division.
The Discussion for the cobalt Beer's Law analysis should include
A summary of the chemical transformation of your cobalt complex and its purpose.
A brief discussion of Beer's Law and its use in the analysis of your sample.
A summary of your results for the percent cobalt by mass and a comparison to the value expected from the formula of the complex. What conclusions can you make about the purity of your sample?
A discussion of the contributions to the uncertainty in your percent cobalt by mass. What measurements limit the uncertainty in your final results? How could you decrease the uncertainty? What about the precision of your two values from two different cobalt complex samples? How could this be improved, if it is greater than the expected uncertainty in you percent cobalt?
In the Discussion section, for the gravimetric analysis , be sure to
Summarize your results and compare to the value expected for the pure complex.
Discuss what your results say about the purity of your sample.
Discuss the uncertainty in your results. How could you improve the accuracy of your results?
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