Pre Lab assignment 3 Spectrophotometric determination of phosphate: Data analysis using a spread sheet program Approximate time required: 3h It is possible to analyze spectrophotometrically the phosphate concentration of an aqueous solution (PO 4 3 (aq)). In an acidic environment, ammonium molybdate and antimonyl tartrate combine with any phosphate present as PO 4 3 (aq) to form an antimony phosphate molybdate complex. Reduction of this complex with ascorbic acid produces a second complex with a deep blue color. To determine the concentration of the complex we measure its absorbance at a wavelength of 880nm by using an instrument called a spectrophotometer. The table below shows the transmittance measured for a series of solutions. As you will see when you make the appropriate plot, something went wrong with one of the standards. You will therefore make calculation in two different ways: with all the data and with the outlaying standard excluded. Sample Concentration (ppm) Transmittance @ 880nm Blank 0.971 Standard 1 0.112 0.883 2 0.130 0.853 3 0.345 0.727 4 0.516 0.606 5 0.650 0.454 6 1.272 0.313 unknown Detn1 0.435 Detn2 0.457 Detn3 0.423 Assignment overview 1. Enter these data in a spreadsheet. 2. Calculate the absorbance for each standard, each sample, and the blank. RevF09 1
3. Correct the measured absorbance of each standard and each sample for the blank. 4. Prepare a plot of blank corrected absorbance (y axis) vs. concentration (x axis). Be sure to label the axes and to include units as appropriate. 5. Use the analysis tool Regression available on Excel or another spread sheet to obtain four linear best fits to the data: (draw the best straight line, which is called trendline in Excel; not curved or connected ) y=mx+b with the problematic standard; y=mx+b without the problematic standard; y=mx with the problematic standard; y=mx without the problematic standard. 6. Calculate the average absorbance for the unknown. 7. From the best fit slopes and intercepts, and from the absorbance of the unknown, obtain four estimates of the concentration of PO 4 3 (aq) in the unknown solution. 8. Decide which estimate of the concentration of PO 4 3 (aq) you think is the best. Label all parts of your work clearly. The detailed instructions below assume that you will use Microsoft Office Excel 2007, which is installed on most public computers on campus. You may use a different version of Excel or other spreadsheet programs if you wish. Virtually, all spreadsheet programs have Help function (in Excel, press F1 key to go to the Help menu), which you may find useful. As in all computer work, remember to save your work often. At the end of this handout, you will find a spreadsheet that I have prepared, but with incomplete numerical results. You may wish to use it as a model. However, notice that the data is not the same. 1) Enter the data Launch the spreadsheet program. The previous prelaboratory assignment Analysis of a titration curve, gives some basic instructions for how to enter data. Be sure to save your work frequently as you go along. 2) Calculate the absorbances from the transmittances A simple formula relates absorbance to transmittance. Suppose the first transmittance is in cell D7. We want to put the calculated absorbance in E7, which is to the right of D7. To do this, enter in cell E7 the text exactly (including the equal sign) = log(d7) Note that the D may be either upper or lower case. Note also that your formula should probably not contain any spaces. If you enter a space, the spreadsheet will think you are RevF09 2
entering text rather than a mathematical formula, although some spreadsheets are smarter than others in this aspect. Remember to control significant figure in your output! Instructions for how to do so are given in the previous prelaboratory assignment. You can repeat the calculation of the absorbance from transmittance for each row of the table. Alternatively and more quickly, you can copy your formula to calculate absorbances for the other cells as follows. By using the mouse or the arrow keys, place the cursor in cell E7 (or whatever cell you want to copy from) and right click. Choose the command Copy. (Experts, use [control]+c)the cell you have chosen to copy from will develop a special border to show that it is ready to be copied. Move the cursor to the destination or copy to cell and click the left mouse button. Hit the return/enter key. (Experts will know that you can copy to more than once cell at a time by selecting a block of destination cells and that you can use [control]+v to paste) Be sure to check to see that the results look reasonable. The copy command has some special properties that can sometimes lead you astray. You can examine the formula of the cell with the newly pasted information by placing the cursor there and click the left mouse button. 3) Correct absorbances for blank The idea here is subtract the blank absorbance from the absorbances for the standards and for the samples. Suppose the first absorbance you want to correct is in cell E7 and suppose the blank value is in cell E4. The cell to the right of E7 will be F7. To calculate the corrected absorbance in cell F7, enter in cell F7 the text =E7 $E$4 Make sure that your result has the right number of significant figures. To calculate blankcorrected absorbances for other solutions by copying this formula, proceed as described in the previous section. Note that by placing the $ symbol in front of the E and in front of the 4, the Excel will know not to alter the cell name E7 when you copy the formula. RevF09 3
An alternative is to enter the formula =E7 constant Where constant is the actual numerical value of the absorbance measured for the blank. 4) Plot absorbance versus concentration Prepare the scatter plot with right format. Plot the blank corrected absorbance vs concentration for the six standard solutions. To prepare a plot, use mouse to select part of the table containing the blank corrected absorbance and concentration for the six standards. GO to the Insert menu, in the Chart panel, under Scatter, select Scatter with only Markers. Double Click the graph, which gives you access to Chart Tool. From the Chart Layouts, select the layout which allows you to edit the Chart Title and Axis Title. Double Click the Chart Title on the graph to label your graph. Double Click the Axis Title to label the axes with correct units. 5) Obtain a best fit to the data We want to fit a straight line to our plot of the blank corrected absorbance vs concentration. Blank corrected absorbance=m * concentration + b That is, we want the values of m (the slope) and b (the intercept) in the equation above. The mathematical process used to obtain m and b is called regression analysis. Many hand held calculators offer this capability, and you may wish to use a hand held calculator to check your work. Excel not only does what hands calculators can do but also report a much more extensive set of statistics and other kinds of information. To use the Excel, you will have to tell it which data to fit and whether you want to force fit through the origin (that is, choose a fit in which the RevF09 4
constant b is forced to be zero). You may also want to tell the spreadsheet program where to put the result but if you don t, it will choose its own place. To obtain the parameters of a bestfit using Excel, proceed as follows. Step A Call up the regression software First, make sure that Excel has the regression software available. To do so, click on the Data menu and look to see if Data Analysis is on it. If not, click the Office button. Click Excel Options on the bottom to open the Excel Options dialog. From the left panel, select Add Ins, on the bottom of the right panel, you will find Manage. Choose Excel Add ins for Manage and click Go. An Add Ins window will show up. Check the Analysis ToolPak and click OK. Now you should be able to find the Data Analysis tool from the Data menu. Read Load the Analysis ToolPak section of Excel Help. Use keyword ToolPak in Help to search. From the Data menu, select Data Analysis. In the dialog box that pops up, scroll down to Regression and highlight it by positioning the cursor on it and clicking with the left mouse button. Click OK. A dialog box labeled Regression should appear. Steps B D have comments on how to fill in the Regression dialog box. StepB Regression dialog box: Input the location of the data Input the Y range (blank corrected absorbance in this case). Suppose your blank corrected absorbance data are in cell F7:F12. Enter the text into the dialog blank labeled Input Y Range : $f$7:$f$12 Input the X range analogously. Experts, note that you can also use the mouse to select the data ranges. For Regression to work properly all the x data and all the y data must be contiguous that is, the x data must appear in a column with no blank rows separating them, as must the y data. Therefore, before you can carry out the regression analysis with one standard eliminated, you will have to copy the concentration and corrected absorbance data to a new location on the sheet. If you are unfamiliar with Excel, it may be easier simply retype the data in a new location. Step C Regression dialog box continued: Do you want to force the line through the origin (X 0, Y=0)? If you want to force the best fit line through the origin, then check the option Constant is Zero. Otherwise, leave this unchecked. RevF09 5
Step D Regression dialog box, concluded: Where to put the output? Try experimenting with this one. Just make sure that the output from this regression will not write over something that you have already put on the spreadsheet and want to keep. To avoid headache, save your file before you do the regression. Step E Interpreting the output from Regression As you will see, Regression produces a great deal of statistical information. At this time we are concerned with only two results. Search for the section of the output that looks like this: Your numbers will be different. What you want are the coefficients: The intercept (what we call b), and the X Variable 1 (i.e., the slope of the best fit line, which we have called m). Step F Another way to get best fit line. Another way to do the regression analysis is to add trendline to your plot made in 4). However, doing so, you will not be able to get the detailed statistical information as in the table above. On the graph, right click a marker (one data point), then choose Add Trendline. From the Format Trendline dialog, under Trendline Operations, choose Linear for the Trend/Regression Type. For the 2 plots in which you want to force the trendline to go through the origin, check Set Intercept and set the value to 0.0. Leave this unchecked for the other two plots. Check Display Equation on Chart to have the equation representing the trendline on the chart. The equation will have format y=mx+b or y=mx, depends on whether you force the trendline to go through the origin or not. The value of slop m and intercept b can be read from equations on the charts. From your graph, you can always right click on the trendline to access the Format Trendline dialog. Read Add,Change or remove a trendline in a chart section for detailed instruction from the Excel Help. Search Trendline in help will lead you to this section. 6) Calculate the average, blank corrected absorbance of the unknown Suppose the three blank corrected absorbance values for the unknown are in cells F15:F17. To calculate the average blank corrected absorbance in cell F18, enter in cell F18 the text =average(f15:f17) RevF09 6
For further reference, you may be interested that the text=stdev(f15:f17) returns the standard deviation of the data set and that sure beats calculating the standard deviation by hand. 7) Calculate the concentration of the unknown Your best fits should be of two forms: Blank corrected absorbance =m *Concentration (ppm) + b Here m is the X Variable and b is the Intercept from above (what are the units of m and b?). and Blank corrected absorbance=m* Concentration (ppm) The second form is what you assume when you force the fit through the origin. In this case, only the value if the slope, m, is free to vary. Rearrange these formulas to express concentration in terms of blank corrected absorbance, the slope m, and, when appropriate, the intercept b. Enter these rearranged formulas in different cells, beginning with the = character and use them to calculate the concentration of phosphate ion in unknown. A model solution is attached. Blanked out areas appear where you should make entries. RevF09 7
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