Cadmium Calibration Problem

 

In January 2010, a large number of children’s jewelry pieces imported from China were found by an Ashland chemistry professor to contain high levels of cadmium.  In some cases these were actually 80-90% cadmium.

 

http://www.ashland.edu/news/2010-01-12/current-students/chemistry-professor-abc-s-good-morning-america

 

http://www.cpsc.gov/onsafety/2010/01/guide-for-parents-the-dangers-of-heavy-metals-in-childrens-jewelry/

Cadmium is a toxic heavy metal found to be present above the EPA drinking water limit of 5 parts-per-billion in approximately half of the contaminated sites on the National Priority List.  Cadmium is extracted from the mining process for zinc or copper; cadmium is used extensively in batteries, pigments, and plastics.

A leading university is developing a mobile technology to measure Cd levels in surface water; portable instrumentation would provide real-time analysis and prevent having to transport samples back to a fixed laboratory for analysis. Recent testing with a bench scale model was conducted over a range of cadmium concentrations between 250 parts-per-trillion and the 5 parts-per-billion EPA limit.  Approximately 10-25 challenges at each concentration were made separately to fully characterize the initial performance of this mobile technology.

The datasheet from these experiments provide Cd concentrations, source intensities (Io), and intensities (I) present after passing through the sample.

Requirements:  Create an excel spreadsheet and do the following:

 

1.    Label the worksheet “Calibration Data” and calculate the transmittance and absorbance for each measurement. Format the cells to the nearest ppt for Cadmium concentration and to three decimal places for the Absorbance.

 

2.    Copy the entire data set into a separate worksheet.  Label this new worksheet “Correlation Coefficient.” Add columns that will be used for calculating the correlation coefficient (similar to that shown in Example 5.3.1 of your text). There should be separate and clearly labeled columns for Xi, Yi, Xi-Xbar (mean-centered Xi’s), Yi-Ybar (mean-centered Yi’s), (Xi-Xbar) squared, (Yi-Ybar) squared, and (Xi-Xbar)(Yi-Ybar). The sum of this last column is the dot-product of the multidimensional Xi and Yi vectors. Insert a clearly labeled row at the top showing the sums of these columns. Insert rows above this and calculate the correlation coefficient for concentration and absorbance for the entire data set.   

 

3.    Go back to the Calibration Data worksheet and use the linest function to conduct a least squares fit of the absorbance-concentration data.  Similar to the class handout, clearly label what each of the cells in the least squares fit represent.  Use these regression results and add a clearly labeled column showing predicted absorbances for each concentration.

 

4.    In cells highlighted in yellow background, write out the mathematical equation from the least squares fit.  

 

5.    Generate a plot clearly showing the calibration points and the Least squares fit regression line using the format described in class.

 

6.    A water sample collected near a suspected Cd-contaminated site solution was analyzed ten times and yielded an average absorbance of 0.253 AU.  Calculate the amount of Cadmium predicted by the regression for this reading; clearly show all equations and work in Cells highlighted with a green background.