# CHEM 3201L: Instrumental and Data Analysis Laboratory

Make a graph of this data and determine the linear portion of the graph.
Determine the best linear curve through the data.
Determine the calibration sensitivity.
Compare the analytical sensitivities for 4 and 18 ppm. Verify the statements that distinguished the calibration sensitivity from analytical sensitivity.
Calculate the coefficient of variation for 10 ppm Pb’
6. Determine the signal at the detection limit. Sm=S
7. What is the concentration detection limit. Report the detection limit with confidence limits at a 95 and 99% confidence level. Comment on the range of the confidence limits at the two levels of confidence.
Requirements: 1 spreadsheet | .xls file
CHEM 3201L: Instrumental and Data Analysis Laboratory
Instrumental Analysis Computer Exercise
Introduction
The figures of merit can be used to determine whether an instrumental method is suitable for addressing an analytical problem. This laboratory exercise will consider investigate the concepts of precision, bias, sensitivity, detection limit, and the dynamic range. Students will also be introduced to spreadsheet calculations and linear-regression analysis.
Problem
Standard aqueous solutions of lead were measured by an instrumental method to determine the concentration of Pb in a sample. The following calibration data in arbitrary units were obtained:
Make a graph of this data and determine the linear portion of the graph.
Determine the best linear curve through the data.
Determine the calibration sensitivity.
Compare the analytical sensitivities for 4 and 18 ppm. Verify the statements that distinguished the calibration sensitivity from analytical sensitivity.
Calculate the coefficient of variation for 10 ppm Pb2+.
Determine the signal at the detection limit; .
What is the concentration detection limit. Report the detection limit with confidence limits at a 95 and 99% confidence level. Comment on the range of the confidence limits at the two levels of confidence.
The unknown sample gave a signal of 22.6 units. Determine the analyte concentration and confidence limits at a 95% confidence level. The confidence limits are given by x0 ? tsx0; where x0 = the analyte concentration, and t = a number corresponding to the number of degrees freedom (n ? 2) at a particular level of confidence. In our case, the number of degrees freedom is equal to the number of points on our calibration curve minus 2 giving us 6.
The value of sx0 is by:
where sy/x is a statistical parameter called the standard error and is used to determine the error in the slope and intercept of the regression line (y = bx + a);

Note that m = slope, a = the number of readings, and n = number of points on the calibration curve. You will have to calculate the numerator and the summation in the denominator of the last term.
You do not have to perform this calculation. Click the data tab in excel and look for Data Analysis? tab. If it is not available, then click File Options Add-Ins Analysis ToolPac Go Analysis ToolPac?. Conduct a data analysis and locate the standard error. You can now calculate the standard deviation associated with your sample and the confidence limits of your analyte concentration at a 95% confidence level.
9. What happens to the confidence interval as the number of replicate measurements increase? Prove your response by comparing the confidence interval obtained from a =1 and a = 4 using Equation 1.
10. Make a general statement relating the confidence interval and the number of replicate measurements.
11. The dynamic range extends from limit of quantitation (LOQ) to the limit of linearity (LOL). The LOQ is the smallest concentration of analyte that can be quantitatively be measured. The LOQ can be determined at ten times the standard deviation of the blank signal (10sbl = 10 x 0.004 units). The concentration that corresponds to a signal of 0.04 units is equal to ??.. The LOL is the concentration at which the curve departs from linearity.
Determine the standard deviations for the slope and intercept.
Determine the new concentration for each signal using the equation for the linear curve. Verify that these concentrations exactly correlate to the signals. The new concentrations are nearly the same as the original concentrations suggesting that there is a perfect correlation between the calculated signals and the original concentrations.
Calculate the 95% confidence limits for each concentration by using: x0 ? tsxo.
On the same graph, plot the calibration curve and the 95% confidence limits for each concentration. What region of the calibration curve has the smallest confidence interval?

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