# 0.3 Beer's law and data analysis  (Page 3/3)

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Typical results are shown for the absorbance of $\left[\text{Ti}\left({H}_{2}O{\right)}_{6}{\right]}^{3+}$ measured at 490 nm.

 Concentration (mg/mL) %Transmittance Absorbance 0 100. 0 1 50.0 0.301 2 25.0 0.602 3 12.5 0.903

Over the studied range the solutions obey Beer's Law. If a solution has a measured absorbance of 0.450, we can calculate its concentration to be 1.5 mg/mL.

## Experimental procedure

In this experiment, each lab pair will measure the absorbance of ${\text{CuSO}}_{4}$ at six concentrations. You will create a calibration curve to correlate copper sulfate concentration to absorbance. This curve will be used next week to determine the concentration of an unknown copper sulfate solution and, in turn, the percent yield of a series of chemical reactions.

Materials ${\text{CuSO}}_{4}\cdot {\text{5H}}_{2}O$ distilled water pipette bulb 1cm cuvette 4 - 25 mL volumetric flask for your dilutions

Note: You will be borrowing these and must collect them from your TA. Do not forget to return the flask at the end of the lab). All students will lose 3 points in that lab section if any go missing!

100 mL volumetric flask for the parent solution (in your drawer)10 mL volumetric pipette or 10 mL graduated cylinder

• Measure out an appropriate mass of ${\text{CuSO}}_{4}\cdot {\text{5H}}_{2}O$ to get 100ml of ~0.1M solution and record the mass on your report form. Show your calculation to the TA before making the solution. This is your parent solution. Calculate the molarity using the actual mass measured and record it.
• Do the following dilutions and calculate the concentrations for each.
 Dilution (ml parent : ml total) 0:25 (DI ${H}_{2}O$ ) 5:25 10:25 15:25 20:25 25:25 (parent solution)
• Measure the absorbance of the 6 solutions you have prepared and the unknown given to you by your TA.

## Analysis

Plot the concentration as a function of absorbance for your six solutions. Perform a linear regression analysis and determine the equation of a best-fit line.

## Prelab: spectrophotometry and data analysis–Beer’S law

Hopefully here for the Pre-Lab

Name(Print then sign): ___________________________________________________

Lab Day: ___________________Section: ________TA__________________________

This assignment must be completed individually and turned in to your TA at the beginning of lab. You will not be allowed to begin the lab until you have completed this assignment.

In many of the experiments that you will do throughout the duration of this course you will be asked to analyze your data by making plots and calculating the best fit line through your data. One program commonly used to analyze data in this fashion is Microsoft Excel®. The following exercise will help you through the process used to obtain a plot and linear regression for a set of data.

Suppose you go for a 5 mile run and you tabulate the after each mile as in the following table.

 Distance Traveled (miles) Time (sec) 1 510 2 1026 3 1548 4 2077 5 2612

## Questions:

• Plot the distance traveled in miles vs. the time in seconds.
• Use linear regression to obtain a trendline and give the equation obtained in terms of the variables distance traveled and time and the R-squared value. Comment on the meaning of the R-squared value and its significance when doing data analysis.
• Using the equation you obtained by doing linear regression, estimate how long the 6th mile will take you to run.
• Assuming this linear trend persists, how far have you run if you finish in 2900 sec.

EXCEL INSTRUCTIONS:

• In order to plot this data in excel, you should enter the data exactly as above in to column A (rows 1-6) and column B (rows 1-6).
• To plot the data you will need to go to Insert on the tool bar and then click Chart. A Chart Wizard will appear. Select XY(Scatter) as the Chart type and choose the sub-type that does not have any lines connecting the points, then click next.
• On Step 2, click on the series tab near the top of the screen and click Add.
• You do not need to name the series unless you have multiple plots on one graph, but you can type in a name if you wish.
• To insert the X data, click on the icon at the far left of the x series box.
• Select the x values by clicking on the first one and while the left mouse button is down dragging the mouse down to the last value.
• When the values have been selected click the icon again and repeat for the y values. You may also manually enter the values by separating them with a comma. Don’t forget you need to remember what units you are using when answering questions.
• Click next when you have x and y values entered correctly.
• The next step is just entering title information and changing the appearance of your plot; click next when finished.
• Choose your chart location and then finish. You now need to place a linear regression line on your plot.
• Right click on a data point and pick add trendline.
• Choose linear as the type and click the options tab.
• Check the boxes to get the equation and R-squared value and click ok.

#### Questions & Answers

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