Beer's Law

background [prelab assignment (35 points); due at the beginning of lab]

This laboratory activity is based on investigations 1 and 2 in your *AP chemistry lab manual*; thus, it provides some relevant background for the following prelab questions and this laboratory activity. Investigation 1 is about Beer's law, while investigation 2 is about the calibration curve, which is a reflection of Beer's law.

1. run Beer's law simulation (select "Beer's law" icon): turn "on" light source by clicking on red button and select "absorbance" radio button for the detector. investigate: ___; record values of absorbance and value of variable of interest, x, to "discover" the relationship between the variable of interest and absorbance; absorbance = k x

^{ n}, i.e. what's the value of n ? [10 points]

- the effect of path length on absorbance

- use ruler to measure path length
- change path length by selecting yellow double arrow at the bottom on the sample container using the mouse, hold mouse left click button, then move to simulate varying path length
- the effect of concentration on absorbance

- use mouse to move concentration slider to simulate varying concentration
other aspects of Beer's law

- the effect of wave length on absorbance: select "variable" radio button on wave length panel, then simulate the absorption spectrum by using mouse to move the wave length slider from the far right to the left.

- select Co(NO
_{3})_{2}in solution drop-down menu- select K
_{2}CrO_{4}in solution drop-down menusketch / label absorption spectrum for Co(NO

_{3})_{2}and K_{2}CrO_{4}. how does the spectrum differ / similar ?- what is the relationship between the solution's color and color of the incident light ? what is the rationale / basis of this relationship ?
2. briefly, describe the following [6 points; 2 points / item]

Beer's law; include relationship between absorption and % transmission

standard or calibration curve, and its application / use

spectrophotometer

3. run Beer's law simulation; include screen shot of completed simulation (i.e. your screen shot shows the filled-in standard curve, intensity of the unknown sample, & your calculations to determine [unknown]) [5 points]

4. sketch a data table (i.e. not calculations) for this lab containing entries for all required experimental measurements (i.e. review purpose & content of lab report) [4 points]

5. spectroscopy [10 points]

6. MSDS data on copper (II) nitrate [5 points]a. define / describe spectroscopy;

b. what is the basis of ___ spectroscopy ?

- infared
- ultraviolet
- visible
that is,

(i) what energy state, ___, transitions are associated with the preceding types of spectroscopy ?

translational motion ? vibrational energy ? rotational energy ? electron energy ? nuclear spin ? electron spin ?

c. use / applications of __ spectroscopy ?

- infared
- ultraviolet
- visible
7. review below "methods" section

to lab; otherwise, you might be "lost" during the lab, since you won't know how to use the colorimeter; because, this issue won't be addressed during the prelab session (due to shorter block period)prior

purpose

generate a standard (or calibration) curve

compare the determination of the concentration of Cu

^{2+}in an unknown sample (range: 25 - 250 mM) using an algebraic- versus graphical- method in conjunction with the preceding calibration curve.

materials

aqueous solution of copper (II) nitrate

- 250 mM; dilute to generate known [Cu(NO
_{3 })_{2 }] - to be used to generate the calibration curve- unknown [Cu(NO
_{3 })_{2 }]colorimeter (a "cheap" spectrophotometer)

water; beakers; test tubes; micropipets; tissue paper

methods - use of probe device - record in your lab notebook, since you will use the colorimeter in a subsequent lab [see vodcast; may use your smart phone during lab to access the link]. remainder of lab methods = student design.

- turn-on Xplorer data collection device
- insert colorimeter into Xplorer device
- open lid, then insert small glass vial (cuvette) filled with water into colorimeter
- close lid; should display %T ~ 100 or Abs ~ 0 for all wavelengths; press "+" on Xplorer - to cycle thru various setting (red, green, blue, & orange, where reading % T or Abs
**if**%T not ~ 100% or ABS not ~ 0 ,**then**press green button on colorimeter / wait till lights goes off**else**goto next step- replace cuvette with samples; press "+" on Xplorer - to cycle thru various setting; record data; repeat with other samples
- DO NOT PRESS ANY OTHER BUTTON DURING YOUR MEASUREMENT

data analysis

student design

content of the lab report [50 points]

data analysis [15 points]

figure 1: standard curves using Excel: include all wavelengths, i.e. colors, and equation & R

^{2 }value of the "best" color to use in the analysisfigure 2: based on preceding graph, using the "best" color (to analyze the data) and graph paper, do a "free-hand" drawing of the graph

determination of the [Cu

^{2+}] in your sample - show your work using both methods

- algebraic method: use results of Excel output in figure 1
- graphical method: use graph in figure 2 and draw imaginary lines to connect the value of the absorbance (on the vertical axis) to the graph then to the value of the concentration (on the horizontal axis).
statistical analysis (include interpretation of p-value) of class data

discussion [15 points]

is there a difference in the determination of [Cu

^{2+ }] using both methods described in the purpose ? Support your conclusion based on statisticswhat is the rationale of choosing a specific wavelength of light for your determination of [Cu

^{2+}] ? [hint: see prelab question 1 in the below cdf based simulation]rationalize why blue light has the lowest absorbance by the Cu

^{2+}solutionerror analysis (in regards to a cuvette containing the sample) [10 points]

how could the presence of fingerprints on the cuvette affect your determination of [Cu(NO

_{3})_{2}] ? elaborate / justify your answer.when would the volume of the sample in the cuvette affect your determination of [Cu(NO

_{3})_{2}] ? elaborate / justify your answer.supplemental questions: in regards to figure 1 on p. 26 in the AP chem student lab manual, [10 points]

justify the validity of the equation associated with the figure using Beer's law

if the concentration in the left test tube is 75 µM, then what is the concentration in the right test tube ? justify your answer.

**resources**:

Beer's law: derivation / regression analysis [calculus based presentation]

for Excel 2007 tutorials to analyze the calibration curve, see vodcast (@ lab / stats tab)

simulations (requires cdf player plugin): guided inquiry into exploring the considerations to select the wavelength to use in the Beer's law lab.