Beer’s Law

Source: Smaa Koraym at Johns Hopkins University, MD, USA

1. Lab Setup for Beer’s LawExpand

   In this lab, you will combine aqueous solutions of FeCl₃ and NaSCN to form an orange-red [Fe(NCS)]²⁺ complex. When FeCl₃ is dissolved in water, the iron center is surrounded by six water molecules. This acidic complex easily loses protons from its water molecules, which can lead to iron hydroxides precipitating from solution.

   To prevent this, your solutions will include enough HNO₃ to keep the iron in solution, primarily as near colorless [Fe(H₂O)₆]³⁺ and yellow [Fe(H₂O)₅(OH)]²⁺. For this lab, we'll refer to the starting iron complexes collectively as Fe³⁺.

   The [Fe(NCS)]²⁺ complex forms when [SCN]- exchanges with another group on iron, with nitrogen interacting with iron. This exchange is reversible, so there's an overall equilibrium between the formation and loss of the [Fe(NCS)]²⁺.

   The thiocyanate-iron interaction gives the [Fe(NCS)]²⁺ solutions their intense color. You'll ultimately relate the UV-Vis absorbance intensity to the concentration of the [Fe(NCS)]²⁺ complex using Beer's law. This allows you to experimentally measure the equilibrium concentration of the [Fe(NCS)]²⁺ complex, from which you can estimate an equilibrium constant for the overall process.

   • Put on a lab coat, splash-proof safety glasses, and nitrile gloves. The solutions that you will use are highly corrosive, so be careful when handling them.
   • Label three 150-mL beakers as 0'.5 M HNO₃, '1 M FeCl₃ in 0.5 M HNO₃', and '0.5 mM NaSCN in 0.5 M HNO₃'.
   • Label a 400-mL beaker as 'waste'. Label one burette as '[SCN]-' and the other as ‘HNO₃'.
   • Clamp the burettes high enough so that the 400-mL waste beaker can fit under them.
   • Use the 50-mL graduated cylinder to measure 100 mL of 0.5 M HNO₃ into the appropriately labeled beaker in the dispensing hood. Cover the beaker with a watch glass and bring it back to your fume hood.
   • Measure 20 mL of 1 M FeCl₃ into the corresponding labeled beaker. Make sure that the stock bottle is capped before bringing your portion of the solution back to your hood.
   • Measure 40 mL of 0.5 mM NaSCN and pour it into the corresponding labeled beaker.
   • Label and fill a 100-mL beaker with deionized water.
   • Ensure the stopcocks of both burettes are closed. Place a funnel in each burette and pour deionized water into both of them.
   • Place the waste beaker under one burette and open the stopcock. Once the water has drained, close the stopcock, and repeat the process with the other burette.
   • Pour about 5 mL of 0.5 M HNO₃ into the corresponding burette and place the waste beaker under the spout. Open the stopcock to fill the tip with HNO₃ and allow a few mL to drain before closing it.
   • Add about 40 mL of HNO₃ to the burette. Remember that the graduations measure from top to bottom, so you should fill it to about the 10-mL mark. Note: The volume dispensed by a burette is tracked by the difference between the starting and final volume readings.
   • Place the waste beaker under the [SCN]- burette and fill the tip with NaSCN solution in the same way as the HNO₃.
   • Pour the rest of your [SCN]- solution into the burette. Gently tap the burette to dislodge any air bubbles. If there are bubbles in the burette tip, briefly open the stopcock to flush them out.
   • Obtain four squares of plastic paraffin film and two sheets of aluminum foil to finish setting up.
2. Calibration Curve MeasurementsExpand

   You need to know the precise [Fe(NCS)]²⁺ concentrations in your standard solutions to make an accurate calibration curve. However, the complex is in equilibrium with Fe³⁺ and [SCN]-, so only the [Fe(NCS)]²⁺ complex itself counts for this purpose. Thus, your standard solutions will use 0.2 M FeCl₃ so that iron will be in 500 to 2,000-fold excess.

   Any [SCN]- that leaves one iron will find another one so quickly that there will be, effectively, no free [SCN]- in these solutions. You can, therefore, assume that the [Fe(NCS)]²⁺ concentration is equal to the initial NaSCN concentration of the standard solution.

   • Label the 50-mL volumetric flask as '0.2 M FeCl₃'.
   • Dispense 10 mL FeCl₃ into the volumetric flask. Add a funnel to the flask and pour about 30 mL of deionized water into it.
   • Seal the flask with a square of plastic paraffin film and invert it several times to thoroughly mix the solution.
   • Use a disposable pipette to fill the flask to the line with deionized water and keep the pipette for later. Reseal the flask and invert it several times to mix the solution.
   • Turn on the handheld spectrophotometer and ensure that it is set to measure absorbance.
   • While the light source warms up, wrap five 50-mL beakers in aluminum foil to protect the light-sensitive FeCl₃ solution during the experiment.
   • Label five beakers and five clean disposable pipettes 1 – 5. Lay down paper towels as a clean surface for the glassware that you will reuse.
   • Follow to prepare solutions 1 – 5. For solution 1, add 5 mL of 0.2 M FeCl₃ to beaker 1, and then place it under the burette of HNO₃.

     Table 1: Standard solutions for [Fe(NCS)]²⁺ calibration curve

     λmax

     Solution #	0.2 M Fe3+ (mL)	0.5 mM [SCN]– (mL)	0.5 M HNO3 (mL)	Absorbance at λmax	Total volume (mL)	[Fe(NCS)]2+]
     1	5	0	5	Solvent blank
     2	5	1	4
     3	5	2	3
     4	5	3	2
     5	5	4	1

     Click Here to download Table 1
   • Note the current volume in the burette, and then dispense precisely 5 mL of HNO₃ into the beaker. Mix the solution with a glass stirring rod.
   • Use pipette 1 to fill a cuvette about 75% full of solution 1 and cap the cuvette.
   • Clean the transparent sides of the cuvette with a lab wipe and place it in the spectrophotometer.
   • Acquire a background measurement — a solvent blank.
   • Remove the cuvette, empty it into the waste beaker, and rinse it three times with deionized water. The same cuvette will be used for all measurements to minimize errors associated with cuvette imperfections.
   • Prepare the mid-concentration solution, sample 3. Add 5 mL of 0.2 M FeCl₃ to beaker 3.
   • Dispense 2 mL of NaSCN and 3 mL of HNO₃ into the beaker from the burettes.
   • Mix solution 3 with the glass stirring rod, then use pipette 3 to fill the clean, dry cuvette about 75% full of solution 3.
   • Clean the transparent sides and place it in the spectrophotometer.
   • Measure the absorbance of the solution for about 5 s and identify the wavelength with the maximum absorbance. Record this wavelength in your lab notebook as the λ_max for the [Fe(NCS)]²⁺ complex.
   • Set the spectrophotometer to average readings over 10 s and adjust the wavelength to the λ_max. Save a full absorbance measurement of solution 3. Record the absorbance at λ_max in your lab notebook.
   • Follow the same process for solutions 2, 4, and 5. Make the solutions one at a time or keep the prepared solutions under aluminum foil until you are ready to use them.
   • Add the appropriate solution to the cuvette and measure the absorbance values.
   • Once you have recorded all of the absorbance values at λ_max, sketch a plot of [SCN]- volume versus absorbance value, which should be linear. If you see any outliers, remake the solution and try again.
3. Measurements of Solutions with Unknown [Fe(NCS)]²⁺ ConcentrationsExpand

   In the last part of the lab, you'll prepare four [Fe(NCS)]²⁺ solutions with a 0.02 M FeCl₃ solution so that iron is in 40 to 100-fold excess. At these concentrations, the [SCN]- that leaves an iron center will not necessarily find another iron center immediately. Thus, the [Fe(NCS)]²⁺ will be in equilibrium with Fe³⁺ and [SCN]-, and its concentration will not be equal to the starting [SCN]- concentration.

   • Empty the 50-mL beakers into the waste beaker, remove the labels, and rinse them with deionized water.
   • Dry the beakers and relabel them as 6 – 10. Also label five disposable pipettes as 6 – 10.
   • Empty the volumetric flask of 0.2 M FeCl₃ solution into the waste beaker and rinse it with deionized water. Relabel the rinsed flask as 0.02 M FeCl₃.
   • Use a 1-mL volumetric pipette to transfer 1 mL of 1 M FeCl₃ to the volumetric flask. Add about 40 mL of deionized water to the flask.
   • Seal the flask with plastic film and invert it several times to mix the solution. Open the flask and fill it to the line with deionized water. Reseal the flask and mix the solution well.
   • Prepare solution 6, the new solvent blank. Add 5 mL of 0.02 M FeCl₃ and 5 mL of HNO₃, and then mix with the stirring rod.
   • Pipette the solution into the cuvette and acquire the background measurement as before.
   • Follow to prepare solutions 7 through 10, acquire their spectra, and record their absorbance values at λ_max as you did before. Remember to thoroughly rinse the stirring rod and cuvette with deionized water between each solution.

     Table 2. Solutions with unknown [Fe(NCS)]²⁺ concentrations

     [FeCl3] initial (M)

     0.01

     Solution #	0.2 M Fe3+ (mL)	0.5 mM [SCN]– (mL)	0.5 M HNO3 (mL)	Absorbance at λmax	[[Fe(NCS)]2+]eq	[Fe3+]eq	[[SCN]–]eq	Keq (M-1)
     6	5	0	5	Solvent blank
     7	5	1	4
     8	5	2	3
     9	5	3	2
     10	5	4	1

     Click Here to download Table 2
   • When you are finished, empty the cuvette, volumetric flask, and beakers into the waste beaker and rinse them with deionized water.
   • Collect any excess HNO₃ and NaSCN in their respective beakers. Neutralize the waste and the excess reagent solutions with baking soda and dispose of the waste and the excess FeCl₃ solution in the appropriate waste container.
   • Flush the neutralized HNO₃ and NaSCN solutions down the drain with tap water.
   • Wash your glassware and equipment by your lab-standard procedures.
   • Collect paper towels and other trash from your fume hood and put them in the lab trash.
4. 結果Expand
   • Calculate the concentrations of [Fe(NCS)]²⁺ in the standard solutions. In these solutions, the iron concentration is so high that we can assume that the starting [SCN]^– concentration is the same as the [Fe(NCS)]²⁺ concentration.
   • For each trial, multiply the [SCN]^– stock concentration by the volume of NaSCN added, and divide that by the total solution volume of 10 mL. Repeat for all standard solutions.
   • Create a calibration curve by plotting the absorbance at λ_max for the standard solutions with respect to their [Fe(NCS)]²⁺ concentrations. Find the linear function that fits the data and set the y-intercept = 0, if necessary. Note: Beer's law is expressed by a linear function, which relates absorbance to concentration. Thus, the slope of your calibration curve is equal to the molar attenuation coefficient times the cuvette width, or pathlength, which was 1 cm in this lab.
   • Rearrange the linear equation to solve for concentration. Remember that your molar attenuation coefficient and pathlength will be the same for every trial. Fill in the absorbance for each unknown trial and solve for the equilibrium concentration of [Fe(NCS)]²⁺ for that solution.
   • Estimate the equilibrium constant for [Fe(NCS)]²⁺ in solution. For simplicity, we'll express the constant in units of 1/M.
   • Calculate the starting concentrations of Fe³⁺ and [SCN]^– for each trial. Determine their equilibrium concentrations in each trial by subtracting the equilibrium concentration of the [Fe(NCS)]²⁺ from the starting reagent concentrations for that trial.
   • Fill in the equilibrium concentrations of the product and reactants. Then, solve the equilibrium equation to estimate the constant for this trial. Lastly, compare the constants for the trials.