How to Determine Molar Absorptivity From a Graph
Chem 125 - Experiment II
Solution Color
Experiment II - Solutions & Solution Color
Goals of Experiment II
- How do you successfully prepare a solution of known concentration?
- Why are some solutions colored while others are colorless?
- Is there a pattern of color based on characteristics of the compound itself?
- How do these solutions interact with visible light?
- What is in a solution, and how much of it is there?
- How do you prepare and use a calibration graph?
Questions you should learn from this lesson and know before going into lab
- What is a mole?
- How do you calculate molarity?
- How do you make a solution?
- How does a solution interact with light?
- How do you make an absorbance spectrum?
- How do you dilute a solution?
- How do you make a calibration graph?
- How do you work with Beer's Law?
Questions you should learn in lab
- What makes some solutions show color and others not?
- How does the solution color relate to its absorbance spectrum?
- How are concentration and absorbance related?
- How can you determine the concentration of an unknown sample?
You should also have a general understanding of the periodic table.
When looking at the relationship of color of a solution, and the elements themselves there are certain characteristics in the periodic table that should be known. Charge, electron configuration, ionic radius, all of these are characteristics of the cation in a particular solution that may have an impact on color.
Think you know the periodic table? Test yourself to find out!!
Need some additional help with understanding the periodic table? Try these great links!
Webelements
PTable
Experiment Goal
Preparing a solution of known concentration
Preparing a solution is something that is very critical to many applications in science, medicine, cooking, engine matainence, and other fields. Particularly in chemistry, solutions are made using the concentration concept of molarity. You will go through the different concepts related making a solution, and go through a step by step use of calculating molarity.
Terms you will need to know for the experiment
Atomic Weight
Molecular Weight
Mole
Molarity
Volume
Concentration
Concepts you will learn
What is a mole?
What is molarity?
Why are volume and concentration important to making a solution?
Skills you will learn
How to determine molecular weight
How to weigh material
How to calculate molarity
How to work with volumetric flasks
Preparing a solution of known concentration
What is a mole?
The first thing you will need to understand when making a solution is the concept of a mole. A mole is a number 6.02 x 1023 to be exact. All chemistry calculations are calculated in moles. The concept of a mole is just like the concept of a dozen. There are 12 objects in a dozen, just like there are 6.02 x 1023objects in a mole. When working with different elements, they all have different atomic weights.
The atomic weight is how many grams of that element will make up one mole (or 6.02 x 1023 atoms) When this is applied to a ionic or molecular compound, the molecular or formula weight of the compound is determined by combining the atomic weight of all the atoms in the compound. The atomic weights for each atom can be found on any periodic table.
The first thing you should ALWAYS do is convert grams to moles. If you are given something in grams, then determine the formula weight and find out how many moles it is. All chemistry calculations are done with moles because they are numbers not weights. When baking, you do not weigh out 173 grams of egg, you would use 1 egg
Do you really know what a mole is? Test yourself below!
Preparing a solution of known concentration
Volume & Concentration
When you're making a solution of a given compound, you need to know what concentration you want, and what volume you want. These are important because they relate to how much of your compound you need.
You will also need to find the molecular weight of the compound like you did on the first page.
The volume of your container is important, because if there is a larger volume, you need more material.
Test yourself!
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The next important step after you select a volume is the concentration
The concentration is the amount of something in a given container.
The higher the concentration, the more of the sample there is.
Moving from right to left in this picture the concentration is increasing, and you can see the solutions getting darker.
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An example of concentration is stated below
There are 36 eggs in 3 cartons, so the concentration is 12eggs/carton
The graph below shows how the concentration changes as you remove eggs from the cartons. There are 3 cartons of 12 eggs to start with. 36eggs/3 cartons. The concentration is 12eggs/carton. As you remove eggs from the cartons, the concentration goes down. There are still 3 cartons, but now less eggs.
Preparing a solution of known concentration
Molarity
Molarity is a measurement of concentration.
Specifically for molarity, it is the number of moles in a given volume
There are 6 moles of NaCl in 3 liters of water, so the Molarity (Concentration) is 2 moles / liter. The molarity of the soluion is 2.0
The main equation for calculating molarity is that molarity = the number of moles in one liter of solution
The video below shows exactly how to setup and use the molarity equation to determine the number of moles needed to make 100mL of a 0.1M solution
Now use the equation in the video to solve these problems. You may need to determine the molecular weight of compounds as well, so have your periodic table ready!
Still wanting some extra practice on calculating molarities, and volumes and moles? Visit the link below for a bottomless molarity worksheet!
Bottomless Worksheet of Molarity!
Preparing a solution of known concentration
Laboratory Details
Now that you're able to calculate molarity and know volumes and concentrations, let's take a look at what you will do in lab.
1). Preform calculations to determine how many grams of your assigned samples you need to weigh out to pepare 100mL of a 0.1M solution
See the previous page for help!!
2). Actually weigh out the amount of material you need for each solution. The video below will show you how to accurately weigh out solid chemicals.
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3.) Next you will dissolve your solid chemical in the appropriate solvent.
Check To Make Sure You Use The Appropriate Solvent!!
Using the video below, try and answer the following questions.
4). You have now made a solution!!
Experiment Goal
Obtaining an Absorbance Spectrum
In obtaining an absorbance spectrum, you are getting a graph representation of how light is interacting with a solution, and how that relates to the solution color. This interaction is very important in scientific and medical fields and that color can give a lot of information. The color of a solution can give information on concentration of chemicals, how much acid is present, if a reaction has happened, or even if something has gone bad or not. In the following pages, you will learn how obtain an absorbance spectrum for each of the samples you prepared, and use that spectrum to relate to why the solution is the color that it is.
Terms you will need to know for the experiment
Light
Color
Wavelength
Absorbance
Transmittance
Concepts you will learn
How does light interact with a solution?
What types of light will a solution absorb or transmit?
How are absorbance and transmittance related?
How do absorbance and transmittance relate to the color of the solution?
Skills you will learn
How to use a spectrophotometer
How to obtain an absorbance spectrum
How to use that absorbance spectrum to relate to solution color
Obtaining an Absorbance Spectrum
Solution Color
The solution made was Cu(NO3)2 where the cation was Cu2+. You will notice that the solid was blue, and the solution it made in water, was a blue color. Many times when you look at data in the CRC Handbook, it gives you the color of the SOLID form of the compound.
Match the following solid colors with the solution colors you would expect.
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Did you match the right colors?
There are many things that can change a soluiton color. Many of them are based on the placement within the periodic table, and how it is set up.
Another aspect that can effect the color of a solution is the charge of the cation. Take a look at the video below.
Notice that the Vanadium solutions are all different colors, but they are all the same cation. The difference is that the cation has a DIFFERENT charge, which changes the electron configuration, and how light interacts with the solutions. This will be very important for future experiments involving redox reactions, as you are changing the charge of the cations. More on that later!
When you're in lab, look at the solutions that you make. Some questions you can ask yourself as you're making them are:
- Why do some solutions have a color, while other solutions are colorless?
- Do cations in some areas of the periodic table display colors while others do not?
- What are special about these areas that could cause changes in light interaction?
- Are there exceptions within the areas?
- If so, why? What's different?
- Why were some solutions made in water, while others were made in base or acid? What are they trying to get us to see?
Obtaining an Absorbance Spectrum
Light & Solutions
Most of the light that all of you see, like the light from the sun, is white light. But did you know that the light coming from the sun is made up of many different colors?
It's time you are introduced to Mr Roy G. Biv, the keeper of the colors!!
White light is primarily made up of these seven colors, but the color is different at each wavelength.
You will see the individual colors of each of these wavelengths.
Bright White Light!
When you look at a solution, there is light from all around interacting with it. This is how you are able to see the color that the solution is.
Much of the time, you are seeing how things interact with white light. This light is the light that comes from the sun, and many light bulbs.
It is comprised of all the colors of the rainbow (ROY G. BIV)!!! But what does that have to do with solution color? The color of a solution depends on how the light (of many colors) interacts with the solution, and is a combination of colors from that rainbow!
Below shows how white light would interact with a sample that you have.
1). All the colors of light in white light, hit the solution.
2). Each wavelength of light interacts with the molecules in the solution.
3). Some colors of light are blocked by the molecules and Absorbed, while others pass through and are Transmitted
A question to consider:
If you have a sample of a blue solution, what color light would be the most transmitted?
Obtaining an Absorbance Spectrum
The Absorbance Spectrum
You've looked at what light does all at once, but for many things, including this experiment, the light is broken down into wavelengths. Each wavelength has it's own color (Found Already!). When you see how each wavelength of light interacts with the solution on its own, you can generate an absorbance spectrum (graph) for your solution.
Each wavelength can absorb differently, below is an example of how that happens.
1). The different colors of light hit the solution one at a time.
2). Each color of light interacts with the molecules and some part of the light is Absorbed, while the rest is Transmitted.
3). The amount of light that is Transmitted passes through the solution to the detector.
4). The machine then can convert the amount of light that is Transmitted into the amount of light that was blocked or Absorbed by the solution.
As the light interacts with the sample, you can ask yourself.
- If i have a red solution, what wavelengths would absorb the least?
Once the light interacts with your solution, you can graph it, much like this spectrum of Chlorophyll A
A question to think about:
- Look at the spectrum for Chlorophyll A.
- What color is clorophyll?
- Where is that color on the spectrum?
- What is the absorbance at this color?
Absorbance vs. Transmittance
Absorbance and Transmittance are related. As one goes up, the other goes down
Absorbance is the amout of light that is blocked by sample molecules
Transmittance is the amout of light that passes through the solution.
But HOW are they related?
Obtaining an Absorbance Spectrum
Laboratory Details
You will take each of the solutions you already made, and create an absorbance spectrum for each one. To do this you will use the spectrophotometer to select a wavelength of light and measure and record the absorbance of the sample at that wavelength.
Use the labeled picture below to guide youself through the steps for taking an absorbance measurement.
1). Tune the spectrophotometer to the desired wavelength
2). Load a cuvette with the solvent used in your sample
What did you use to make your solution? Water? Acid? Base? This is your solvent, and this is what you will use to tare the spectrophotometer.
Make sure the clear sides of the cuvett are in the direction of the light.
3). Place the cuvette in the spectrophotometer, and close it. Then tare the spectrophotometer.
This is just like taring a balance. You are telling the spectrophotometer that whatever light it is measuring, should be equal to zero absorbance.
4). Once the spectrophotometer is tared, then remove the solvent cuvette, and load a cuvette with your sample. Record the absorbance value that it gives you.
5). This procedure NEEDS to be repeated at EACH wavelength.
Absorbance is different for EVERY chemical at EVERY wavelength, so every time you change one of them, the spectrophotometer will need to be tared
Once you have your data all recorded, then you can plot each of your absorbance spectra
Y-axis will be the absorbance values
X-axis will be the wavelength
Look at the absorbance spectra that you create.
- Look at the maximum absorbance in your graph
- Look at the minimum absorbance in your graph
- What color are your solutions?
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Experiment Goal
Generating and Using a Calibration Graph
Calibration Graphs are used to determine many things. In this experiment you are using a calibration graph to relate absorbance and concentration. They are used in many fields to relate a quantity with something you can physically measure. In the lab, you will prepare standards of a known concnetration, and plot a calibration graph. You will then use that graph to figure out the concentration of an unknown sample.
Terms you will need to know for the experiment
Dillution
Linear
Straight Line
Line of Best Fit
Absorbance
Concentration
Unknown
Concepts you will learn
What is a dillution factor?
What is a line of best fit?
What is a calibration graph and how do you use it?
Skills you will learn
How to dillute samples
How to generate and plot a calibration graph
How to work with the calibration graph to be able to determine an unknown
Generating and Using a Calibration Graph
Solution Dilution!
Now that you've taken absorbance spectra and plotted absorbance vs. wavelength, it's time to make a calibration graph, and plot absorbance vs. concentration. First though, you'll need solutions of different concentrations, and to do that, you need to make dillutions.
Dillution measurments use the equation:
Where M1 is the molarity of the first solution and M2 is the molarity of the second, and V1 and V2 are the volumes.
This is actually a condensed equation of two molarity equations. Let's walk through how it comes to this.
You want to make a 50mL of a 0.03M solution . You have a 0.1M solution .
We can start with the Molarity Equation
Start with what you want. You want 50mL of a 0.03M solution. You have a volume and a concentration so you can find how many moles of your compound will be in there. Try doing this!
Scroll here to check your answer!
Now that you know the number of moles you need, now you need to find a volume of your current solution, that has that many moles in it. Your current solution is 0.1M So how many mL would you need, to have that many moles?
Scoll here to check your answer!
Now that you found how many mL of your stock solution you need, how many mL of water will you need to add?
Scroll here to check your answer!
That was the long way of doing this problem. You can also use the simplified equation of
You want 50mL of a 0.03M solution. You have a volume and a concentration for one of the solutions, so that will go on one side
M1 = 0.03M
V1 = 50mL
You also have the concentration of the other solution. You have a stock solution of 0.1M
M2 = 0.1M
Now that you've worked through a problem, try some additional practice problems!
Generating and Using a Calibration Graph
Laboratory Details
When you're actually in the lab, then you can do these calculations yourselves on real samples. Many times though, you can decide for yourself what the volumes you need are. 1mL, 10mL, 20mL, 100mL Just remember, you have to be able to measure the volumes needed accurately. To do that, you will use your burets.
This is what a CLOSED buret looks like. When filling the buret, make sure that it is closed so that what you pour in, doesn't pour right out!
When you are making your dilutions, you will need two (2) burets, one for you initial stock solution, and one for your solvent (whatever you used to make your stock solution, e.g. water, acid, ammonia)
- You will fill your two burets to above the fill line, then open the buret to adjust the volume to the filled mark.
- You will then measure out the desired amount of your solution, and then the desired amount of your solvent.
- Mix it, and then you have your diluted solution.
The video below shows exactly what you will do in lab.
Now try to answer these questions about the video. You may need to watch it again.
Generating and Using a Calibration Graph
Beer's Law
In the example of a calibration graph for this experiment, you are plotting absorbance vs. concentration, as opposed to an absorbance spectrum where you are plotting absorbance vs. wavelength. But how are wavelength and concentration related to absorbance? They are all related in through the Beer-Lambert Law.
The main absorbance equation is the Beer-Lambert Law which is:
Where A is the absorbance
ε is the molar absorptivity constant . This is different for every chemical, at every wavelength
l is the path length , the distance of solution that the light has to travel through
c is the concentration of the solution
The absorbance is based primarily on those three factors
Molar Absorptivity Constant
The Molar Absorptivity Constant is specific for every single solution, and at every wavelength. When you are taking an absorbance spectrum, and measuring the absorbance at different wavelengths, this is the only factor that is changing, as the concentration of the solution remains the same, and so does the pathlength. The path length of each vial is the same, and the concentration of each of these solutions is the same, yet the solutions are all different colors and will therefore absorb differently. The only difference to change the absorbance, is the Molar Absorptivity Constant.
Questions to think about:
- Would the absorbance change if you use a different solvent?
- Which of the three factors would be affected by the change in solvent?
Path Length
The path length also affects absorbance. With a longer path length, the light has to travel through more solution, and can hit more molecules, and be absorbed. This would make the aborbance increase and make the solution appear darker.
The pictures below show how solutions appear when you look through a longer pathlength.
The image to the left shows a container with three compartments. Each compartment has the same solution but filled to different levels. When looking through the solutions horizontally, they all appear the same color because the path length is the same for all three. However, when you look at the image to the right, where the view is from the top, you can see that the solutions get darker as you move from left to right.
This can also be seen in absorbance spectra, where as the pathlength is increased, the absorbance is also increased.
Using this information, and the spectra in the figure, see how the path length would effect the absorbance in the following questions.
Some important information is that path length is rarely ever changed away from 1.0 cm.
Concentration
The last component of Beer's Law, is concentration. Concentration effects the absorbance very similarly to path length. If the concentration of solution is increased, then there are more molecules for the light to hit when it passes through.
As the concentration increases, there are more molecules in the solution, and more light is blocked. This causes the solution to get darker because less light can get through.
Generating and Using a Calibration Graph
The Calibration Graph
When you take an absorbance spectrum, you are looking at the absorbance based on wavelength. But when making a calibration graph you are looking at the absorbance based on concentration.
The two plots above are an Absorbance spectrum on the left, and a calibration plot on the left.
Both are plotting absorbance, but the spectrum plots it vs. wavelength (molar absorptivity constant) and the calibration plot is vs. concentration.
Try a Math Question about the two graphs above!
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IMPORTANT NOTE!!!!!!
Beer's Law ONLY is linear at LOW concentrations!
If the absorbance of your sample is above 1.0 you will need to dillute your sample in order to lower the absorbance
You cannot extrapolate your calibration line, because there is a deviation from a straight line at higher concentrations.
Having trouble with straight lines? Not to worry, here are some very helpfull sites to help you out!
- For information on "The Equation of a Straight Line"
- For information on "Best Fit Line"
- For information on "Scatter Plot with Fitted Regression Line (Excel)" 2003 Format
Generating and Using a Calibration Graph
Now You Try!
Now try opening a plotting progam and try making a calibration plot of your own. Please use the following values.
The Wavelength used for this calibration graph was 410nm REMEBER THIS!!!
Make sure to include the following whenever you make your calibration graphs!
ALWAYS make sure they are labeled!
- Title (Include wavelength used)
- Axis
- Axis Titles
- Line of Best Fit
- Equation of the Line of Best Fit
Hint for plotting a line of best fit!
Make sure to FORCE your best fit line to go through the origin
Beer's Law has an intercept through the origin, so your best fit line should reflect that.
Another way to find the slope of a line, when you do not have a fitting program available, on a test for example, would be to calculate the slope. This would give you a less accurate slope, but would still be acceptable when a fitting program is not available.
IMPORTANT NOTE!!! On ANY Report or Exam, ALWAYS show your work when you preform any calculation!
Generating and Using a Calibration Graph
How to Work with Plots
You have two different plots, you absorbance spectrum on the left, and your calibration plot on the right.
First a couple questions
First look at the absorbance spectrum. These spectra were taken using different concentrations.
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Choosing Your Wavelength
Look at the images above. The left is an absorbance spectrum of 0.13mM plastocyanin, while on the right is a calibration plot at two wavelengths.
Is the slope of the calibration line at 550nm greater than, less than, or equal to the slope at 600nm?
You can choose any wavelenght to create a calibration plot, the only differerence will be the slope of the line.
When you actually choose your wavelength to create your calibration graph, you would generally like to choose a wavelength where there is room for the concentration to decrease. Look at the spectrum above. Do you think 450nm would be a good wavelength to use for a calibration graph? You would not choose that wavelength because when you lower the concentration, you would not be able to see much of a difference in the absorbance, and the calculations would be inaccurate. You would most likely want to choose wavelengths like 600nm or 250nm where there is a lot of room for absorbance change.
Generating and Using a Calibration Graph
Using your Calibration Graph!
Now for the fun part! Using the calibration plot that YOU made from the data two pages ago. We are going to determing the concentration of an unknown solution. Make sure you have your plot ready, because here we go!
Here's a typical problem. You take 3mL of your unknown sample and 7mL water and mix them together. The dilluted sample gives an absorbance of 0.432. What is the concentration of the initial unknown?
Where do you begin?! Well, you have your calibration graph, and it SHOULD look something like this, all properly labeled.
1). You have an absorbance, and you have a straight line equation that relates absorbance to concentration. This is the line of best fit through your data.
2). Now this is the absorbance of your DILUTED solution. But what was the concentration of your ORIGINAL solution? Remember you dilluted it once, so you can use the Dilution Equation
Ready to try one on your own?
Need some practice? Here are a few more problems. Try to figure them out on your own!
Common Errors In Calibration Plots
- Spectrophotomer is not calibrated
- Abs readings are incorrect
- Diluted samples are prepared incorrectly or contaminated
- Inappropriate wavelength chosen for calibration graph
- The calibration line is not a "best fit" line
Post Experiment Problems
After you finish your experiment, see if you can answer these problems below. These problems are very similar to those that will be found on your exams, and are an indication of if you are understanding the material fully. Make sure to read the questions carefully and think about your answers, as you may see similar problems later on (hint hint!)
Question Set 1
This question set deals with the first part of this tutorial. The preparation and dilution of solutions.
a). You need to prepare 100mL of 0.1M Cu(NO3)2
How many grams of Cu(NO3)2 * 3H2O will you need to weigh out?
b). Instead of using a volumetric flask, a student used a graduated cylinder to add 100mL of water to a beaker containing the solid. The resulting solution was too concentrated. Why?
c), You add 5 mL of 0.10 M Cu(NO3)2 to 15 mL of distilled water. What is the concentration (M) of Cu2+ (aq) in the resulting solution (assume that the final volume is 20 mL)?
d). How many mmol of NO3 - (aq) are in the resulting solution?
e). You need to prepare 25 ml of 0.25 M nickel perchlorate, Ni(ClO4)2.(aq). The reagent available is Ni(ClO4)2•3H2O.
How many grams of Ni(ClO4)2•3H2O should you weigh out?
f). How many mmol of perchlorate anions, ClO4 - , are in the 25 ml, 0.25 M solution?
g). You also need to prepare a 0.10 M solution of nickel perchlorate. How many mL of the 0.25 M Ni(ClO4)2(aq) should you add to a 10 mL volumetric flask in order to make a 0.10 M solution (after you have added the 0.25 M Ni(ClO4)2, the volumetric flask will be filled to the line with water to give 10 mL of solution)
h). You prepare 0.10 M Rb2S from 0.50 M Rb2S. Only 50 mL of 0.50 M Rb2S is available. What volume (mL) of 0.10 M Rb2S can you make using 50 mL of 0.50 M Rb2S?
Question Set 2
This question set deals with the second part of this tutorial. The preparation and usage of absorbance spectra and calibration graphs, as well as the use of the Beer Lambert Law.
These questions involve using a spectrophotometer to determine the concentration of a ion (M+) aqueous solution. The graphs below show the absorption spectrum for a 0.40 M solution of M+ and a calibration graph
a). What color is the aqueous solution M+?
b). At what wavelength was the calibration graph obtained?
c). A solution M+ is diluted by taking 4.00 mL of M+ solution and adding enough water to give 20.0 mL. The absorbance of the diluted solution is 0.65 at the wavelength that was used to construct the calibration graph (above). What is the molarity of the undiluted sample?
The graph below shows the absorption spectra for an indicator in acidic and basic solutions. In both cases [indicator] = 1.0 x 10-3 M.
d). What color is this indicator in acid and basic solution?
e). Based on the above specta, which of the following statements are correct?
1. As the solution becomes more basic, % transmission increases at l = 600 nm. (Note that the above graph gives absorbance, not % of transmission.)
2. In acidic solution, the absorption coefficient ( e ) increases as l increases from 500 to 600 mm.
f). An acidic solution of the indicator has an absorbance of 0.25 at l = 575 nm. What is [indicator] in this solution?
Final Thoughts
READ THE DIRECTIONS!!
You're Done! See you next experiment!
Questions?
For questions please attend the office hours of the GSI's or contact Nancy Kerner
nkerner(at)umich.edu
How to Determine Molar Absorptivity From a Graph
Source: http://websites.umich.edu/~chem125/softchalk/Exp2_Final/Exp2_Final_print.html
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