Science Buddies: "Ask an Expert"

Hello,
I'm really having a tough time with 2 things. First, I don't completely understand how to find the total concentration of dye from the light absorption. Second, what are the units for the equation, especially the molar absorption coefficient?
Thanks, IMK

Hi IMKudaimi,

I’m assuming that you are working on the project described here:

https://www.sciencebuddies.org/science- ... inks.shtml

To calculate the dye concentration from the light absorption you have to calibrate your spectrophotometer. This involves measuring the light absorption for solutions with known dye concentrations. These data are used to make a chart showing the straight-line relationship between the dye concentrations and the light absorption values. The chart can be used to find the dye concentration in sports drink sample for which you’ve measured the light absorption.

The units for the variables included in equation 1 are given in the background section of the project. The unit for the molar absorption coefficient is Liters/(mole X cm).

I hope this helps. Please post again if you have more questions.

A. Norman

Thank you.
A couple of other things.
So when you find the Molar absorption coefficient, you multiple the liters of the drink by something? Or am I understanding it wrongly?
Also, so you mean for the concentration, you compare the sports drink light absorption to the other dye concentrations' (the ones you put food coloring in) light absorption? If it's the same light absorption, it's the same total concentrations?
Lastly, after subtracting the resistence of the water from the average resistance of the drink, and put that on the y-axis, do you put the concentration levels on the x-axis or something else? Or am I missing something there too/

Thanks, IMKudaimi

And one more thing, when measuring the path length in cm, is it just till it reaches the solution or from the resistor to the LED? And what is the x in moles x cm? I understand moles per liter for concentration but not moles x cm for the molar absorption coefficient?

Hi IMKudaimi,

The molar absorption coefficient is a factor in the Beer-Lambert equation (equation 1 in the project background). But you don’t calculate the coefficient’s value in the project. The calibration curve that you make according to the project procedure includes the molar absorption coefficient and path length so that you don’t need to “find” either factor.

Take a look at equation 1. The molar absorption coefficient is a constant for a given chemical (the blue dye) and light wavelength. The path length is also a constant for a given cuvette size (the container for your dye solutions). Because these two factors are constants in this experiment, the light absorption (A in equation 1) only varies if the amount of dye in the solution changes (the concentration, or c in equation 1).

Concentration refers to the number of moles of the dye per liter of solution. Let’s say that the path length is 1 cm. The light absorption has no units. So the units of the molar absorption coefficient must cancel the concentration (moles/Liter) and the path length (cm) units. Thus the coefficient has units of Liters/mole multiplied by 1/cm. This also can be written as Liters/(mole X cm). Here the “X” means “multiply by”.

The purpose of the calibration curve is to show the relationship between the concentration of the blue dye and the absorbance (resistance) of the dye solution. Once you have this relationship you can use it to find the concentration of blue dye in “unknown” solutions like the sports drinks.

The calibration curve is a graph of the dye concentration on the x-axis and the resistance on the y-axis. Your calibration curve should be a straight line. Find the resistance value you measured for a sports drink sample on the y-axis of the calibration graph. Next, move along a horizontal line from the resistance value on the y-axis to the point where the horizontal line intersects the calibration curve. Now move along a vertical line to the x-axis. The intersection at the x-axis is the concentration for your sports drink sample.

I hope this helps. Please post again if you have more questions.

A. Norman

Thank you very much and just 2 last things:
1. Does the higher the resistance, the higher the concentration come into play here (is that true)? Does that mean the trend line will be up with the higher concentration and resistance?
2. And what if the calibration curve cannot be in a straight line because of the data you found?

Thanks, and this is probably all for now,
IMKudaimi

Hi IMKudaimi,

Higher concentration of dye in the solution causes higher resistance in your spectrophotometer’s photoresistor. The resistance is directly related to light absorption so higher concentration also means more light absorption. And yes, the calibration data will show an upward trend.

The calibration data should “fit” a straight line. That means that you should be able to draw in a straight line that is positioned so that your calibration data points are as close to the line as possible. It’s OK if some of your data lie above and below the line. Just try to draw in a line with the data evenly distributed around it. This is called a “best fit” line and it represents the average relationship between the independent variable (dye concentration) and the dependent variable (resistance).

An example chart that shows a “best fit” line for a data set can be viewed at this link:

http://serc.carleton.edu/mathyouneed/gr ... stfit.html


I hope this helps. Please post again if you have more questions.

A. Norman

Thanks you, and one very last thing:
When you write your calibration curve, do you label whenever you hit it while moving horizontally, do you label the drink? Also are there any labels for the solutions with known concentrations on the calibration curve?
Thank you very much, IMKudaimi

Hi IMKudaimi,

I’m not sure what you mean by “label”. When you make an x-y chart the usual practice is to plot some kind of marker or symbol for each data point. If this is the type of label you are asking about, I think you should mark your calibration data this way.

You could also put text identifiers next to some or all of the data points. I think that text labels next to your “unknown” sports drink data could be a good way to display your results. But you may find that too much text on your chart looks “cluttered”. Another option is to use different symbols to plot the data for the “unknown” drinks and include a legend on the chart to identify the various symbols. Or you could make a separate chart to display the results for “unknown” drinks. For example, a bar chart showing the dye concentrations you found might work well.

I hope this helps. Please post again if you have more questions.

A. Norman

Thank you,
I've run into a problem. Each time I put my dye samples with known concentrations, all of them say 0.07. I know that's impossible. What could I have done wrong?
IMKudaimi

Hi IMKudaimi,

I’m sorry that you are having a problem with your experiment. Some items you might check are as follows.

1. Is your multimeter set up to read resistance? You might want to refer to the link below for some details on how to do this.

https://www.sciencebuddies.org/science- ... resistance

2. Does your photoresistor respond to changes in light? You can check this by measuring the resistance is a darkened room (or with the photoresistor covered). The resistance should be very high – in the mega ohm range. Now measure the resistance with the lights on. The resistance should be much lower.

3. Are all the wires on your breadboard correctly placed and securely connected? You might want to re-check each of your connections.

I hope this helps. Please post again if you have more questions.

A. Norman

Hello,
I bought a new multimeter since the other one didn't work and for some reason all the sample solutions say 0.3. I was told that the multimeter is working as long as it does not display a 0. But is it really possible for all the solutions to have the same resistance? And if so, how can I make my calibration curve?
Thanks, IMKudaimi

Hi IMKudaimi,

Your calibration solutions should not have the same resistance readings. Rather, higher dye concentrations should give greater resistance readings.

Is your multimeter set to read resistance? If so, you may need to adjust the range of the meter. There’s more detailed information on setting up the multimeter in the tutorial (see the link in my previous post) and in steps 4 through 10 in part 1 of the project procedure.

Are you making resistance measurements for your solutions with the spectrometer circuit covered by a cardboard box to block ambient light? If not, “stray” light from the room may be interfering with your resistance measurements (see step 6 in part 1 and step 15 in part 2 of the procedure).

Does your photoresistor change resistance when the amount of light changes? Steps 4 through 10 in part 1 of the procedure describe one way to test the photoresistor. The resistance should be high when the photoresistor is in the dark and low when the photoresistor is in the light.

I hope this helps. Please post again if you have more questions.

A. Norman

Thanks, I was finally able to get it to work.
But there's one thing left: If I turn to 2000 ohms, then what decimal place is it? Is 794 actually 7.94?
Thanks, Idrees

Hello Idrees,

Glad to hear that your experiment is working now.

When you have your multimeter set to the 2000 ohms range a resistance of 794 ohms will display as 0.794 kilo ohms. In other words, you move the displayed decimal one place to the right for each zero in the range to get the resistance value in ohms.

The following link shows some examples of resistance readings with different range settings.

https://learn.sparkfun.com/tutorials/ho ... resistance

Good luck with your project. Please post again if you have more questions.

A. Norman

Thank you,
Now, after I find the concentration after measuring on the calibration curve, if i put the results on a table, then should I say, for instance, "The total concentration of this sample is 16 ?" Do I say 16 micrometers? Or something else?
Idrees

Also, one more thing,
I was using a proportional calculator to find where the results would intersect with the calibration curve, but they would always be different. For example, if I used the proportion for the 4.25 micrometers, which was 794 over 4.25, if I used it to find out the proportion for 1302 over X, it wouldbe different than using the proportion 1319 over 17. Why?
Thanks, Idrees

And after subtracting the blank sample from the other samples with known concentration, do I do the same for the sports drinks? And do I graph the water since now it is above the other samples on the scatterplot chart?

Hi Idrees,

You should report the sports drink concentrations with appropriate units. For this experiment you can use micromoles per liter (or uM/L) for the concentration units. For example you could say “the concentration for this sample is 16 uM/L” or “the concentration is 16 micromoles per liter”.

Regarding your next question, you found that the ratio of resistance/concentration was different for various samples from your calibration experiment. One explanation for this is that there’s some variation in the measurements and/or sample preparation. As a result of experimental variation, your calibration data might not form a perfect straight line. Instead, the data might “scatter” around a line. The inconsistent ratios you found might be due to this scatter.

The equation for a straight line is

Y= mX + b

where m is the slope of the line and b is the intercept (the intersection of the line and the Y-axis). You can see from this equation that the ratio Y/X is a constant (and equal to m) only if the intercept (b) is zero. In your experiment an intercept of zero implies a resistance of zero with no blue dye in the solution. Due to data scatter and some other possible factors, the intercept value for your data may not be zero. If that is the case then you will have different resistance/concentration ratios.

A better way of using the calibration data is to find the “best fit” of the data to a straight line. You can do this graphically or use a mathematical procedure called linear regression. Once you have a “best fit” line you can use the graph or linear equation to find the sports drink concentrations. Some details about the equation for a line are available at the following links.

https://www.mathsisfun.com/equation_of_line.html

https://www.mathsisfun.com/data/scatter-xy-plots.html

And about your last question. I think you should subtract the resistance for the blank sample from the sports drink readings. The purpose of subtracting the blank is to account for light loss due to the cuvette and other factors. All of these factors are present in the sports drink samples so it is appropriate to subtract the blank for these samples as well as the calibration standards.

The water sample is the blank. So the dye concentration is zero. Also, the resistance is zero after subtracting the blank from itself. My suggestion is to exclude the blank from your calibration chart.

I hope this helps. Please post again if you have more questions.

A. Norman