How to Calculate Concentration With a Spectrophotometer

By John Brennan
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Spectrophotometry is an invaluable tool in chemistry and biology. The basic idea is simple: different substances absorb light/electromagnetic radiation better at some wavelengths than at others. That's why some materials are transparent while others are colored, for example. When you shine light of a given wavelength through a solution, the higher its concentration, the more light it will absorb. To calculate the concentration, you need to compare your reading with readings for standards of known concentration. The procedure below is a fairly generic procedure written with a chemistry teaching lab in mind, but it can be modified for other settings as well.

As always when working in a lab, put on your goggles, gloves and long-sleeved coat to ensure your own safety.

Squeeze the rubber bulb to empty it of air, then place it atop your graduated pipet and allow the bulb to relax so it sucks water up into the pipet. Next, remove the bulb, and cap the top of the pipet with your finger; this will seal the pipet so that the solution inside doesn't flow out until your finger is removed. Lift the edge of your finger slightly to let a little solution flow out of the pipet, until you reach your desired volume. Practice with some water and a beaker to get a feel for how the graduated pipet works. The link under the Resources section has a film clip to show you how to use a pipet in case you've never worked with one before.

Label 5 test tubes as standards 1-5. You can label them using masking tape and a pen or using a dry erase marker.

Choose five concentrations for your standards. You want the standard concentrations to be separated from each other by about the same interval -- e.g., 0.1 molar, 0.2 molar, 0.3 molar, etc. -- and in about the same range as what you expect your unknown will be. For the time being, use the following five concentrations, but remember that you will need to modify these when performing your own experiment:

Standard 1: 0.1 molar

Standard 2: 0.2 molar

Standard 3: 0.3 molar

Standard 4: 0.4 molar

Standard 5: 0.5 molar

Next, take the 1 molar standard solution and add the following amounts to test tubes 1-5. Remember, these amounts are calculated using the concentrations listed above, so you may need to modify them as needed when performing your own experiment.

Standard 1: 0.8 milliliters

Standard 2: 1.6 milliliters

Standard 3: 2.4 milliliters

Standard 4: 3.2 milliliters

Standard 5: 4 milliliters

Rinse the graduated pipet, then transfer the following amounts of deionized water:

Standard 1: 7.2 milliliters

Standard 2: 6.4 milliliters

Standard 3: 5.6 milliliters

Standard 4: 4.8 milliliters

Standard 5: 4.0 milliliters

Basically, the idea is to bring the amount of solution in each tube up to 8 milliliters.

Cap each of the standards tubes with parafilm and invert them to mix.

Mark another five test tubes as "Unknown 1-5." Add the same amounts of your unknown or test solution to each as you used with the 1 molar solution for the standards. In other words, unknown 1 will contain 0.8 milliliters of test solution and 7.2 milliliters of water, unknown 2 will contain 1.6 milliliters of test solution and 6.4 milliliters of water, and so forth.

Cap each of the unknowns with parafilm, and carefully invert to mix.

Turn on the spectrophotometer and allow it to warm up. The length of time necessary will depend on the model and the manufacturer.

Set the wavelength on the spectrophotometer. The wavelength will depend on the type of chemical in your experiment. For now, assume 500 nm, although remember that you will need to change this for different experiments.

Calibrate your spectrophotometer. The calibration procedure will vary depending on the device you are using. For the Spectronic 20, a common model in teaching labs, you will first adjust the machine so that it reads "0 percent T" when no cuvette is loaded, then adjust it so it reads "100 % T" when a blank cuvette containing deionized water only is loaded. These procedures may vary depending on the kind of machine you are using, so consult the manufacturer's instructions for details.

After the machine is calibrated, take the standard 1 test tube and pour the contents into a clean cuvette until they reach the fill line. Wipe the cuvette with a kimwipe to remove any fingerprints or other dirt. Insert the cuvette into the spectrophotometer and record the "%T" reading.

Repeat this procedure for all 10 samples. BE CERTAIN to clean the cuvette between samples to make sure your results are as accurate as possible.

Take the results for your standards and enter them into a spreadsheet/graphing program like Excel or OpenOffice.

Using the spreadsheet program, divide 100 percent by each of the "%T" values for the standards, then take the log of the result. This calculation will give you the absorbance. If you input the formula, your spreadsheet program will do the calculation for you.

Example: If the %T is 50.6, the formula you input into the spreadsheet program would be as follows:

log (100 / 50.6)

The spreadsheet program will do the arithmetic.

Do the same for all five unknown/experimental values.

Graph the absorbance values for all five standards, with concentration on the x-axis and absorbance on the y-axis. Using the spreadsheet program, fit a linear equation to this graph. The equation will be of the form y = mx + b. Most spreadsheet programs will have a linear regression function. Consult the user's manual for your spreadsheet program for details about how to use the linear regression feature.

Take the equation for the best-fit line from your spreadsheet program and solve it for y by subtracting b from both sides and dividing both sides by m. The result will look like the following:

(y - b)/m = x

where b and m are values found by your spreadsheet program.

Check your absorbance values for the unknowns, and pick three that fall about in the same range as the standards. Use these three absorbance values for your remaining calculations. If all five fall in the same range as the standards, you can use all five instead, but you need to use at least three.

Plug each of the three absorbance values into your equation in place of y. Remember that your equation was in the following form:

(y - b)/m = x

So, you'll want to plug the absorbance value for each unknown into the equation in place of y, then calculate x. You can use the spreadsheet program to do this calculation for you and make it quicker. You have now calculated the concentration of the chemical of interest in three of your diluted unknowns. The original solution was diluted to prepare these unknowns, however, so you now need to work backwards and calculate the concentration of the original solution based on the dilution factor.

Each unknown sample you inserted into the spectrophotometer was diluted by a different amount. Consequently, you should now divide the concentration you have calculated based on the absorbance for each unknown reading by the following:

Unknown 1: Divide by 0.1

Unknown 2: Divide by 0.2

Unknown 3: Divide by 0.3

Unknown 4: Divide by 0.4

Unknown 5: Divide by 0.5

Remember, however, that these figures are based on the assumption you are using the dilutions outlined above. Remember to change these values if you diluted your samples by a different amount.

Add your results together, and divide them by the number of results. This will give you an average. Report this number as your finding for the concentration of the original solution.

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