Determining the equilibrium constant of a chemical reaction can provide important information about the extent to which it will form products over time.

Every chemical reaction is associated with an equilibrium constant, K, which reflects the ratio of the concentrations of the products and reactants when the reaction has stopped progressing. To measure K, these concentrations must be determined.

If a reaction contains a single colored component, its interaction with light can be measured to discern its concentration. The concentrations of the uncolored components can then be calculated indirectly using the balanced chemical equation. This video will illustrate the use of a spectrophotometer to empirically determine the equilibrium constant for an iron thiocyanante reaction.

Most chemical reactions proceed in both forward and reverse directions. As the reaction progresses, it reaches a point where the forward and reverse reactions occur at the same rate. This is known as chemical equilibrium. At this steady state, the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients, corresponds to the equilibrium constant, K. To measure K for a system of interest, the coefficients should be known, and the concentrations must be determined, either directly or indirectly. According to the Beer-Lambert law, the concentration of a colored species is proportional to its absorbance, which is the amount of energy it absorbs at a specific wavelength of light. This can be expressed mathematically, where A is absorbance, epsilon is the molar attenuation coefficient, which is compound-specific, l is the path length through the sample, and c is concentration. A calibration curve is created by testing multiple solutions of known concentration, and plotting the resulting absorbance values. With this calibration curve, solutions of unknown concentration can be studied. Absorbance measurements are used to determine the concentration of the colored species. Then, the concentrations of the remaining reactants and products can be calculated. The following procedure will study the reaction of iron three with thiocyanate to form an iron thiocyanate complex.

Once the concentrations have been determined, the value for K can be calculated with an Initial-Change-Equilibrium, or ICE, table which will be explained further in the results.

Now that you understand how spectrophotometric methods can be used to determine the equilibrium constant, you are ready to begin the procedure.

Before measuring the sample, a calibration curve must be generated.

To begin, zero a UV-vis spectrophotometer using distilled water as a blank to represent no absorbance. When inserting a cuvette into the spectrophotometer, ensure that it is oriented so light passes through the transparent sides, and that the liquid level is above the path of the beam.

Then, prepare 5 test tubes containing the indicated volumes of each reactant solution as shown in the text protocol, which will yield varying concentrations of the product. Cover each tube with a gloved finger, and gently shake to mix. Allow the tubes to rest for 10 min.

Use a Pasteur pipette to transfer a small quantity of the mid-concentration sample, solution 3, to a cuvette, and place it in the spectrophotometer. Acquire a spectrum and record the λmax (maximum wavelength), lambda max, and its absorbance. Then, beginning with the most dilute solution, measure the absorbance of all remaining solutions at the λmax (lambda max). Use the same cuvette for all measurements, making sure to rinse 3 times in between each sample. Repeat this process for solutions 2 – 5.

Plot the measured absorbance versus concentration of iron thiocyanate for each solution. Determine the line of best fit for the data. The slope of this line is the molar attenuation coefficient.

Now that the data for the standard solutions has been acquired, prepare four medium test tubes containing the indicated volumes of solutions as shown in the text protocol.

Cover each tube with a finger and gently shake to mix. Allow them to stand for at least 10 min. This resting period allows the solutions to reach chemical equilibrium.

Use a Pasteur pipette to transfer a small quantity of solution 6 to the cuvette, and place it in the spectrophotometer. Acquire a spectrum and record the absorbance measured at the predetermined λmax. Repeat this process for solutions 7 through 9.

Once all of the samples have been measured, the molarity and absorbance data for solutions 1 – 5 can be analyzed. A large excess of thiocyanate was used to ensure that all of the iron reacted, which simplifies the analysis.

The data is plotted to create a calibration curve. The path length of light, l, is typically 1 cm, and can be factored out of the calculations. The slope of the line, which was calculated to be 7600, is therefore the attenuation coefficient. For the test solutions 6 – 9, this value and the absorbance are used to calculate the iron thiocyanate concentrations at equilibrium. With this data, the ICE table could then be utilized.

The initial reactant concentrations are based on the known molarities of iron and thiocyanate added to the solution, and the total volume of the reaction. Because the product is formed from the 1:1 reaction of iron and thiocyanate, the equilibrium concentration of each decreases by the amount of product formed. The equilibrium concentration of each species is now known. These values are used to calculate the equilibrium constant for each solution. The values are roughly constant over the range of concentrations studied.

The concept of the equilibrium constant is important to a wide range of scientific fields. The equilibrium constant can be used to provide useful information about the extent to which a reaction will form products over time. In this example, two reactions containing crystal violet were observed.

The first solution was composed of crystal violet and sodium hydroxide. The color was observed to rapidly change from purple to colorless. This reaction has a very large K value, indicating that the products form nearly completely over time.

Crystal violet was then reacted with sodium acetate. This solution remained purple indefinitely. This reaction has a very low K value, so it does not proceed forward to a significant degree.

Finally, the dissociation constant — a specific type of equilibrium constant — can be used to describe protein behavior. In this example, changes in the structure of RNA were monitored in magnesium reaction buffers.

Purified RNA was mixed into solution with known concentrations of magnesium, and allowed to reach equilibrium. Then, the resulting RNA structure was plotted.

In this case, higher concentrations of magnesium caused reactive sites on RNA to be less protected, producing a Kd that was half the value.

You've just watched JoVE's introduction to spectrophotometric determination of the equilibrium constant. You should now understand the relationship defined by the Beer-Lambert law, how to determine concentration from absorbance using a spectrophotometer, and how to calculate an equilibrium constant using equilibrium concentrations.

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