# Chemical Equilibrium

Let's calculate the equilibrium constant for a reaction using observed concentrations.

You need this equipment: 6 test tubes, test tube rack, pipette, 4 50-mL beakers, 3 10-mL graduated cylinders, 25-mL graduated cylinder, white paper, metric ruler

You need these materials: distilled water, .0020 M NaSCN, .20 M Fe(NO3)3

The condition in which the concentrations of all reactants and products in a closed system cease to change with time is called chemical equilibrium. Chemical equilibrium occurs when opposing reactions are proceeding at equal rates. The rate at which the products are formed from the reactants equals the rate at which the reactants are formed from the products. For equilibrium to occur, neither reactants nor products can escape from the system.

For any equilibrium reaction, there can be calculated a constant, K, that represents the ratio of the rate of the forward reaction to the rate of the reverse reaction. If this number is greater than 1, then the reaction will produce more products than reactants. If this number is smaller than 1, then the reaction will produce more reactants than products. The equilibrium constant can be calculated using the law of mass action.

The law of mass action expresses the relationship between the concentrations of the reactants and products at equilibrium in any reaction. For example, in the general equilibrium equation aA + bB ⇔ pP + qQ, where A, B, P, and Q are the chemical species involved, and a, b, p, and q are their coefficients in the balanced chemical equation, the equilibrium constant is expressed by the following equation:

K = [P]p[Q]q ÷ [A]a[B]b

The square brackets in this equation signify molar concentrations. This relationship is called the equilibrium-constant expression. In order to calculate the equilibrium constant, one need only substitute the observed molarities and the known stoichiometric coefficients with their corresponding symbols in the equilibrium-constant expression.

In this experiment, the reaction Fe3+ + SCN- ⇔ FeSCN2+ will be observed. Color intensity will be used as the gauge of concentration of FeSCN2+, since that ion has a reddish color. One standard solution will be prepared, and five other solutions of decreased concentration will be prepared to be compared with the standard. By comparing the color intensities and measuring the depths of the solutions, an equation can be set up to compare the concentration of the known solution to the concentration of the unknown solution. By multiplying the concentration of the standard by the depth of the standard and dividing by the depth of the unknown solution, the concentration of the unknown solution can be calculated. This is the basis for this experiment.

The value of the equilibrium constant can be calculated by using the concentrations obtained by the aforementioned method in the equilibrium-constant expression.

Procedure: (view)

1. 5 mL of .0020 M NaSCN was added to each of the six test tubes.
2. 5 mL of .20 M Fe(NO3)3 was added to the first test tube.
3. 10 mL of .20 M Fe(NO3)3 was added to the 25-mL graduated cylinder. The cylinder was filled to 25 mL with distilled water. The contents of the graduated cylinder were shaken to distribute the contents evenly.
4. 5 mL of the diluted solution was added to test tube 2. All but 10 mL of the solution was disposed from the cylinder, and again the cylinder was diluted to 25 mL. This procedure was repeated until each successive test tube had 5 mL of diluted solution added to it.
5. Once all of the test tubes had been filled with the diluted solution, each test tube was compared in color intensity to the standard test tube number 1. To compare the test tubes, the standard was placed on the left and the other test tube to the right. The test tubes were wrapped with a piece of white paper and were held over a piece of white paper under a light source. In order to judge color intensities, the test tubes were viewed from this perspective: (view)
6. If the color intensities did not appear equal, then some solution was pipetted out of the standard test tube, number 1. The solution was placed into a 50-mL beaker in case too much was taken out.
7. This comparison was performed for all five test tubes.

Observations: (view)

Test tube number Height of liquid (cm) Comparative height of standard (cm)
2 8.2 7.6
3 8.2 6.1
4 8.2 4.6
5 8.0 3.5
6 8.0 1.3

Results: (view)

In test tube 1, the initial concentration of Fe3+ is .1 M, because the solution was .2 M and the volume was doubled. The concentration of SCN- is constant, at .001 M.

Test tube [Fe3+] [SCN-]
1 0.1 0.001
2 0.04 0.001
3 0.016 0.001
4 0.0064 0.001
5 0.00256 0.001
6 0.001024 0.001

The equation for this reaction is Fe3+ + SCN- ⇔ FeSCN2+. The amount of FeSCN2+ can be determined by multiplying the concentration of FeSCN2+ by the depth of the standard test tube and dividing by the depth of the test tube being analyzed. The amount of Fe3+ will be determined by subtracting the amount of FeSCN2+ that forms from the original amount of Fe3+. The amount of SCN- can be determined by subtracting the amount of FeSCN2+ that forms from the amount of SCN- that was originally in the test tube.

Test tube [FeSCN2+] [Fe3+] [SCN-]
1 0.001 0.099 0
2 0.000927 0.039073 0.0000731707
3 0.000744 0.015256 0.000256098
4 0.000561 0.005839 0.000439024
5 0.000438 0.002123 0.0005625
6 0.000163 0.000862 0.0008375

To calculate K, the mass-action expression must be used. For this experiment, the mass action expression is:

[FeSCN2+] ÷ [Fe3+][SCN-]

To calculate K, simply substitute the determined concentrations for their corresponding symbols in the mass-action expression.

Test tube K
2 324.1781
3 190.4001
4 218.8341
5 366.4442
6 225.2233

Discussion: The values of K were within the general range of values specified as acceptable (100 to 999). There are several sources of error in this experiment. First and foremost, human error in determining color intensities produces a wide variety of possible values for the concentrations and thus for K. Furthermore, since graduated cylinders are highly inaccurate volumetric measuring devices, there is volumetric error, which affects concentration. Small errors accrue so that the last test tube analyzed has the most error. There were possible errors while preparing solutions. If the solutions were not thoroughly mixed, then the sample of solution used to precipitate the FeSCN2+ ion could have been of a higher molarity than the overall solution. Proper mixing is easy, yet any improper mixing produces crucial errors. Discrepancies in the widths of the test tubes made measuring the depth of the liquid less precise than it should have been; although the manufacturer makes each test tube a certain width, it is not precise to any measurable degree. There is no way to avoid measuring error, but it has a direct effect on the values of K that were calculated.

The theory associated with this experiment is the collision theory. This experiment was about equilibrium. Equilibrium is the condition at which the rate of the forward reaction equals the rate of the reverse reaction. Concentration is one of the factors that determine the rate of the reaction. The collision theory explains why concentration has a direct relationship to the rate of reaction. Solutions of higher concentrations have more collisions per unit time. With more collisions come more reactions; thus, higher concentration relates directly to more reactions. In order for two solutions of different concentrations to match each other in color intensity (or amount of ions present), there must be less of the more highly concentrated solution.

There are many ramifications to this experiment. Personal ramifications include the practice of the new laboratory technique of observation of color intensity as a means to calculating concentration. In industry, it is critical to know the equilibrium constant for any given reaction so that the rates and magnitudes of reactions can be controlled. For example, knowing the equilibrium constant for the Haber reaction, N2 + 3H2 ⇔ 2NH3, is critical for being able to control the speed and output of the reaction. The Haber reaction is just one example; the same principle applies for all chemical reactions, especially on a larger scale.

Questions: (view)

1. a. In order to ignore the other equilibria present, their equilibrium constants must be much smaller than the other equilibrium being studied. If the equilibrium constants are too large, then they will interfere with the equilibrium being studied.
b. The competing equilibria should have very little, if any, effect on the value of K determined in this experiment. Since FeSCN2+ is the only colored ion, no other ions will enter into the observation of color intensity. Thus, their existence is not critical to the observation of color intensity.

2. The assumption that all the SCN- in test tube 1 was converted to FeSCN2+ is reasonable. There should be a 95 to 99% reaction completion rate; the amount of SCN- that does not convert is impossible to calculate using available methods, and is therefore small enough to be negligible. The best value of K in this experiment is probably the median value, 218.8. The percent of SCN- in test tube 1 that was converted to FeSCN2+ can thus be determined:

```    218.8 = [FeSCN2+] ÷ [Fe3+][SCN-]
218.8 = (x) ÷ (.1−x)(.001−x)
x = .00095589
[SCN-] = .001−.00095589 = .00004411
% conversion = .00095589 ÷ .001 × 100 = 95.59% conversion
```

3. The values of K determined for test tubes 3, 4, and 5 are probably more reliable than those determined for tubes 2 or 6 because in tube 2, there is an overwhelming amount of Fe3+ that remains in the solution. In test tube 6, all of the measuring errors have accrued to the point that concentrations are not what they should be; the volumes are distorted from their supposed values. It is the most inaccurate sample because of the overdilution of Fe3+ that occurs in the 25-mL graduated cylinder.

4. The rationale behind the procedure and methodology in this experiment is simple. Since the concentrations can be calculated by comparing color intensities of samples to a known standard, setting up five trials will produce a variety of concentrations with different color intensities. Using the concentrations to satisfy a mass-action expression allows the values of K to be calculated for different concentrations of the colored ion, FeSCN2+. The value of K does not change with concentration, but accruing errors in the procedure make the value of K vary.

Conclusion: This experiment was successful. Although imprecise, the values of K were in the general range specified as correct. New procedures were practiced, and further understanding of equilibrium was gained.

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