Experiment 16
Chemical Equilibrium: Finding a Constant, K_c

When Fe³⁺ and SCN^- are combined, equilibrium is established between these two ions and the FeSCN²⁺ ion. In order to calculate K_c for the reaction, it is necessary to know the concentrations of all ions at equilibrium: [FeSCN²⁺]_eq, [SCN^-]_eq, and [Fe³⁺]_eq. You will prepare four equilibrium systems containing different concentrations of these three ions. The equilibrium concentrations of the three ions will then be experimentally determined. These values will be substituted into the equilibrium constant expression to see if K_c is indeed constant.

In order to determine [FeSCN²⁺]_eq, you will use the colorimeter shown in Figure 1. The FeSCN²⁺ ion produces solutions with a red color. Because the red solutions absorb blue light very well, the blue LED setting on the colorimeter is used. The computer-interfaced colorimeter measures the amount of blue light absorbed by the colored solutions (absorbance, A). By comparing the absorbance of each equilibrium system, A_eq, to the absorbance of a standard solution, A_std, you can determine [FeSCN²⁺]_eq. The standard solution has a known FeSCN²⁺ concentration.

Figure 1

To prepare the standard solution, a very large concentration of Fe³⁺ will be added to a small initial concentration of SCN^- (hereafter referred to as [SCN^-]_i. The [Fe³⁺] in the standard solution is 100 times larger than [Fe³⁺] in the equilibrium mixtures. According to LeChatelier's principle, this high concentration forces the reaction far to the right, using up nearly 100% of the SCN^- ions. According to the balanced equation, for every one mole of SCN^- reacted, one mole of FeSCN²⁺ is produced. Thus [FeSCN²⁺]_std is assumed to be equal to [SCN^-]_i.

Combining two general equations, A_eq = k[C]_eq and A_std = k[C]_std, we can obtain the relationship given below, which has been made specific to this experiment. Assuming [FeSCN²⁺] and absorbance are related directly (Beer's Law), the concentration of FeSCN²⁺ for any of the equilibrium systems can be found by:

Knowing the [FeSCN²⁺]_eq allows you to determine the concentrations of the other two ions at equilibrium. For each mole of FeSCN²⁺ ions produced, one less mole of Fe³⁺ ions will be found in the solution (see the 1:1 ratio of coefficients in the equation on the previous page). The [Fe³⁺] can be determined by:

[Fe³⁺]_eq = [Fe³⁺]_i - [FeSCN²⁺]_eq

Because one mole of SCN^- is used up for each mole of FeSCN²⁺ ions produced, [SCN^-]_eq can be determined by:

[SCN^-]_eq = [SCN^-]_i – [FeSCN²⁺]eq

Knowing the values of [Fe³⁺]_eq, [SCN^-]_eq, and [FeSCN²⁺]_eq, you can now calculate the value of K_c, the equilibrium constant.