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Determination of Kc for a Complex Ion Formation

  • Page ID
    379780
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    Objectives
    • Find the value of the equilibrium constant for formation of \(\ce{FeSCN^{2+}}\) by using the visible light absorption of the complex ion.
    • Use the equilibrium constant to predict the equilibrium concentration of product, and the absorption of the reaction mix.

    In the study of chemical reactions, we first study reactions that go to completion. Inherent in these familiar problems—such as calculation of theoretical yield, limiting reactant, and percent yield—is the assumption that the reaction can consume all of one or more reactants to produce products. In fact, most reactions do not behave this way. Instead, reactions reach a state where both reactants and products are present. This mixture is called the equilibrium state; at this point, chemical reaction occurs in both directions at equal rates. Therefore, once the equilibrium state has been reached, no further change occurs in the concentrations of reactants and products.

    The equilibrium constant, \(K\), is used to quantify the equilibrium state. The expression for the equilibrium constant for a reaction is determined by examining the balanced chemical equation. For a reaction involving aqueous reactants and products, the equilibrium constant is expressed as a ratio between reactant and product concentrations, where each term is raised to the power of its reaction coefficient (Equation \ref{1}). The value of this constant at equilibrium is always the same, regardless of the initial reaction concentrations. At a given temperature, whether the reactants are mixed in their exact stoichiometric ratios or one reactant is initially present in large excess, the ratio described by the equilibrium constant expression will be achieved once the reaction composition stops changing.

    \[a \text{A} (aq) + b\text{B} (aq) \ce{<=>}c\text{C} (aq) + d\text{D} (aq) \]

    with \[ K_{c}= \frac{[\text{C}]^{c}[\text{D}]^{d}}{[\text{A}]^{a}[\text{B}]^{b}} \label{1}\]

    We will be studying the reaction that forms the reddish-orange iron (III) thiocyanate complex ion, \(\ce{Fe(H2O)5SCN^{2+}}\) (Equation \ref{2}). The actual reaction involves the displacement of a water ligand by thiocyanate ligand, \(\ce{SCN^{-}}\) and is often call a ligand exchange reaction.

    \[\ce{Fe(H2O)6^{3+} (aq) + SCN^{-} (aq) <=> Fe(H2O)5SCN^{2+} (aq) + H2O (l)} \label{2}\]

    For simplicity, and because water ligands do not change the net charge of the species, water can be omitted from the formulas of \(\ce{Fe(H2O)6^{3+}}\) and \(\ce{Fe(H2O)5SCN^{2+}}\); thus \(\ce{Fe(H2O)6^{3+}}\) is usually written as \(\ce{Fe^{3+}}\) and \(\ce{Fe(H2O)5SCN^{2+}}\) is written as \(\ce{FeSCN^{2+}}\) (Equation \ref{3}). Also, because the concentration of liquid water is essentially unchanged in an aqueous solution, we can write a simpler expression for \(K_{c}\) that expresses the equilibrium condition only in terms of species with variable concentrations.

    \[\ce{Fe^{3+} (aq) + SCN^{-} (aq) <=> FeSCN^{2+} (aq)} \label{3}\]

    In this experiment, you will create several different aqueous mixtures of \(\ce{Fe^{3+}}\) and \(\ce{SCN^{-}}\). Since this reaction reaches equilibrium nearly instantly, these mixtures turn reddish-orange very quickly due to the formation of the product \(\ce{FeSCN^{2+}}\) (aq). The intensity of the color of the mixtures is proportional to the concentration of product formed at equilibrium. As long as all mixtures are measured at the same temperature, the ratio described in Equation \ref{3} will be the same.

     

    Avoiding crowds at the spectrophotometer and the hood

    This lab has experimental and computational tasks. If you find yourself in a line at the spec or the hood, ask yourself whether you could work on the computational tasks instead, making better use of your time.

    Measurement of [\(\ce{FeSCN^{2+}}\)]

    Since the complex ion product is the only strongly colored species in the system, its concentration can be determined by measuring the intensity of the orange color in equilibrium systems of these ions. To measure the color of the complex, we will use spectrophotometry at a wavelength of 447 nm and use a standard curve to estimate concentrations of the colored complex.

    A standard curve is a plot of absorbances, \(A_{447 \mathrm{nm}}\), vs. concentrations, \(c\), for several solutions with known concentration of \(\ce{FeSCN^{2+}}\). We will provide the standard curve, and you will use it to estimate unknown concentrations from their absorbance.

    Calculations

    In order to determine the value of \(K_{c}\), the equilibrium values of \([\ce{Fe^{3+}}]\), \([\ce{SCN^{–}}]\), and \([\ce{FeSCN^{2+}}]\) must be known. The equilibrium value of \([\ce{FeSCN^{2+}}]\) will be determined by spectrophotometry as described above; its initial value was zero, since no \(\ce{FeSCN^{2+}}\) was added to the solution.

    The equilibrium values of \([\ce{Fe^{3+}}]\) and \([\ce{SCN^{-}}]\) can be determined from a reaction table ('ICE' table) as shown in Table 1. The initial concentrations of the reactants—that is, \([\ce{Fe^{3+}}]\) and \([\ce{SCN^{-}}]\) prior to any reaction—can be found by a dilution calculation based on the values from Table 2 found in the procedure.

    Students at each bench are responsible for calculating one set of initial concentrations and writing it on the board after checking that everyone got the same answer. Be prepared to show your work to everyone in case there is a question about your results. The initial concentrations for mixture 1 are already given in the results sheet. The "shower" bench will do mixture 2, the "projector" bench will do mixture 3, and the "fire alarm" bench will do mixture 4.

    Once the reaction reaches equilibrium, we assume that the reaction has shifted forward by an amount, \(x\). The equilibrium concentrations of the reactants, \(\ce{Fe^{3+}}\) and \(\ce{SCN^{-}}\), are found by subtracting the equilibrium \([\ce{FeSCN^{2+}}]\) from the initial values. Once all the equilibrium values are known, they can be applied to Equation \ref{3} to determine the value of \(K_{c}\).

    Table 1:

    Reaction \ref{3} \(\ce{Fe^{3+}}\) \(\ce{+\quad SCN^{-}}\) \(\ce{<=> FeSCN^{2+}}\)
    Initial Concentration \([\ce{Fe^{3+}}]_{i}\) \([\ce{SCN^{-}}]_{i}\) 0
    Change in Concentration \(- x\) \(- x\) \(+ x\)
    Equilibrium Concentration \([\ce{Fe^{3+}}]_{i} - x\) \([\ce{SCN^{-}}]_{i} - x\) \(x= [\ce{FeSCN^{2+}}]\)

    The reaction "ICE" table demonstrates the method used in order to find the equilibrium concentrations of each species. The values that come directly from the experimental procedure are found in the shaded regions. From these values, the remainder of the table can be completed.

    Procedure

    Materials and Equipment

    Solutions: Iron(III) nitrate (2.00 x 10–3 M) in 1 M \(\ce{HNO3}\); Potassium thiocyanate (2.00 x 10–3 M).

    Materials:

    Test tubes (large and medium size), stirring rod, two 10- mL graduated pipets, Pasteur pipets, ruler, spectrometers and special-size test tubes at the spectrophotometer.

    Safety

    The iron(III) nitrate solutions contain nitric acid. Avoid contact with skin and eyes; wash hands and all glassware thoroughly after the experiment. Collect all your solutions during the lab and dispose of them in the proper waste container.

    Part A: Solution Preparation

    Into a clean, dry 150-mL beaker, pour 30-40 mL of 2.00 x 10–3 M \(\ce{Fe(NO3)3}\) (already dissolved by the stockroom in 1 M \(\ce{HNO3}\)). Then pour 25-30 mL of 2.00 x 10–3 M \(\ce{KSCN}\) into a clean, dry 50-mL beaker. At your work area, label five clean and dry medium test tubes to be used for the five test mixtures you will make. Add 5.00 mL of your 2.00 x 10–3 M \(\ce{Fe(NO3)3}\) solution into each of the five test tubes. Next, add the correct amount of \(\ce{KSCN}\) solution to each of the labeled test tubes, according to the table below. Then, add the appropriate amount of deionized water into each of the labeled test tubes. Stir each solution thoroughly with your stirring rod until a uniform orange color is obtained. To avoid contaminating the solutions, rinse and dry your stirring rod after stirring each solution.

    Four solutions will be prepared from 2.00 x 10–3 M \(\ce{KSCN}\) and 2.00 x 10–3 M \(\ce{Fe(NO3)3}\) according to this table. Note that the total volume for each mixture is 10.00 mL, assuming volumes are additive. If the mixtures are prepared properly, the solutions will gradually be darker in color from the first to the fourth mixture. Use this table to perform dilution calculations to find the initial reactant concentrations.

    Table 2: Test Mixtures

    Experiment # V in mL
    \(\ce{Fe(NO3)3}\) Solution
    V in mL
    \(\ce{KSCN}\) Solution
    V in mL
    Water
    1 5.00 1.00 4.00
    2 5.00 2.00 3.00
    3 5.00 4.00 1.00
    4 5.00 5.00 0.00

     

    Part B: Spectrophotometric Determination of \([\ce{FeSCN^{2+}}]\)

    To measure the absorbance, transfer your solution into one of the special-size test tubes next to the spectrophotometer, and insert it into the instrument. Once the reading is stable, record it. Then, using the standard curve provided, record the corresponding concentration of the complex. Repeat for all 4 equilibrium mixtures.

    Part C: Determine the equilibrium constant

    For each mixture, determine all the concentrations at equilibrium (using an ICE table or other method of choice), and calculate the equilibrium constant. If our theoretical assumptions and our experimental data were perfect, you should get the same equilibrium constant for all four measurements. In practice, it probably makes sense to average the four values to get the best estimate of the "real" equilibrium constant.

    Part D: Predict the equilibrium concentrations for a new set of starting concentrations

    For a solution containing 1.00 x 10–3 M \(\ce{Fe^{2+}}\) and 0.60  x 10–3 M \(\ce{SCN-}\), what is the equilibrium concentration of the \(\ce{FeSCN^{2+}}\) complex? Use an ICE table (or other method) to predict the equilibrium concentration. Also, figure out the recipe to get those initial concentration of iron and thiocyanide ions (experiment *5* in the tables on the summary sheet). Then, make the mixture and test the concentration of complex formed spectrophotometrically to check your prediction.


    This page titled Determination of Kc for a Complex Ion Formation is shared under a CC BY-NC license and was authored, remixed, and/or curated by Santa Monica College.