Chesapeake Campus – Chemistry 112 Laboratory

LAB #8 –Determination of an Equilibrium Constant

Objectives

After completing this lab, you will be able to:

• Create a standard curve using a spectrophotometer.
• Calculate the equilibrium constant, K, for the formation of the complex Fe(SCN)2+ IntroductionBackground:

  *You may wish to review the Introduction from Lab 4: Absorption Spectroscopy to make ure you understand how to use a spectrophotometer. For this lab, it will be assumed that you have reviewed the protocol involved with using the Spectrophotometer, calculating absorbance, and making a standard curve.

  A chemical reaction of the sort expressed by the following chemical equation, aA+bB ⇿ cC+dD

  actually consists of two competing processes: the forward reaction, that is the formation of the products, C and D, from the reactants, and the reverse reaction, which is the formation of the reactants, A and B, from the products. When the rates of these two processes equal each other, there is no net change in the concentration of either the products or the reactants, and the reaction is said to be at equilibrium. The ratio of the equilibrium concentrations of the products to the equilibrium concentrations of the reactants is a constant, as shown by the following equation:

  [C]c [D]d
  K = [A]a[B]b Equation 1

  where K is the equilibrium constant. The brackets signify the concentrations of the various species in molarity, and the lower case letters represent the number of moles of each substance involved in the balanced equation. The equilibrium constant is dependent on temperature. Also, reactants and products that appear as pure solids or pure liquids in the chemical equation (as opposed to species in solution or gaseous species) do not appear in the equilibrium constant expression.

  You will examine equilibrium conditions of the reaction between iron (III) and thiocyanic acid:

Fe3+ (aq) + SCN- (aq) ⇿ FeSCN2+ (aq) The expression for this equilibrium constant is:

K = [FeSCN2+] Equation 2 [Fe3+] [SCN−]

In order to determine the value for this K, it is necessary to find the equilibrium concentrations of each of the species involved in the expression. We can carry out the reaction under conditions where the concentration of H+ remains constant and thus is known. In addition, we can determine the concentration of FeSCN2+ spectrophotometrically, and then use this value in calculating the equilibrium concentrations of SCN- and Fe3+ knowing their initial concentrations and the stoichiometry of the reaction.

Calculations

The equilibrium concentration for FeSCN2+
The value for [FeSCN2+] at equilibrium will be determined from a spectrophotometric

measurement employing Beer’s Law (see Lab 4: Absorption Spectroscopy):
A = εcb Equation 3

where A is the absorbance of a solution, ε is the molar absorptivity, c is the concentration of the solution in moles/liter and b is the length of the absorption cell that contains the solution. You and your classmates will prepare a series of standard solutions in order to construct a calibration curve. (A standard solution is one whose concentration is accurately known.) In preparing these standards, a LARGE excess of Fe3+ ion is used so that all the SCN– ion is converted to FeSCN2+. Thus after mixing, the concentration of FeSCN2+ in the standard solution will be equal to the initial concentration of SCN-. The absorbance of a solution can be measured directly on a spectrophotometer. The wavelength of light must be specified and is usually chosen to coincide with a wave- length wherein the substance absorbs most strongly. In the equilibrium you will examine, the wavelength of choice is 447 nm for the FeSCN2+ complex.

Once the absorbance values of these standard solutions have been determined, you will plot absorbance, A, versus concentration, c, for the species FeSCN2+. The concentration of FeSCN2+ at equilibrium will be determined using this curve and the absorbance values that you obtain for the equilibrium solutions.
The equilibrium concentrations for Fe3+ and SCN-

It is now necessary to determine the equilibrium concentrations for Fe3+ and SCN-. Upon examination of the chemical equation for the reaction, we see that for every mole of FeSCN2+ formed, one mole of Fe3+ and one mole of SCN- are consumed. Therefore, the equilibrium number of moles of Fe3+ or SCN-, is equal to the initial number of moles of Fe3+ or SCN-, minus the number of moles of FeSCN2+ present at equilibrium.

Notice that the ICE chart below takes advantage of the 1:1 ratio between all substances in this reaction. Here we will work with moles and then use volume to convert moles of each substance at equilibrium to the concentration used in the equilibrium calculation.

Fe3+ (aq)

a – x

+

SCN- (aq)

b – x

↔ FeSCN2+ (aq) 0

+x x

Initial moles Change Equilibrium moles

We can calculate the number of moles of FeSCN2+ using the equilibrium concentration obtained from the spectrophotometric measurement. Thus, the concentrations of Fe3+ and SCN- at equilibrium can be calculated using the following expressions:

[Fe3+]= a−x V

[SCN-] == b−x V

where a = initial number of moles of Fe3+, b = initial number of moles of SCN-, x = number of moles of FeSCN2+ at equilibrium and V = total volume of equilibrium solution.

The equilibrium constant, K

We can now substitute the equilibrium concentrations of all the species into the equilibrium expression (Equation 2) and calculate K.

Le Chatelier’s Principle

When the conditions of a system at equilibrium are altered, the system responds in such a way as to maintain the equilibrium. In 1888, Henri-Lewis Le Chatelier described this phenomenon in a principle that states, “when a change in temperature, pressure or concentration disturbs a system in chemical equilibrium, the change will be counteracted by an alteration in the equilibrium composition.” You will observe this principle at work in the reversible reaction between the iron (III) ion and the thiocyanate ion:

Fe3+ (aq) + SCN– (aq) ⇿ FeSCN2+ (aq) Equation 4

You will selectively alter the concentration of one of the ions by adding a reagent that reacts to form an insoluble salt with the ion, causing it to precipitate out of solution. In addition, you will observe the effect that a temperature change has on the solution at equilibrium, which will allow you to conclude whether the reaction is exothermic or endothermic.