Using Colourimetry to Calculate Equilibrium Constant

This is part of the HSC Chemistry course under the topic Calculating Equilibrium Constant

HSC Chemistry Syllabus

  • conduct an investigation to determine Keq of a chemical equilibrium system, for example:

 Keq of the iron(III) thiocyanate equilibrium (ACSCH096)


Colourimetry and Iron(III) Thiocyanate Equilibrium 

What is Colourimetry?

Colourimetry is an analytical technique widely used in chemistry to measure the concentration of a coloured substance in a solution. One application of this method is to determine the equilibrium constant of a reaction. In this article, we will focus on the use of colorimetry to calculate the equilibrium constant for the formation of iron thiocyanate, a common topic in HSC Chemistry courses.


The Iron(III) Thiocyanate System

The reaction of interest is the formation of iron thiocyanate complex, which is a reversible reaction:


$$Fe^{3+} (aq) + SCN^- (aq) ⇌ FeSCN^{2+} (aq)$$


The equilibrium constant, Keq, for this reaction can be determined by measuring the concentration of each species at equilibrium.


Using Colorimetry to Determine Concentrations

Colorimetry relies on the principle that the absorbance of light by a coloured solution is proportional to the concentration of the coloured substance. In our case, the coloured substance is the iron thiocyanate complex (`FeSCN^{2+}`), which has a deep red colour.

The relationship between absorbance and concentration is described by the Beer-Lambert Law:


$$A = εcl$$


Where A is the absorbance, ε is the molar absorptivity, c is the concentration, and l is the path length (usually 1 cm).

To use colorimetry for determining the concentration of `FeSCN^{2+}`, follow these steps:


1. Prepare a series of standard solutions: Create a range of `FeSCN^{2+}` solutions with known concentrations by mixing known volumes of `Fe^{3+}` and `SCN^-` solutions. Make sure to use the same total volume for each solution to maintain consistency.

2. Measure the absorbance: Use a colorimeter or spectrophotometer to measure the absorbance of each standard solution at a specific wavelength (typically around 447 nm for `FeSCN^{2+}`). Make sure to set the instrument to zero absorbance using a blank solution (i.e., only water without `FeSCN^{2+}`).

3. Create a calibration curve: Plot the absorbance values against the known concentrations of `FeSCN^{2+}` in your standard solutions. This curve will allow you to determine the concentration of `FeSCN^{2+}` in an unknown solution based on its absorbance.


Figure 1: Calibration curve showing the absorbance value of various standard solutions of iron(III) thiocyanate. 


4. Measure the absorbance of the equilibrium mixture: Prepare an equilibrium mixture by mixing known volumes of `Fe^{3+}` and `SCN^{-}` solutions and allowing the reaction to reach equilibrium. Measure the absorbance of this mixture using the same wavelength as before. 


5. Determine the concentration of `FeSCN^{2+}`: Use the calibration curve to find the concentration of `FeSCN^{2+}` in the equilibrium mixture based on its absorbance.


Table 1: equilibrium concentrations determined from measuring the absorbance of each iron(III) thiocyanate equilibrium mixture.

Calculating the Equilibrium Constant

Now that you have determined the concentration of `FeSCN^{2+}` at equilibrium, you can calculate the equilibrium constant, `K_{eq}`. To do this, you also need to determine the concentrations of `Fe^{3+}` and `SCN^-` at equilibrium.

Since you know the initial concentrations of `Fe^{3+}` and `SCN^-` and the amount of `FeSCN^{2+}` formed, you can calculate the concentrations of the reactants at equilibrium:


$$[Fe^{3+}]_{eq} = [Fe^{3+}]_{initial} - [FeSCN^{2+}]_{eq}$$

$$[SCN^-]_{eq} = [SCN^-]_{initial} - [FeSCN^{2+}]_{eq}$$


With these concentrations, you can now calculate the equilibrium constant:


$$K_{eq} = \frac{[FeSCN^{2+}]_{eq}}{[Fe^{3+}]_{eq} \times [SCN^-]_{eq}}$$


Table 2: equilibrium constant is calculated using equilibrium concentrations.


Previous section: Calculating Reaction Quotient, Effect of Temperature on Equilibrium 

Next section: Gibbs Free Energy and Equilibrium (Extension)