Determination of Thermodynamic Quantities for a Chemical
Reaction
Gezahegn Chaka, Ph. D.; Sudha Madhugiri, Ph. D.
Collin College Chemistry Department
Objectives
To calculate the thermodynamic quantities such as the changes in standard enthalpy,
standard entropy, and standard free energy using equilibrium constant values calculated
at various temperatures for a system of complexation reaction in aqueous solution.
Introduction
Thermodynamic parameters are extremely important in determining the feasibility of a
reaction and in real life a reaction which violates thermodynamic principles cannot be
performed. Many times, under standard state conditions, these parameters such as
enthalpy of a reaction
reaction (
, entropy of a reaction
and Gibb’s free energy of a
can be calculated by using the tabulated thermodynamic data and
without ever entering a lab and performing the reaction under consideration. However,
another useful application of these sets of data is that, the same information can be used
to calculate an experimentally derived quantity, the equilibrium constant (K). You
probably have learnt that a high equilibrium constant indicates a favorable reaction and
that a favorable reaction needs to proceed with a decrease in Gibb’s free energy. This
means we need a negative value for
for a favorable forward reaction and this should
lead to an equilibrium constant which is >1.
The Gibb’s Free energy can be used to calculate the equilibrium constant K by using the
relationship
Go = - R T lnK
(1)
In this experiment, we are going to turn the process around and use the equilibrium
constant K to calculate the free energy change Go. For this to happen, it becomes
essential for us to use a reaction which is reversible and the direction of the reaction needs
to be temperature sensitive. There are many reactions that fall under this category.
Copyright© 2014 Gezahegn Chaka and Sudha Madhugiri
However, CoCl2 . 6H2O lends itself to this type of experimentation as it can form
complexes with chloride ion ([CoCl4]2-) and water molecules ([Co(H2O)6]2+) each favored
at different temperature.
Co2+ ion binds with six molecules of water and forms an octahedral complex
[Co(H2O)6]2+, which is red in color, referred to as aqua complex. If chloride ion is
added to the complex, the water ligands slowly get replaced by the chloride ions
sequentially and Co2+ ion forms a tetrahedral complex [CoCl4]2- which is blue in color,
referred to as chloro complex. This transition is particularly useful for this experiment
because it is temperature dependent.
[Co(H2O)6]2+ (aq) + 4Cl- (aq)
Red
[CoCl4]2- + 6H2O(l)
Blue
As these complexes are colored, visible spectroscopy can be used to study these reactions
at various temperatures and the data obtained can be used to calculate the equilibrium
constant ‘K’ and then subsequently the thermodynamic quantities Gº, Hº and Sº.
The standard free energy change at a given temperature is itself related to both the change
in enthalpy, and the change in entropy, by the following equation:
∆Gº = ∆Hº - T∆Sº
(2)
This is a linear equation of the form y = mx + b. The slope of such a graph is related to the
change in standard entropy and the change in the standard enthalpy is related to the
y-intercept.
The Experiment
The complexation reaction between cobalt(II) and chloride ion in aqueous solution as
shown in the following chemical equation will be investigated.
[Co(H2O)6]2+ (aq) + 4Cl- (aq)
[CoCl4]2- + 6H2O(l)
The concentrations of the [Co(H2O)6]2+ and [CoCl4]2- in the equilibrium mixture will be
determined by a spectrophotometric method.
Copyright© 2014 Gezahegn Chaka and Sudha Madhugiri
Part 1: Take an aliquot of the 0.05 M CoCl2·6H2O solution that is in 6.0 M HCl. Use the
UV-visible spectrophotometer to record the absorbance spectrum of the equilibrium
mixture between 400 and 800 nm. For best results, record the absorbance every 10 nm
between 400 and 800 nm. Notice that you will see two peaks. One corresponding to the
aqua complex and another corresponding to the chloro complex .
Use Microsoft Excel to plot the absorbance versus wavelength data and determine λmax for
each of the complexes.
Part 2:
Set the wavelength of the spectrophotometer at the max value close to the 700 nm
obtained in part 1. Measure the absorbance values for the 0.05 M CoCl2·6H2O solution at
various temperatures 10oC, 20 oC, 30 oC, and 40 oC.

Calculate the concentration of the products formed in parts 2 using Beer’s Law.
The reported molar absorptivity value for for [CoCl4]2- at around 700 nm is
577.2 M-1cm-1.

Use the measured absorbance for the chloro complex and calculate the equilibrium
concentration of the chloro complex. Then, calculate the equilibrium
concentrations of the aqua complex using the ICE table.

Calculate the concentration of Cl- in the equilibrium mixture using chemical
stoichiometry principles and the ICE table.

Calculate the equilibrium constants for the reaction at those temperatures and
calculate the corresponding standard Gibbs free energies using equation 1.
Microsoft Excel can be very helpful to perform all these calculations easily.
Plot the data of temperature in Kelvin versus standard Gibbs free energies to determine
standard enthalpy and entropy changes for the reaction.
Copyright© 2014 Gezahegn Chaka and Sudha Madhugiri
Critical Data to Include in your Lab Report:

A table of equilibrium constants (K) for the reaction at the corresponding
temperatures using the law of mass action.

A table of free energy values (∆G) for the reaction at the corresponding temperatures.
This is most conveniently done using equation (1).

A graph of ∆Gº = ∆Hº - T∆Sº using equation (2) including the experimentally
determined ∆Sº and ∆Hº. The slope of this is related to change in standard
entropy. The y-intercept is related to the change in standard enthalpy.

All calculations

Discussions of how the data obtained relates to each other and what it means in terms
of spontaneous and nonspontaneous reactions.
References:
DeGrand, M. J.; Abrams, M. L.; Jenkins, J. L.; Welch, L. E. J. Chem. Educ. 2011, 88,
634-636
http://chemeducator.org/first/papers/s00897092213a.htm
Copyright© 2014 Gezahegn Chaka and Sudha Madhugiri