Investigating Thermodynamic Relationships of Substituted Hydrocarbons

Introduction

There are multiple ways to measure the change in thermodynamic parameters (i.e., Gibb’s free energy, ΔG; enthalpy, ΔH; and entropy, ΔS) during a chemical reaction. Gas chromatography provides one methodology for determining these values because the retention times reported are a result of a reaction between the mobile phase running through the column and the stationary phase that resides on the column. Here, you will measure the equilibrium constant experienced between the mobile and stationary phases which will allow you to isolate the ΔG, ΔH, ΔS of the reaction.

The equilibrium constant is referred to as the distribution coefficient, Kc, and it can be expressed in terms of the capacity factor, k′

K_c = k′β

where β is the column phase ratio, a quantity typically given by the manufacturer. The Vernier Mini GC has a column phase ratio value of approximately 200.

Once the equilibrium constant (or distribution coefficient) is known, it is possible to determine various thermodynamic quantities. The standard Gibb’s free energy change involved in the mobile phase-stationary phase transition is calculated by:

ΔG^°= –RT ln(K_c)

By analyzing the retention time at more than one temperature, the enthalpy and entropy changes involved in the process can also be found.

ΔG^°=ΔH^°–TΔS^°

Objectives

In this experiment, you will

• Collect and analyze GC data from various samples.
• Calculate the equilibrium constant between the various compounds and the GC column.
• Use the equilibrium constant to identify the change in free energy of solution.
• From the temperature dependent data, calculate the change in enthalpy and entropy of the solution.
• Observe the changes in Gibb’s free energy with the number of carbon atoms in the samples studied.