CHEM 1412 Concept Review: Free Energy & Thermodynamics

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Entropy and the Second Law of Thermodynamics

Entropy:  The level of randomness or “disorder” within a system.  This disorder is related to the number of possible energy and motion arrangements or “microstates” that exist within a system.  Entropy is represented by the symbol “S”.

$S=k\cdot\ln W$

Where k is the Boltzmann constant and W is the number of possible microstates in a system.

 

The Second Law of Thermodynamics:  For every spontaneous process, the entropy of the universe will always increase.  This law is expressed in the following two equations:

Reversible process (At equilibrium):	$\Delta S_{universe}=\Delta S_{system}+\Delta S_{surroundings}=0$
Irreversible process (Spontaneously moves forward):	$\Delta S_{universe}=\Delta S_{system}+\Delta S_{surroundings}>0$

 

Other relationships related to entropy and the equations above are as follows:

$\Delta S_{surr}=-\frac{\Delta H_{system}}{T}$      AND      $\Delta S=\frac{q_{rev}}{T}$          (Only true for systems at constant T)

Where T is the temperature in Kelvin, is the enthalpy change of the system, and q_rev is the heat change for a reversible process.

 

$\Delta S^\circ=\sum nS^\circ\left(products\right)-\sum mS^\circ\left(reactants\right)$

Where “n” and “m” are stoichiometric coefficients of the balanced chemical equation

 

 

Gibbs Free Energy:  What It Is and What It Tells You

Gibbs Free Energy (G):  The amount of chemical energy present within the chemical substances that is free to do useful work.  The maximum amount of work that is capable of being done by a reaction can be determined by the change in Gibbs Free Energy from reactants to products, which is represented by the symbol “∆G”.  This quantity is dependent upon two other thermodynamic quantities, ∆H (enthalpy) and ∆S (entropy, see above definition).  The equation relating them is given below:  

$\Delta G=\Delta H-T\Delta S$

The sign of ∆G (positive or negative) can be used to determine whether or not a process is spontaneous. 

 

-∆G means spontaneous:  A negative value for Gibbs means that the products of a reaction have less energy that is free to do work than the reactants.  This is because the reaction releases some of the reactants’ energy and can use it to do work, making that energy unavailable later on.  Since the reactants have more energy than the products to begin with, no outside energy is needed to make the reaction proceed, and the reaction can occur on its own. 

+∆G means non-spontaneous:  A positive value for ∆G indicates that the products of a reaction have more energy that is free to do work than the reactants.  Since energy cannot be created or destroyed (1^st law of thermodynamics), such a reaction cannot occur on its own.  For the products to have more free energy than the reactants, energy must be added from the outside environment (i.e.-from another reaction, electricity, etc.) for the reaction to proceed.

 

$\Delta G^\circ_{rxn}=\sum n\Delta G_{\:f}^\circ\left(products\right)-\sum m\Delta G_{\:f}^\circ\left(reactants\right)$

∆G_f^o or “free energy of formation” is the free energy change corresponding to the formation of 1 mole of a given substance from its component elements in their standard state under standard conditions (25^oC and 1 atm pressure).  Many of these standard values can be found in the back of your book in Appendix II, Section B or on the internet.  You will NOT be required to memorize these.

 

 

A Closer Look at Gibbs Energy:

 

Reversible Process (at equilibrium):	$\Delta G=\Delta H_{system}-T\Delta S_{system}=0$
Irreversible Process (spontaneous):	$\Delta G=\Delta H_{system}-T\Delta S_{system}<0$
Unsustainable Process (non-spontaneous):	$\Delta G=\Delta H_{system}-T\Delta S_{system}>0$

 

Sign of $\Delta H$	Sign of $\Delta S$	Low Temperatures	High Temperatures
$-$	$+$ (makes –TΔS negative)	Spontaneous ($\Delta G<0$)	Spontaneous ($\Delta G<0$)
$-$	$-$ (makes –TΔS positive)	Spontaneous ($\Delta G<0$) The reaction releases enough energy to overcome the activation energy barrier and the surroundings are capable of receiving the excess energy, allowing the system to attain a more ordered state that forming the products requires.	Non-spontaneous ($\Delta G>0$) High temperatures make it impossible for the system to release enough heat into the surroundings for the system to attain a more ordered state.
$+$	$+$ (makes –TΔS negative)	Non-spontaneous ($\Delta G>0$) The reactants cannot absorb enough energy from the surroundings to attain the more disordered state of the products due to low temperatures.	Spontaneous ($\Delta G<0$) The reactants can easily absorb enough energy from the surroundings to attain the more disordered state of the products due to high temperatures.
$+$	$-$ (makes –TΔS positive)	Non-spontaneous ($\Delta G>0$)	Non-spontaneous ($\Delta G>0$)

 

 

Gibbs Energy vs. Work

$\Delta G=-w_{\max}$

Where w_max is the maximum amount of work that a process is capable of doing

 

 

Gibbs Free Energy at Non-Standard Conditions

$\Delta G=\Delta G^\circ+RT\ln Q$

Where $\Delta G^\circ$ is the standard free energy change for the reaction, $\Delta G$ is the free energy change for the reaction under non-standard conditions, Q is the reaction quotient, T is the temperature in Kelvin, and R is the Ideal Gas Constant $\left(8.314\:\frac{J}{mol\cdot K}\right)$

 

 

Gibbs Free Energy and Equilibrium Constant

$\Delta G^\circ=-RT\ln K$

Where K is the equilibrium constant