# Gibbs free energy

1800s, Josiah Willard Gibbs, (1839-1903) submitted scientific papers which mathematically combined both enthalpy and entropy (the measure of energy release and disorder in a system respectively) that also incorporates the second law of thermodynamics:

Entropy can never decrease, only increase for a reaction to take place.

in order to measure the amount of free energy present within any given system.[1]

According to the second law of thermodynamics, a chemical reaction can only proceed spontaneously if there is a net increase in disorder I the universe. An increase in disorder of the universe can be expressed most conveniently in terms of a quantity called the free energy, G of a system. The value of G is of interest only when a system undergoes a change, such as a reaction, in such a case the value of delta G is critical. Energetically favourable reactions are those that decrease free energy and have a negative delta G, these reactions  add more to disorder to the universe.[2]

## Contents

### Why doesn't free energy = enthalpy - entropy?

#### Reasoning behind Gibbs equation

The signs for enthalpy and entropy must be opposites to each other, "because one function tends to a maximum and the other tends to a minimum." [3]As a consequence the one equation proposed for this "unknown energy function"[4] could be: ====

X= U - S
(where X = Function, U = Enthalpy, S = Entropy) [5]

Although this must be carried out under standard conditions, so U must be substituted for an H to demonstrate a constant pressure. (of 1atm) In addition to this, the units are wrong in our current equation; as we know, enthalpy is measure in joules (J) of energy, entropy on the other hand is measured in joules per kelvin. (J K-1) Thus, we must also multiply entropy (S) by temperature in Kelvin. (T) Giving us the following equation when delta symbols are incorporate to represent that this function is for free energy changes:

dG = dH - dTS
(where G = Free energy, H = Enthalpy, S = Entropy, T = Temperature, d = Change in associated function) [6]

#### Application

We can now determine each individual component of this equation, enthalpy change being determined via "calorimetric measurment" [7] to give us our value for dH; entropy can then be found if dG and temperature are known, the opposite can be said for determining dG itself with dS being our known value instead. For a reaction to be possible, it has been stated that the entropy of the universe is always increased. Consequently for a reaction to take place, dG must always be negative, with dS in the the equation for free energy exceeding that of the enthalpy change dH.

### References

1. Sadi, Carnot. (2013). Willard Gibbs. Available: http://www.eoht.info/page/Willard+Gibbs. Last accessed 28th Nov 2013.
2. Alberts et al.Molecular Biology of the Cell,(2008) 5th Ed. Page 75
3. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
4. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
5. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
6. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
7. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.