# 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

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