Free Energy, Entropy, Thermodynamic Equilibrium

Entropy, Free Energy and Thermodynamic Equilibrium

Chemical reactions are performed by mixing the reactants and regulating external conditions such as temperature and pressure. Two basic questions though arise:

1. Is it possible for the reaction to occur at the selected conditions?
2. If the reaction proceeds, what determines the ratio of products and reactants at equilibrium? 

Both questions are answered by chemical thermodynamics:

Thermodynamics can tell us whether a proposed reaction is spontaneous (possible) under particular conditions even before the actual experiment.
Thermodynamics can also predict the ratio of products and reactants at equilibrium provided that the reaction is spontaneous.

Note: Thermodynamics cannot answer though how fast a reaction will proceed.

 

After many years of observation scientists concluded that the characteristic common to all spontaneous processes (processes that occur without outside intervention) is an increase in the property called entropy (S).

 

How entropy is defined?

A precise, quantitative definition of entropy was proposed by the Austrian physicist Ludwig Boltzmann in the late 19th century. According to this definition entropy is related to probability:

If a system has several states available to it, the one that can be achieved in the greatest number of ways (has the largest number of microstates) is the one most likely to occur. The state with the greatest probability has the highest entropy.

S = k_B . lnΩ

Where,

k_B is Boltzmann’s constant (R/N_A)

Ω is the number of microstates corresponding to a given state (including both position and energy)

Note: The above definition of entropy is not useful in a practical sense for the typical types of samples used by chemists because those samples contain so many components (for example 1 mole of gas contains 6.022 x 10²³ individual particles).

 

How entropy is associated with chemical processes?

Entropy changes, ΔS – not S – are associated with changes of state (from solid to liquid, liquid to gas…). Since a change of state – for example from solid to liquid – at a substance’s melting point is a reversible process, we can calculate the change in entropy for this process by using the equation:

ΔS = q_rev / T = ΔΗ / Τ      (at constant temperature T and pressure P)

Where:

ΔS change in entropy that occurs during the change of state

q_rev  = ΔΗ / Τ  energy required for the reversible process to occur (for example energy required to melt 1 mole of solid at the melting point, ΔΗ is the enthalpy change of fusion)

T is the temperature where the change of state occurs (melting point, boiling point)