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Enthalpy and Entropy

Key Facts & Summary:

  • Enthalpy is the heat content of a system. The enthalpy change of a reaction is equivalent to the amount of energy lost or gained during the reaction.
  • A reaction is favoured if the enthalpy of the system decreases over the reaction
  • Entropy refers to the measure of the level of disorder in a thermodynamic system
  • For any process to occur to occur spontaneously, it is a necessary condition that the entropy of the system undergoing the process should increase.
  • Gibbs Free Energy is used to measure the amount of available energy that a chemical reaction provides

Thermodynamics is the study of the relationship between heat and work and we need to be familiar with the 3 important laws of thermodynamics, in order to understand this topic.

The law of thermodynamic

-First law: Energy is conserved; it can be neither created nor destroyed.

-Second law: In an isolated system, natural processes are spontaneous when they lead to an increase in disorder, or entropy.

-Third law: The entropy of a perfect crystal is zero when the temperature of the crystal is equal to absolute zero (0 K).

Enthalpy

Enthalpy is the heat content of a system. As we all know, the heat can go in or out of the system. If this system is a chemical reaction, the change of heat is called enthalpy change. Knowing if the enthalpy of the system increases or decreases,during a chemical reaction is a crucial factor to understand if that reaction can happen.The change in the enthalpy of the system during a chemical reaction is defined as the change in its internal energy plus the change in the product of the pressure times the volume of the system:

ΔH = ΔE + Δ(PV)

 where ΔH = change of enthalpy

ΔE = change of internal energy

             Δ (PV) = change of Pressure x Volume of the system

As enthalpy is a state function and it is dependent on the changes between the initial and the final state. Based on this, we can define two types of chemical reactions: exothermic and endothermic.

Exothermic reactions are those in which there is a release of heat and energy is given out to the surroundings. In this type of reaction he enthalpy of the products is lower than the enthalpy of the reactants and consequently the enthalpy change or ∆H is negative.

Endothermic reactions are those in which there is an absorption of heat from the surroundings environment. Here, the enthalpy of the products is higher than the enthalpy of the reactants and the enthalpy change or '∆H' is positive.

The enthalpy of a reaction can be calculated as follows:

∆H = ∑ nH  products -∑ mH reactants

where n =  coefficients of the products

m = coefficients of the reactants

∑ = sum of

Also, The difference between ∆H and ∆E for a system is small for reactions that involve only liquids and solids because, as you can imagine, there is little change in the volume of the system during the reaction. However, this difference can be significant for reactions that involve gases, if there is a change in the number of moles of gas in the course of the reaction.

Entropy

Entropy refers to the measure of the level of disorder in a thermodynamic system. It is measured as joules per kelvin (J/K) and denoted by the symbol 'S'.  For any spontaneous process, the entropy of the system should increase. Entropy is calculated in terms of change as well and defined with the following formula:

 ∆S = ∆Q / T

where ΔS = change of entropy

ΔQ= change of heat content of the system

             T = temperature of the system

This equation is for a thermodynamically reversible process.

Ludwig Boltzmann defines entropy as the measure of the number of possible microscopic configurations of the atoms and molecules in accordance with the macroscopic state of the system. It can be described with the following equation:

S = KB ln W

where,
S = the entropy of an ideal gas

KB = Boltzmann's constant

W = the number of microstates corresponding to a given macrostate

Based on this definition, solids have lowest entropy due to their more regular crystalline structure; liquids have an intermediate entropy as they are more ordered than gas but less ordered than solids; Gases are known to have the highest entropy as they have the most disorder.

Relationship between enthalpy and entropy

In order to define the relationship that exists between entropy and enthalpy, we need to introduce a new concept: The Gibbs free energy

Gibbs Free Energy is used to measure the amount of available energy that a chemical reaction provides. As reactions are usually temperature dependent, and sometimes work significantly better at some temperatures than others, the ΔGf° values known are only valid at 25°C (298.15 K).

Similar to the equations for ΔH and ΔS for a system,  ΔG is defined as the difference between the sum of the free energy of formation values of the products and reactants:

ΔG reaction = ΣΔG products - ΔΣG reactants
or simplified

ΔG  = ΣΔG  - ΔΣG

If a reaction is not spontaneous, its ΔG will be positive. If a reaction is spontaneous, its ΔG will be negative.

It's important to note that spontaneous does not necessarily mean that the specific reaction proceeds at high rate. A spontaneous reaction can take ages to go to completion. A classic example is the rusting of metal.

Going back to enthalpy and entropy, we can define the relationships between these two values, correlating them with the Gibbs free energy. For all temperatures, including 25°C, the following equation can be used to determine spontaneity of a chemical reaction:

ΔG = ΔH – TΔS

This equation is valid only if:

  • The temperature is in Kelvin, which is done by adding 273.15 to the Celsius temperature.
  • S of the reaction is converted to kJ/K.

The value calculated for ΔG is considered an approximate, especially as the temperature moves further away from 25°C as both ΔH and ΔS will vary with temperature. A change of ΔS will impact ΔG tends less. This is because ΔS is measured in units of J/K and when converted to kJ/K it is numerically small. A small change of ΔH  but can have a great impact on ΔG.

Further readings

https://chem.libretexts.org/Textbook_Maps/Organic_Chemistry/Map%3A_Organic_Chemistry_%28Smith%29/Chapter_06%3A_Understanding_Organic_Reactions/6.06_Enthalpy_and_Entropy

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch21/gibbs.php

Chemistry: An Introduction to Organic, Inorganic and Physical Chemistry by Prof Catherine Housecroft, Prof Edwin Constable