Enthalpy and Entropy

Enthalpy and Entropy are two significant terms related to thermodynamics. Both of them are partly related to each other in a reaction because the fundamental rule of any reaction is releasing or absorbing heat or energy. Relying on these two factors, a new product is formed through a standard reaction of several compounds.  

What is Enthalpy?

Enthalpy is defined as a change in internal energy and volume at constant pressure. It deals with the heat contained in any system. Thereby, it changes when heat enters or leaves a system. For example, it increases when heat is added and decreases when heat is withdrawn from that system. There are some molecules that take part in this change are called “internal enthalpy” and the molecules that do not are referred to as “external enthalpy”. The enthalpy is represented through the following equation.

                                                   E= U+ PV

Where E is enthalpy, U is the internal energy of any system, P is pressure, and V is volume. 

Change in Enthalpy

The change of enthalpy in a reaction is almost equivalent to the energy gained or lost during a reaction. Also, it is concluded that if the enthalpy decreases, a reaction is successful. The reason behind it is if a system participates in a reaction, it releases energy. Hence, its own energy content gets low, according to the fundamental concept of energetics. 

It happens because, during a chemical reaction, some bonds of reactions need to be broken to produce the product. Therefore, it requires some energy to break the bonds, and in return, some energy is released as well after the product is formed. This change in enthalpy is represented by  ΔH.

 Also, the equation looks like, 

                                  ΔH = ΔU +PΔV

Standard Enthalpy Change

It refers to a change in enthalpy that occurs in a reaction taking place under standard conditions and where the reactants are in a standard state. These standard states are also denoted as “reference states”. The symbol of standard enthalpy change is Delta H nought or H. In case of this change in a reaction; the symbol will become  ΔH⁰ᵣ. For example, record the standard enthalpy change in the reaction between H and O₂ to form water or H₂O. 

2H₂(g) + O₂(g)  →  2H₂O(I)         ΔH⁰ᵣ = -572kJmol⁻¹

If you observe the reaction, you will see that the energy is not at any specific substance. Instead, it is denoting that, if 2 moles of hydrogen gas reacts with 1 mole of oxygen gas, 2 moles of liquid water is made, and 572 kJ heat is created. 

Standard Conditions are-

298 K (25⁰ C).

Pressure- 1 bar or 100kPa. 

The concentration of a solution has to be 1 mol dm⁻³.

Standard States 

In case of a reaction, all the physical and chemical states have to be in standard condition. It means that the standard state of water is in liquid form and not in ice or water vapour. Similarly, the standard state of oxygen is its gas form. However, in the case of allotropic elements, we have to consider the one which is the most energetically stable. For example, oxygen under standard conditions exists as both O₂ and ozone (O₃), but O₂ is more stable energetically; hence it is oxygen’s standard state. 

Standard Enthalpy Change of Formation

It is expressed as ∆H⁰f. It happens when only 1 mole of product is formed in a reaction.

 For example,               

2H₂(g)        +      ½ O₂(g)       —--→      H₂O(I)   ΔH⁰f = -286kJmol⁻¹  

Don’t worry about fractions as 1 mole of water formed. That’s why the fraction in equations has to be there on the left-hand side. This reaction shows that to form 1 M of liquid water, 286 kJ heat evolves. 

Standard Enthalpy Change of Combustion 

It happens when in the presence of oxygen, 1 mole of any compound is completely burned. As burning always produces heat, the value of this change will be negative in all circumstances. Following is an example of such a reaction.

CH₄(g) + 2O₂(g)  →  CO₂(g) + 2H₂O(I)         ΔH⁰c = - 890kJmol⁻¹ 

From the above equation, it is proved that, whatever compound is burned, has to take 1 mole of its heat energy only. Also, it is to be noted that, the standard enthalpy change of combustion for hydrogen is the same as a change of formation of water.  

Types of Enthalpy Changes

The different types of enthalpy changes are:

• Enthalpy of Formation: It is the amount of energy required when one mole of a compound is formed from its constituent elements.

• Enthalpy of Combustion: It is the change in enthalpy when one mole of a compound is burnt completely in the presence of oxygen.

• Enthalpy of Neutralization: It is the change in enthalpy when one gram equivalent of acid reacts with base and forms water.

• Enthalpy of Hydrogenation: It is the change in enthalpy when one mole of an unsaturated organic compound reacts with excess hydrogen and becomes completely saturated.

What is Entropy?

Entropy is the measure of the disorder of the energy of a collection of particles. This idea is derived from Thermodynamics, which explains the heat transfer mechanism in a system. This term comes from Greek and means “a turning” point. It was first coined by Rudolf Clausius, a German physicist. He documented a precise form of the Second law of thermodynamics through entropy. 

It states that any spontaneous change in an isolated system for irreversible reaction always leads towards increasing entropy. For example, when we put a block of ice on a stove, these two make an integral part of a single isolated system. Thereby, the ice melts and entropy increases. Since all the spontaneous processes are irreversible, we can say that the entropy of the universe is increasing. Moreover, it can be concluded that more energy will be unavailable for work. Due to this, it is said that the universe is “running down”. 

The S.I unit of entropy is Joules per Kelvin. Also, it is expressed as ΔS, and the following is its equation. 

              ΔSsystem = Qrev / T

Where S denotes the change in entropy, Q denotes the reverse of heat and temperature is represented by T in the Kelvin scale. 

Absolute Entropy

It is a related term and is expressed by S. It is derived from the third law of thermodynamics. The entropy is zero at absolute zero, and it is made so by adding a constant. 

Entropy Characteristics

It increases with mass. In the course of vapourisation, melting and sublimation, entropy increases. When liquid or hard substances dissolve in water, entropy increases. In contrast, when gas is dissolved in the water, it decreases. In malleable solids such as metals, entropy is higher.

On the other hand, entropy is lesser in brittle and hard substances. As chemical complexity increases, the entropy increases as well.  

Calculation of Entropy 

In an isothermal reaction, the entropy change is defined as:   

ΔS = the change in heat (Q) divided by absolute temperature or T. The equation is as follows:

                 ΔS = Q/T

For a reversible thermodynamic process, entropy can be expressed in calculus as an integral from the initial state of a process to its final state that is dQ/T. More specifically, entropy is a measure of the probability and molecular randomness of a macroscopic entity. In a system that can be presented by variables, they can predict a certain number of changes. If each configuration is probable equally, then the entropy is the natural logarithm of the total number of changes, multiplied by Boltzmann's constant.

                                    S = kBln W                                        

Where kB is Boltzmann's constant, S is entropy, ln is the natural logarithm, and W denotes the number of possible states.

Note: Boltzmann's constant= 1.38065 × 10⁻²³ J/K.

Enthalpy and Entropy Relation

Also, enthalpy entropy and free energy are closely related to each other as both entropy and enthalpy are combined into a single value by Gibbs free energy. This free energy is dependent on chemical reactions for doing useful work. This relation was first stated in the 1070’s by Josiah Willard Gibbs. It is expressed by G. The equation is as follows -

                                                   G=H-TS

Where H is enthalpy, T is temperature and S is entropy. If we subtract the product of T and S from Enthalpy, we get Gibbs free energy.

 In constant temperature,

ΔG = ΔH – TΔS 

The direction of a chemical reaction is determined by ΔG. For a spontaneous process, G is negative, and for a non-spontaneous process, G is positive. 

DIY Question: Find out the value of T from the enthalpy and entropy change for the reaction below. 

Br₂(l) + Cl₂(g) → 2BrCl(g) 

Where ΔH is 30 kJ mol⁻¹ and ΔS is 105 J K mol⁻¹ 

Since, △G=0, then only system is at equilibrium. 

So, △G = △H - T△S 

At equilibrium, △H = T△S 

Teq = △H/△S​

     = 30 × 10³/105  

     = 285.7 K

Applications of Gibbs Free Energy Equation

1. The free energy and entropy change in KJ per mole when liquid water boils at atmospheric pressure of 1 atm respectively are…? (Latent heat of water is 2.0723 KJ g-1.)

ΔH vap of water= 2.0723 x 18 = 37.30 KJ mol-1

ΔS vap = ΔH vap / Tb =  37.30KJ mol-1/373 K = 0.1KJ mol-1K-1

ΔGvap = ΔHvap – TΔSvap = 37.30 - 373 x 0.1 = 0

Thus, the free energy and entropy change in KJ of water are 0 and  0.1KJ mol-1K-1

2. Enthalpy and entropy changes of a reaction are 40.63kJmol−1 and 108.8JK−1mol−1,  respectively. Comment on the feasibility of the reaction at 27∘C.

ΔH  = 40.63 KJmol−1 = 40630J mol-1K-1

ΔS = 108.8JK−1mol−1

T = 27 + 273 = 300 K

ΔG = ΔH – TΔS = 40630 - 300 x 108.8 = 7990J mol-1

The Enthalpy and entropy changes of a reaction are 40.63 KJmol−1 and 108.8JK−1mol−1, the value of ΔG is positive and hence the reaction is nonspontaneous. 

3. The enthalpy and entropy change for the reaction are 30 KJ/mol and 105 J/K/mol, find out if T= 285.7K. Comment on the feasibility of the reaction.

Given ΔH  = 30 KJ/ mol = 30000 J/mol

ΔS = 105J/K/mol

T = 285.7 K

ΔG = ΔH – TΔS = 30,000 - 105 x 285.7 = 0

Hence the reaction is in equilibrium

Interesting Facts

• The definition of entropy was developed in early 1850 by Rudolf Clausius

• The word enthalpy comes from the Greek word enthalpos meaning to put heat to

• Calorie and British thermal unit, BTU are also the units of enthalpy.

Key Feature

• Change in enthalpy is the heat evolved or absorbed from the system at constant pressure during a chemical reaction and it is the measure of the internal energy of the system.

• Change in entropy is the measure of molecular randomness

• The relation between change in entropy and enthalpy is given by Gibbs free energy equation ΔG = ΔH – TΔS