Entropy and free energy, Chemistry tutorial

Introduction:

What does the term Thermodynamics bring to mind?

Thermo = heat

Dynamics = motion or change

The science of Thermodynamics was build up around the study of steam engines and how to proficiently turn fuel into helpful work. Therefore statements of the laws of thermodynamics will often have this type of language. 

First Law:   

For a closed system, the change in the internal energy of the system is equivalent to the sum of the energy in the form of heat exchanged between the systems and surroundings (q) and the work done on the system (w).    

ΔEsystem = q + w

However, the Laws of Thermodynamics are far more thoughtful than simply explaining the efficiency of steam engines. They comprise the basic principles which govern all the energy changes.  We will observe how the concepts of heat and work simplify to the two principle ways which energy can be exchanged between the system and surroundings. This will be clearer after we build up the ideas personified in the Second Law however first; here other statements of the First Law are.

a) Internal energy of the isolated system is constant.     

Eisolated = constant  

b) Energy is conserved.   

c) The net energy of the universe is constant.   

Euniverse = constant

d) The change in energy of the universe is zero.     

ΔEuniverse = 0

The First Law hypothesizes the theory of internal energy, 'E', and state us that while energy might change forms, it is neither created nor destroyed. 

If the Laws of Thermodynamics state us the basic principles which govern all the energy changes, there should be the other law which state us the allowed direction of change.

The Second Law of Thermodynamics sums up this idea and is one of the most profound laws in the nature. Here is the statement of second law:  

Second Law:   

All the physical and chemical changes take place in such a way that at least some energy disperses:   

  • The net concentrated or organized energy of the universe decreases
  • The net diffuse or disorganized energy of the universe increases.   

The Second Law has to do by moving from concentrated energy to the dispersed energy in the form of arbitrary thermal motion.  

The First Law is concerning the amount of energy.  The Second Law is regarding the quality of the energy. The First Law hypothesizes the thermodynamic variable 'E', the internal energy.  The Second Law hypothesizes a new thermodynamic variable 'S', the Entropy, a measure of the dissipated energy in a system at every temperature which is unavailable to do work. Entropy consists of units:

ΔEnergy per degree = (Joule/Kelvin)

Entropy:

The first law is regarding the amount of energy. The second law is regarding the quality of the energy. The first law states the thermodynamic variable 'E', the internal energy. The second law states a new thermodynamic variable 'S', the entropy that is a measure of the dissipated energy in a system at a specific temperature. Similar to the internal energy, entropy is the state function and it consists of units of energy per Kelvin, J/K.

Most of the different terms are employed to illustrate entropy: disorganized, random, chaotic, dispersed, diffuse, unconcentrated, disordered, dissipated and delocalized. In all cases, these words refer to the arbitrary molecular energy in a system in the form of rotational, translational and vibrational motion of the particles. Increasing the temperature raises the arbitrary motion of the particles in a substance and, therefore, increases its entropy.

Spontaneous change for all time takes place in the direction of increasing total entropy. The isolated system, one that can't exchange matter or energy by the surroundings (assume a thermos bottle), will never spontaneously reduce in entropy. This will remain unchanged or move to higher entropy. Therefore, entropy change is about the dispersal of energy, in the form of matter or the thermal energy.

Here are a few statements of the second law by using the theory of entropy:

a) All the physical and chemical changes take place in such a way that the total entropy of the universe increases.

ΔSuniverse = ΔSsystem + ΔSsurroundings > 0 for the spontaneous process

b) Entropy of the isolated system never spontaneously decreases.

ΔSisolated ≥ 0

Computing Entropy Change:

1) Standard Entropy Change for a Phase Change:

Whenever a solid melts, it experiences an increase in the entropy. The temperature remains constant throughout this method and at constant pressure, the energy change is equivalent to ΔHfusion. The entropy change for this method is ΔHfusion/Tmelting point. Likewise, whenever a liquid boils the entropy change for this method is ΔHvaporization/Tboiling point. The general expression for the change in entropy for any phase change is represented by:

ΔSphase change = ΔHphase change/TPhase change

2) Standard Entropy Change for a Chemical Reaction:

Likewise to the standard enthalpy change for the reaction, ΔHºrxn, the standard entropy change for the reaction, ΔSºrxn, can be computed from the standard molar entropy values, where each and every standard molar entropy value is multiplied via the stoichiometric coefficient in the balanced chemical equation.

ΔHºrxn = ∑ΔHºf (products) - ∑ΔHºf(reactants)

ΔSºrxn = ∑Sº(products) - ∑Sº(reactants)

ΔSºrxn is the entropy change whenever pure unmixed reactants in their standard states are transformed to pure unmixed products in their standard states. The standard state is the most stable state of the element or compound at a pressure of 1 bar, a fixed temperature, generally 25 °C, and concentrations of 1 M for any solutions.

The sign of ΔSºrxn can frequently be expected by taking into account the stoichiometric of a reaction and the physical states of the products and reactants. If the total number of moles of gas raises going from reactants to products, we can calculate that the sign of ΔSºrxn is positive. The products are higher in entropy as compare to the reactants. On the contrary, if the number of moles of gaseous products is less than the number of moles of the gaseous reactants, the sign of ΔSºrxn is negative.

3) Entropy Change in the Surroundings:

The reaction between oxygen and hydrogen to form water consists of a negative entropy change even although the reaction is spontaneous. This is possible as the reaction is highly exothermic. Since the heat of the reaction expands outward, it raises the thermal energy of the molecules in the air surrounding the chemical reaction. As an outcome, the increased entropy of the surroundings more than compensates for the fact that the entropy of the system has reduced.

ΔSsurr > - ΔSsystem

The change in entropy of surroundings is associated to 'q', the amount of heat transferred throughout a chemical or physical change, and the temperature at which the change occurs.

ΔSsurr = -qsystem/T

For a process which occurs at constant pressure, qsystem is the enthalpy change for the reaction, ΔHrxn.

ΔSsurr = -ΔHrxn/T at constant pressure

For the exothermic reaction, ΔSsurr is positive and the entropy of surroundings increases. The Exothermic reactions make entropy in the surroundings that helps drive the reaction forward.

For the endothermic reaction, ΔSsurr is negative and the entropy of the surroundings reduces. Endothermic reactions reduce entropy in the surroundings. For the endothermic reaction to be spontaneous, the entropy change of the system should be a positive value, large adequate to compensate for the decrease in entropy, the endothermic reaction reasons to the surroundings.

Gibbs free energy:

Gibbs free energy, represented by 'G', joins enthalpy and entropy into a single value. The change in free energy, ΔG, is equivalent to the sum of the enthalpy plus the product of the temperature and entropy of the system. ΔG can predict the direction of the chemical reaction beneath two conditions:

a) Constant temperature

b) Constant pressure.

If 'ΔG' is positive, then the reaction is non-spontaneous (that is, the input of external energy is essential for the reaction to take place) and if it is negative, then it is spontaneous (that is, takes place without external energy input).

Gibbs energy was introduced in the year 1870 by Josiah Willard Gibbs. He at first termed this energy as the 'available energy' in a system. His paper published in the year 1873, 'Graphical Methods in the Thermodynamics of Fluids' outlined how his equation could predict the behavior of systems whenever they are combined. This quantity is the energy related by a chemical reaction that can be employed to do work, and is the sum of its enthalpy 'H' and the product of the temperature and the entropy 'S' of the system. This quantity is stated as follows:

G = H - TS

Or more entirely as:

G = U + PV - TS

Here,

U = Internal energy (SI unit: joule)

P = Pressure (SI unit: pascal)

V = Volume (SI unit: m3)

T = Temperature (SI unit: Kelvin)

S = Entropy (SI unit: joule/Kelvin)

H = Enthalpy (SI unit: joule)

Gibbs Energy in Reactions:

Spontaneous is the reaction which is considered to be natural as it is a reaction that takes place by itself devoid of any external action towards it. Non spontaneous - requires constant external energy applied to it in order for the procedure to continue and once you stop the external action the method will cease. Whenever solving for the equation, if change of 'G' is negative, then it is spontaneous. If change of 'G' is positive, then it is non spontaneous. The symbol which is generally utilized for 'FREE ENERGY' is 'G' and can be more correctly consider as the standard free energy change.

In the chemical reactions comprising the changes in thermodynamic quantities, a variation on this equation is frequently encountered:

ΔG = ΔH - TΔS

ΔG = Change in free energy

ΔH = Change in enthalpy (or temperature)

TΔS = Change in entropy

As the changes of entropy of chemical reaction are not calculated readily, therefore, entropy is not generally utilized as a criterion. To obviate this complexity, we can make use of 'G'. The sign of ΔG points out the direction of a chemical reaction and find out if a reaction is spontaneous or not.

ΔG < 0: reaction is spontaneous in the direction written (that is, the reaction is Exergonic)

ΔG = 0: the system is at equilibrium and there is no total change either in the forward or reverse direction.

ΔG > 0: The reaction is not spontaneous and the procedure carries spontaneously in the reserve direction. To drive such a reaction, we require encompassing input of free energy (that is, the reaction is endergonic)

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