Module 4
Use of free energy in chemical equilibria
The branch which deals with the movement of energy from one form to the other and the relationship that exists between heat and temperature with energy and the work done is called as thermodynamics. Thermodynamics is a branch of Science that deals with the different forms of energy and work done in a system. Thermodynamics is only confined to Large scale response of a system which we are observed and measured in experiments
Energy:
It referred to the energy content that is present within the system. The energy represents the overall energy contained in the system and may include many forms of energy such as potential energy, kinetic energy etc. In a chemical reaction, we know the energy transformations and basic thermodynamics gives us information regarding energy change associated with the particles present in a system.
Factors affecting the internal energy
The internal energy of a system may change when:
- Heat passes into or out of the system,
- Work is done on or by the system or matter enters or leaves the system
Work:
Work done by a system is defined as the amount of energy exchanged between a system and its surroundings. Work is completely determined by external factors such as an external force, pressure or volume or change in temperature etc.
Heat:
Heat in thermodynamics is defined as the kinetic energy of the molecules of the substance or material. Heat and thermodynamics together form the basics which help process designers and engineers to optimize their processes and harness the energy associated with chemical reactions economically.
Fig. 1:
Any thermodynamic system in an equilibrium state possesses a state variable called the internal energy (E). Between any two equilibrium states, the change in internal energy is equal to the difference of the heat transfer into the system and work done by the system.
- Enthalpy:
Enthalpy a process or activity takes place at constant pressure, the heat released or absorbed is equal to the Enthalpy change. Enthalpy is occasionally called or known as “heat content”, “enthalpy” is derived from the Greek word which means “warming”. Enthalpy(H) is the sum of the internal energy(U) and the result of pressure(P) and volume(V).
Enthalpy H is written as,
H = U + PVm
Where, H = is the Enthalpy of the system
U = is the Internal energy of the system and is entirely dependent on the state functions T, p and U.
Enthalpy can also be written as
ΔH=ΔU+ΔPV.
P = is the Pressure of the system
V = Volume of the system Enthalpy is not directly measured, but the change in enthalpy (ΔH) is measured, which is the heat lost or added by the system,
Entropy:
It was Introduced by the German Physicist Rudolf Clausius in 1850, and is a highlight of 19th century Physics. The word“entropy” is derived from the Greek word, which means “turning”. It was derived to provide a quantitative measure for the spontaneous changes and Clausius introduced the concept of entropy as a precise way of expressing the Second Law of Thermodynamics, Clausius form of the second law states that spontaneous change for an irreversible process in an isolated system
Is a measure of randomness or irregularity or disorder of the system?
The more or the randomness, higher is the entropy.
Solid state has the lowest or least entropy, the gaseous state has the highest entropy and the liquid state has the entropy that lies between the two.
Entropy is a state function. The changes in its value during any process, is called the entropy change.
ΔS = S2 -S1 = ∑S products – ∑S reactants
1) When a system absorbs heat, the molecules begin to move faster because the kinetic energy increases. Therefore, disorder increases. Greater the heat absorbed, greater will be the disorder.
2) For equal amount of heat absorbed at low temperature, the disorder will be more than at high temperature. This proves that entropy change is inversely proportional to temperature.
ΔS = eve / T
Entropy change during a process is defined as the quantity of heat (q) absorbed isothermally and reversibly divided by the absolute Temperature (T) at which the heat is absorbed
- Free Energy
Gibbs Free Energy is a measure of the potential for reversible or maximum work that may be done by a system at constant temperature and pressure. It is a thermodynamic function that was discovered in 1876 by Josiah Willard Gibbs to assume if a process will occur spontaneously at constant temperature and pressure. Gibbs free energy G is defined as
G = H - TS
Where H, T, and S are the Enthalpy, temperature, and entropy. The SI unit for Gibbs energy is the kilojoule.
Gibbs free energy combines both the enthalpy and entropy into a single value.
Gibbs free energy is the energy t with a that associates itself with a chemical reaction. It equals the enthalpy minus the temperature of the product and the entropy of the system.
G=H-TS
At constant temperature
ΔG = ΔH– TΔS
ΔG predicts the direction of a chemical reaction. If ΔG value is negative, then the corresponding reaction is spontaneous. If ΔG value is positive then reaction is non-spontaneous.
ΔGº=ΔHº-TΔSº
Where
ΔGº = Gibbs free energy (J or KJ)
ΔHº=enthalpy
T=Temperature
ΔSº=Entropy
Gibbs free energy is the energy that is available to do quality work.
A reaction will spontaneously occur if ΔG<0 (exergonic reaction)
A reaction will not spontaneously occur if ΔG>0 (endergonic reaction).
If ΔG value is less than zero, there is a thermodynamic force for the reaction or it drives the process in the forward direction.
When ΔG is positive, then reactants are favoured, when ΔG=0 system is at equilibrium.
- EMF
Electromotive force, or, as it is often written, e.m.f., is described as that source of energy which enables electrons movement around an electric circuit.
For any object to move from rest, there has to be some energy change. To ensure electrons movement round an electrical circuit, they should receive energy from a source of e.m.f. Which usually is a battery or a generator.
For every coulomb of electricity to move completely around an electrical circuit, a certain amount of electrical energy is needed, which depends on the particular circuit. The e.m.f. Is expressed in volts and is numerically the number of joules of energy given by the source of e.m.f. To each coulomb to enable movement around the circuit. The symbol for volt is the capital letter V.
Thus
Joules colombs=volts.
It follows that:
Joules=volts × coulombs = volts × ampers × seconds.
A 12-volt (12-V) battery is able to give 12 joules (12 J) of energy to each coulomb to enable movement around an electrical circuit.
The symbol for e.m.f. Is the capital letter E.
Example:
Calculate the energy supplied by a 12v battery when a current of 4 A flows for 10 minutes.
Energy supplied = Volts x amperes x seconds
= 12 x 4 x (10 x 60) Joules
= 28,800 J
- Cell Potential
(1) “The difference in potentials of the two half – cells of a cell known as electromotive force (emf) of the cell or cell potential.”
The potential difference of the two half – cells of a cell arises because of the flow of electrons from anode to cathode and flow of current from cathode to anode.
(2) The emf of the cell or cell potential can be calculated from the values of electrode potentials of two half – cells constituting the cell. The following three methods are in use
(i) When oxidation potential of anode and reduction potential of cathode are taken into consideration
Oxidation potential of anode + Reduction potential of cathode 
(ii) When reduction potentials of both electrodes are taken into consideration
(iii) When oxidation potentials of both electrodes are taken into consideration
Oxidation potential of anode – Oxidation potential of cathode 
- Nernst Equation
Any change in the Gibbs free energy G directly correspond to changes in free energy for processes at constant temperature and pressure, change is the maximum non-expansion work obtainable under these conditions in a closed system; ΔG is negative for spontaneous process, positive for nonspontaneous process, and zero for processes at equilibrium.
It takes into consideration the values of the standard electrode potentials, temperature, activity and the reaction quotient for the calculation of cell potential. For any cell reaction, that occurs Gibbs free energy can be related to standard electrode potential as:
ΔG =-nFE
Where, n = number of electrons transferred in the reaction,ΔG= Gibbs free energy, E= cell potential F = Faradays constant (96,500 C/mol) and. Under standard conditions, the above equation can be written as,
ΔGo =-nFEo
According to the theory of thermodynamics, Gibbs free energy under general conditions can be related to Gibbs free energy under standard condition and the reaction quotient as:
ΔG=ΔGo + RT lnQ
Where, Q= reaction quotient, R= universal gas constant and T= temperature in Kelvin. Incorporating the value of ΔGo andΔG, from the first two equations, we get the equation:
-nFE = -nFE0 + RT lnQ
E = E0 – (RT/nF) lnQ
By conversion of Natural log to log10, the above equation is called as the Nernst equation. Here, it shows the relation of the reaction quotient and the cell potential. Special cases of Nernst equation:
E = Eo − (2.303RT/nF) log10Q
At standard temperature, T= 298K:
E = Eo − (0.0592V/n) log10Q
At standard temperature T = 298 K, the 2.303RTF, term equals 0.0592 V.
Under Equilibrium Condition
As the redox reaction in the cell progresses, the concentration of reactants decreases while the concentration of products increases. This process goes on until equilibrium is achieved. At equilibrium, ΔG = 0. Hence, cell potential, E = 0. Thus, the Nernst equation can be modified to:
E0 – (2.303RT/nF) log10Keq = 0
E0 = (2.303RT/nF) log10Keq
Where, Keq = equilibrium constant and F= faradays constant. Therefore, the above equation gives us a relation between standard electrode potential of the cell where the reaction takes place and the equilibrium constant.
- Applications of Nernst Equation
One of the major applications of Nernst equation is in determining ion concentration
- It is also used to calculate the potential of an ion of charge “z” across a membrane. It is used in oxygen and the aquatic environment.
- It is also used in solubility products and potential-metric titrations.
- It is also used in pH measurements and to determine the Concentration Cell is an electrochemical cell.
Acid Base reactions
The very basic and important compounds present in the world are the Acids and bases, they form the centre of all reactions, several theories are put forth regarding the Acid Base behaviour.
The Arrhenius theory
The Swedish physicist Svante Arrhenius had proposed this theory, according to him, in any aqueous solution the acid is the substance that is shown to increase the Hydronium ion (H3O+) concentration, on the other hand for a given aqueous solution a base is a substance that increases the concentration of hydroxide ion (OH−) concentration. Well-known acids examplesinclude Hydrochloric acid (HCl), Sulphuric acid (H2SO4), Nitric acid (HNO3), and acetic acid (CH3COOH). Examples of Bases includes such common substances as caustic soda (sodium hydroxide, NaOH) and slaked lime (calcium hydroxide, Ca (OH)2). Another common base which is ammonia (NH3), reacts with water to gives a solution that is basic in nature, when we consider the following balanced equation.NH3(aq) + H2O(l) → NH4+(aq) + OH−(aq)(This reaction occurrence is minimal; the hydroxide ion concentration is small but measurable.)
Oxidation reduction or (redox reactions) these reactions involve one or more electrons from a reducing agent to an oxidizing agent. The Redox reactions has the effect of reducing the apparent or real electric charge on an atom with respect to the substance being reduced and increase the electric charge on an atom for the substance that is being oxidised. Simple redox reactions include the reactions of a substance or an element reacting with oxygen. For example, magnesium burns in oxygen to form magnesium oxide (MgO). The product formedis an ionic compound, made up of Mg2+ and O2− ions. In the reaction each oxygen atom accepts two electrons and getsreduced on the other hand each oxygen atom gives out two electrons and gets oxidised.
Another common redox reaction is one step in the rusting of iron in damp air. The reaction is as follows
2Fe(s) + 2H2O(l) + O2(g) → 2Fe (OH)2(s)Here iron metal is oxidized to iron dihydroxide (Fe (OH)2); elemental oxygen (O2) is the oxidizing agent.
The solubility product constant (Ksp) is the equilibrium constant for a solid that dissolves in an aqueous solution. All of the rules for determining equilibrium constants continue to apply. An equilibrium constant is the ratio of the concentration of the products of a reaction divided by the concentration of the reactants once the reaction has reached equilibrium. Consider this reaction:
AgCl(s)→Ag+(aq)+Cl−(aq)AgCl(s)→Ag+(aq)+Cl−(aq)
The equilibrium expression for the reaction is:
Keq=[Ag+] [Cl−][AgCl]Keq=[Ag+] [Cl−][AgCl]
Because the AgCl is a solid, its concentration before and after the reaction is the same. The equilibrium equation can therefore be rearranged as:
Ksp=[Ag+] [Cl−]Ksp=[Ag+][Cl−]
For substances in which the ions are not in a 1:1 ratio, the stoichiometric coefficients of the reaction become the exponents for the ions in the solubility-product expression:
PbCl2⇌Pb2++2Cl− gives Ksp=[Pb2+][Cl−]2PbCl2⇌Pb2++2Cl− gives Ksp=[Pb2+][Cl−]
Ba3(PO4)2⇌3Ba2++2PO42− gives Ksp=[Ba2+]3[PO42−]2Ba3(PO4)2⇌3Ba2++2PO42− gives Ksp=[Ba2+]3[PO42−]2
- Water Chemistry
Water is a chemical compound consisting of two hydrogen atoms and one Oxygen atom. The name water typically refers to the liquid state of the compound. The solid phase is called as ice and the gas phase is called as steam. Under specific conditions, water also forms a supercritical fluid. Water is the main compound found in living organisms. Approximately 62 percent of the human: body contains water. The word "water" comes from the Old English word water or from the Proto-Germanic water or German Wasser. All of which mean "water" or "wet." The boiling point of water is 99.98 degrees C (211.96 degrees F; 373.13 K).
Water is amphoteric. Which means, it can act as both an acid and as a base.
- Hard and soft water:
Hard water: is water that contains a required quantity of dissolved minerals (like calcium and magnesium) As rainwater falls, it is naturally soft. However, as water flows through the ground and into waterways, it picks up minerals like chalk, lime and mostly calcium and magnesium and becomes hard water. Since hard water contains essential minerals, it is essentially used as drinking water. Not only because of the health benefits, but also the flavour. Water that does not produce lather with soap readily is called hard water. Water hardness is usually measured as calcium hardness in milligrams per litre (mg/l) OR parts per million (ppm) OR in grains per gallon (GPG).
For e.g.: sea water, river water, spring water, lake water and well water.
Soft water: water that shows the absence of dissolved salts of such metals as magnesium, iron, or calcium, which are known to form insoluble deposits such as appear as scale in boilers or soap curds in bathtubs and laundry equipment, soft water is neither healthy nor desirable to drink. Water that readily produces lather with soap is called soft water.
For e.g.: Rain water, distilled water, demineralised water.
Corrosion is the disintegration of a metal due to the chemical reactions between the metal and the surrounding environment. Both the types of metal and the environmental conditions, particularly gasses that come in contact with the metal, determine the form and rate of the corrosion.
All metals can corrode. Some metals, like pure iron, deteriorate very fast. Stainless steel, and, metals that combines with iron and other alloys, is slower to corrode and is therefore used more efficiently.
All small group of metals, are called the Noble Metals, and show much less reaction than others. As a result, they deteriorate rarely. They are, in fact, the only metals that are found in nature in their purest form. The Noble Metals, not unexpectedly, are often very valuable. They include gold, rhodium, silver, palladium, and platinum.
Types of Corrosion
There are different reasons for metal corrosion. Some can be prevented from corrosion by adding alloys to a pure metal. Others can be avoided by carefully combining metals or management of the metal's environment. Some of the most common types of corrosion are described below.
- General Attack Corrosion: This particular corrosion is very common form of corrosion attacks the entire surface of a metal structure. It is caused by chemical or electrochemical reactions.
- Localized Corrosion: This corrosion attacks only a part of a metal structure. There are three types of localized corrosion:
- Pitting -- it involves the creation of small holes in the surface of a metal.
- Crevice corrosion – it is the corrosion that occurs in stagnant locations such as those found under gaskets.
- Filiform corrosion –they are the corrosions that occurs when water gets under a coating such as paint.
- Galvanic Corrosion: This corrosion occurs when two different metals are placed together in a liquid electrolyte such as salt water. In essence, one metal's molecules are drawn towards the other metal, resulting in the corrosion only one of the two metals.
- Environmental Cracking: When environmental conditions are stressful enough, some metal can begin to crack, weaken, or become brittle and fatigue.
Corrosion Prevention
An effective prevention system begins in the design stage with a proper understanding of the environmental conditions and metal properties. Engineers who work with metallurgical experts should select the proper metal or alloy for every situation. They should also be aware of possible chemical interactions between metals used for surfaces, fittings, and fastenings.
H.G.T Ellingham proposed the Ellingham diagram to predict the spontaneity of reduction of metal oxides. Ellingham diagram was basically a curve which related the Gibbs energy value with temperature.
Ellingham diagram for reduction of oxides
Fig. 2: Ellingham diagram for reduction of oxides
Ellingham diagram is a plot between ΔfGo and T for the formation of oxides of metals. A general reaction expressing oxidation is given by
Z x M (s) + O2(g) 2MxO (s)
It is evident from the reaction that the gaseous amount of reactant decreased from left to right, as the product formed is solid metal therefore molecular randomness all decreases from left to right, thus ΔS is negative. Hence for most reactions the formation of MxO(s) curve is positive.
Except for the process, where change of phase takes place, each plot is a straight line. The temperature at which change of phase takes place is indicated by a positive increase in the slope. For E.g. The melting is indicated by an abrupt change in the curve in Zn, ZnO plot.
The metal oxide (MxO) is stable at a point in a curve, below ΔG is negative.
The feasibility of reduction of the oxides of the upper line by the element is represented by the lower line and is determined by the difference in the two ΔrGº after the point of intersection in Ellingham diagram.
References:
- The law of thermodynamics: A very short Introduction by Peter Atkins
- Chemical thermodynamics at a glance by H. Donald Broken Jenkins
- Physical chemistry by Robert A. Alberty
- Applied water chemistry by Recknow Research group, University of Massachusetts Amherst
- Water and life “The unique properties of H2O” by Ruth M Lyndea-beel, Simon Conway Moms, John D. Barrow, John. L. Fimly.
