Chemical thermodynamics
Thermodynamics implies the flow of heat. All physical and chemical processes are followed by energy changes and the study of these energy changes and the conditions under which they take place are included in the subject matter of thermodynamics. The transformation of heat in to work and vice-versa is governed by thermodynamics. There are two ways by which thermodynamics can be studied (i) when the exchange of heat, electric work, mechanical work etc. in a cyclic process are considered directly or (ii) when the thermodynamics functions such as internal energy, enthalpy, entropy etc. which enable deduction of heat exchanges and work done in a system are studied.
The study of thermodynamics has become inevitable as most of the important generalizations of physical chemistry can be deduced from the laws of thermodynamics. The criteria for predicting the feasibility or spontaneity of a process under a given set of conditions is laid by thermodynamics.
One of the main shortfalls in the study of thermodynamics is that is concerned with the initial and final states of a system and it does not depend upon the process by which it was brought into the trial state and the rate at which these processes have occurred. It must also be noted that the laws of thermodynamics apply only to matter in bulk and not to individual atoms or molecules.
Following are the terms frequently used, and the knowledge of the same is essential in the study of thermodynamics.
SYSTEM
A system is defined as any portion of the universe that we have for our study and it is separated from the rest called surroundings by real or imaginary boundaries. A system may consists of one or more substances.
Systems + surroundings=universe
SURROUNDINGS
The rest of the universe which might be in a position to exchange energy and matter eith the system is called its surroundings.
On the basis of interaction between a system and surroundings, a system is classified in to three types
a) Open system-when a system can exchange both energy and matter with the surrounding it is said to be an open system.
b) Closed system-when the system can exchange the energy with the surrounding but not the matter, then it is said to be a closed system.
c) Isolated system- A system is said to be an isolated system, if it can neither exchange energy nor matter with its surroundings.
MACROSCOPIC SYSTEM
When a system consists of a large number of atoms, molecules or ions then it is called a macroscopic system. Properties such as pressure, volume, composition, density, viscosity, colour etc. which are associated with a macroscopic system are called macroscopic properties.
STATE OF SYSTEM
A system is said to be in a definite state when the macroscopic properties of the system have definite values. Whenever there is a change in any of the macroscopic properties, the system is said to have changed in to a different state. Thus the state of a system is determined by its macroscopic properties.
STATE VARIABLE
Since a change in microscopic properties is a decisive factor in the state of a system these properties are called state variables. It is therefore essential that when a system changes from one state mean initial to another state mean final there is a change in one or more of the macroscopic properties. The change in the state of a system is completely defined when the initial and final states of a system are specified.
The most important state variable are pressure, temperature, volume, mass and composition. Some of them are interdependent. For one mole of an ideal gas PV=RT. If two of the variables are known, then the third can be determined. These are called independent variables. The third variable is generally the volume, and it is the dependent variable. Thus the thermodynamics state of a system consisting of a single gaseous substance may be completely defined by specifying any two of the three variables.
In a closed system consisting of one or more components, mass is not a state variable.
HOMOGENEOUS AND HETEROGENEOUS SYSTEM
A system is said to be homogenous when it is completely uniform throughout and hence a homogenous system consists of only one phase. A phase is defined as a homogeneous and physically distinct part of a system which is bounded by a surface and is mechanically separable from other parts of the system.
A system is said to be heterogeneous when it is not uniform throughout and consists of more than one phase.
PROPERTIES OF SYSTEM-The properties of system can be classified in to two types:
1) Extensive property: Any property of a system whose magnitude depends upon the quantity of material present is called an extensive property. E.g. Mass, volume, energy, heat etc.
2) Intensive property: Any property of a system is independent of the amount of material present in the system is called an intensity property. E.g. pressure, colour, density, temperature, specific heat etc.
THEMODYNAMIC EQUILIBRIUM
A system is said to be in thermodynamic equilibrium when the macroscopic properties do not undergo any change with time. The criteria which determine the attainment of complete equilibrium are:
1) Mechanical equilibrium: A system is said to be in mechanical equilibrium when there is no unbalanced force existing between the different parts of the system or between the system and its surroundings. In other words, if no mechanical work is done by one part by one part of a system on another. this can be achieved only if the pressure remains uniform throughout the system.
2) Thermal equilibrium: A system is said to be in thermal equilibrium if the temperature is the same throughout the system including its surroundings.
3) Chemical equilibrium: A system is said to be in chemical equilibrium if the composition of the system remains the same throughout. 
Thus mechanical equilibrium implies uniformity of pressure, thermal equilibrium implies uniformity of temperature and chemical equilibrium implies uniformity of chemical composition. A system is said to be in thermodynamic equilibrium its properties have definite magnitude.
CYCLIC PROCESS
A process may be defined as the method of operation in which a change in state is affected. When a system returns to its initial state after having undergone a change in state, the path of the process by means of which the transformation is effected is called a cyclic process.
A thermodynamic process is the path of operation by which a system changes from one state to another. There are four important types of processes.
a) Isothermal process: A process is said to be isothermal if the temperature of the system remains constant. When a gas is compressed suddenly, some heat is evolved is removed simultaneously, and hence the temperature will remain constant.
b) Adiabatic process: A process is said to be adiabatic if no heat enters or leaves the system during any step of the process. The system is completely insulated. Under such conditions if an exothermic process takes place, the heat evolved remains in the system and therefore the temperature of the system rises, and if an endothermic process takes place the heat absorbed is supplied by the system itself and therefore the temperature of the system fails.
The difference between isothermic and adiabatic process is that in an isothermal process, the temperature remains constant during each stage of the operation and the system is in position to exchange heat with the surroundings but in an adiabatic process, the temperature gets altered because the system is not in a position to exchange heat with the surroundings.
c) Isobaric process: When there is a change in state of a system, if the pressure of the system remains constant during each step the process is called isobaric process. Consider a mixture of hydrogen and oxygen takes in the ratio 2:1 contained in a cylinder fitted with a weightless piston. When an electric discharge is passed through the mixture the volume of the system decreases. The piston will be moved down so that the pressure of the system remains constant.
d) Isochoric process: A process is said to isochoric if the volume of the system remains constant during each step of the process. Consider the following reaction which takes place in a sealed vessel. On heating dissociation of nitrogen dioxide takes place and hence the pressure of the gas goes on increasing. As the reaction is carried out in a closed vessel the volume remains constant and hence it is an isochoric process.
REVERSIBLE AND IRREVERSIBLE PROCESS
If a process is carried out infinitesimally slowly so that the driving force is only infinitesimally greater than the opposing force then it is called a reversible process, which implies that at any point the process can be reversed by an infinitesimally change in the state of the system.
If any process which does not take place in the above manner i.e. a process in which the change of the system is not carried out infinitesimally slowly then it is called irreversible process. In an irreversible process the changes takes place suddenly or spontaneity and the change taking place in any part of the direct process cannot be exactly reversed by changing the conditions by an infinitesimally smaller quantity.
ENERGY
It has already been stated that whenever a system changes from one state to another it is accompanied by change in energy. Energy may be defined as any property which can be produced from or converted in to work. The magnitude of energy is obtained as a product of the capacity factor and the intensity factor. Intensity factor is the measure of force or the resistance overcomes and the capacity factor is the extent to which it has been overcome when a body performs work or expands energy.
The various form of energy commonly known are kinetic energy, potential energy, electrical energy, radiant energy, chemical energy, mass energy and nuclear energy.
Thermodynamics is a deductive science based on the first, second and third law of thermodynamics. These laws are derived from long experience with energy.
UNITS OF ENERGY
The C.G.S unit of mechanical energy is Erg. It is defined as the work done when a resistance of one dyne through a distance of one cm. The C.G.S unit of thermal energy is one calorie = 0.2389 joule is the unit of energy in the C.G.S system. The relation of unit mechanical work to the thermal unit is called mechanical equivalent of heat. Its numerical value is 4.185 joules. Thus for the expenditure of 4.185 joules of mechanical energy. 1 calorie of heat is produced when a gas is allowed to expand against pressure; the work done is obtained by the product of pressure or intensity factor and volume changes or volume factor.
INTERNAL ENERGY
Consider some commonly known transformations which are combustion of carbon in the presence of oxygen, freezing of liquid by giving out heat and the combustion of fuel in an internal combustion engine to produce mechanical energy. All the above involve energy changes and hence these transformations can only be possible when the substance or changes and hence these transformations can only be possible when the substance or system has some internal energy within it. Thus we can deduce the existence of a property of a system called the internal energy or intrinsic energy. The amount of internal energy depends on the chemical nature as well as upon its temperature, pressure and volume i.e. the thermodynamics parameters of the systems. It also depends on the amount of substance 0r called quantity of matter in the system. It is therefore an extensive property.
It includes the translational kinetic energy of the molecules and other molecular energies like rotational and vibration energies.
Thus internal energy depends on the state of a system and not on the paths taken to bring the system to this state. Hence internal energy is a definite property of a system or a thermodynamic function or state functions. Internal energy E cannot be directly determined or calculated. It is the change in internal energy accompanied in any physical or chemical process that can be measured. Suppose a system is subjected to change of pressure and volume only. Let A and B be the initial and final states of the system and EA and EB be the internal energies associated with the system in its initial and final states respectively. Then the increase in internal energy is given by
∆E = EB-EA
FIRST LAW OF THEMODYNAMICS
The first law of thermodynamics states that energy can neither be created nor destroyed although it can be transformed from one form to another. this is also known as law of conservation of energy.
This energy change is brought about by the evolution or absorption of heat and or by work being done by the system. Because the total energy of the system remains constant, the mathematical representation of first law is

∆E=q – w (i)
Where, q is the amount heat supplied to the system
W is the work done by the system
Thus the first law can otherwise be stated as the net energy change of a closed system and is equal to the heat change of the system and the work done.
To illustrate the mathematical statement of first law, consider the system of an ‘expanding hot gas’. The gas expands by a volume ∆V against a constant pressure P.
The total mechanical work done is given by the relation.
W = P * ∆V (ii)
Therefore from (i) and (ii) it can be deduced that 
∆E = q – P∆V
MORE STATEMENT OF THE FIRST LAW OF THERMODYNAMICS
(I)Whenever energy of a particular type disappears an equivalent amount of another type is produced.
(ii)The total energy of a system and surroundings remains constant or conserved.
(iii)It is impossible to construct a perpetual motion machine that can produce work without spending energy on it.
SOME SPECIAL FORMS OF FIRST LAW OF THEMODYNAMICS
The first law can be mathematically represented as
∆E = q – w
Case I: For a cyclic process involving isothermal expansion at constant temperature of an ideal gas
∆E = 0
q = w
Case II: For an adiabatic no change in volume, there is no work of expansion i.e., w = 0.
Hence ∆E =qv
Case III: For an adiabatic process there is no change in heat gained or lost i.e., q = 0.
Hence ∆E = -w
In other words, change in internal energy is exactly equal to the amount of work done by the system or on the system. When the work is done on the system (-w) the internal energy as well as the temperature of the system increases and when the work is done by the system, (+w) it is done at the expense of internal energy and hence the temperature falls.
Case IV: For an isochoric process (constant pressure)
∆E = q – w
Or ∆E = q - P∆V
ENTHALPY OF A SYSTEM
Consider a system wherein a change in the system is brought about at constant pressure. This change in the volume says VA to AB. The work done by the system will be
w = P (VB – VA)
Substituting this in the equation ∆E = q – w
∆E = q – w
∆E = q – P (VB – VA) 
Or EB – EA = q – P (VB- VA)
i.e., (EB + PVB) – (EA + PVA) = q
i.e., in a constant pressure process, the system also expends energy in doing PV work. Therefore, the total heat content of a system at constant pressure is equivalent to the internal energy E plus the PV energy. The quantity (E – PV) is called the enthalpy of the system and is represented by H. thus enthalpy is defined by the equation.
H = E + PV
E is definite property; P and V are also definite properties which define the state of a system. Thus H, whose value depends on E, P, V must also be a definite property and hence it is a state function.
HB – HA = ∆H = q
∆H is also a definite property depending on the initial and final states of a system and is independent of the path taken by the system. The heat absorbed (q0 under constant pressure is also a definite quantity.
Substituting the value of q in the equation we get
∆H = (EB – EA) + P (VB – VA)
∆H = ∆E + P∆V
Or ∆H = ∆E + w
According to first law,
∆E = q – w, where q = heat transferred
‘q’ absorbed in a process is not a definite quantity. But when q is absorbed in a process at constant pressure it is a definite quantity and is given by ∆H = qp. The ∆H can be measured by measuring the heat change at constant pressure
∆H = HB – HA
If ∆H is positive HB> HA, and the process is said to be endothermic. When ∆H is negative, i.e. if HB
RELATION BETWEEN ∆H AND ∆E
Calorific values of many gaseous fuels are determined using constant volume calorimeters and is given by the expression qv = ∆E.
When any fuel is burnt in the open atmosphere, additional energy of expansion, positive or negative against the atmosphere is involved.
qp = ∆H = ∆E +P∆V
Suppose there are n1 moles of gaseous reactants before a reaction and n2 moles of gaseous products after it, under ideal gas behavior.
PV2 = n2RT 
PV1 = n1RT
P (V2 – V1) = RT (n1 – n2)
Or P ∆V = RT∆n
Substituting the value of P ∆V. in equation we have
∆H = ∆E + ∆n RT
HEAT CAPACITY
Heat capacity is defined as amount of heat required to raise the temperature of a substance through one degree centigrade. It is the capacity to absorb heat and store energy. There are two heat capacities. It is capacity at constant volume CV and heat capacity at constant pressure Cp. The amount of heat capacity at constant volume. Similarly the amount of heat required to raise the temperature of a substance through one degree centigrade when the volume is kept constant and pressure is allowed to increase, is called heat capacity at constant volume. Similarly the amount of heat required when the pressure is kept constant and volume is allowed to increase is called heat capacity at constant pressure.
The two heat capacities are expressed as Cv = [dE/dT] and Cp = [dH/dT]
Thus the heat capacity at constant volume is defined as the rate of change of internal energy with temperature at constant and the heat capacity at constant pressure is the rate of change of enthalpy with temperature at constant pressure.

SECOND LAW OF THERMODYNAMICS
The first law of thermodynamics states that whenever one form of energy disappear, an equivalent amount of another kind reappears so that the total amount of energy remains the same. But the first law fails to explain under what conditions and to what extent it is possible to bring about the conversion of one form of energy in to another. it is also fails to explain the direction in which the process of transformation would occur. The principle which determines the direction as well as the extent of a chemical change is provided by the second law of thermodynamics. Knowledge of some terms is necessary before taking up the study of the second law.
SPONTANEOUS PROCESS
A process which proceeds on its own accord, without the intervention of any external force is said to be a spontaneous or natural process. The reverse process, which does not proceed on its own, is referred to as a non-spontaneous or unnatural process.
E.g. of spontaneous process – melting of ice as soon as it is taken out of the refrigerator, rusting of iron when exposed to moist air, flow of water from a higher level to lower level, flow of heat from a hot body in to a cold body etc.
FEATURES OF SPONTANEOUS REACTION
1. A spontaneous change is one way or unidirectional.
2. If a system is in equilibrium state mean unstable a spontaneous change is inevitable.
3. Once a system is in equilibrium state, it does not undergo any further spontaneous change if left undisturbed.
4. A spontaneous change is accompanied by decrease in internal energy or enthalpy or enthalpy and increase in entropy.
5. All spontaneous processes are accompanied by decrease in free energy of the system.
A spontaneous change is always accompanied by a decrease in internal energy or enthalpy ∆H. it implies that these reactions will be exothermic. Incidentally, melting of ice and evaporation of rain water will be exothermic. Incidentally, melting of ice and evaporation of rain water are endothermic reactions which proceed spontaneously. It is therefore obvious, that there is some other factor which governs spontaneity in addition of ∆H. This factor is known as entropy.
SPONTANEITY AND RANDOMNESS
In the examples cites viz. melting of ice and evaporation of water, there is an increase in the randomness or disorder of the system. The water molecule in ice melts in ice is highly organized and permits only little movement of its molecules. As the ice melts the water molecules move about freely. The movement of molecules becomes still freer when the water is evaporated. The molecules can roam throughout the entire atmosphere. In other words, the randomness of the molecules increases when ice melts to water and water evaporates. Increases in randomness favor a spontaneous change.
A change that brings about randomness is more likely to happen than the one that brings order. Sequence is more likely to occur than the ordered one even in physical or chemical processes.
DEFINITION OF ENTROPY
Entropy is a thermodynamic state function that is a measure of the randomness or disorderliness of the molecules of the system. Entropy is represented by the change in disorder accompanying a process from start to finish and it is represented by ∆S.
The change in entropy is given by
∆S = S final > S initial
∆S is positive when S final > S initial
The process accompanied by an increase in entropy tends to be spontaneous.
STATEMENT OF SECOND LAW 
The second law of thermodynamics states that whenever a spontaneous process takes place, it is accompanied by an increase in the entropy of the universe. More specifically the term ‘universe’ is taken to mean the system and its surroundings.
∆Suniverse = ∆Ssystem + ∆Ssurroundings
The second law as stated above implies that when an irreversible process occurs the entropy of the system and surroundings increases. In other words, ∆Suniverse > 0, When a reversible process occurs, the entropy of the system remains constant i.e., ∆Suniverse = 0. Since the entire universe is undergoing spontaneous change, the second law can be stated as “The entropy of the system is constantly increasing”.
MATHEMATICAL DEFINITION OF ENTROPY
IN 1854 Clausius formulated a mathematical definition of entropy. According to him when a system is not undergoing any change (physical or chemical) and there is no exchange of heat then the entropy q/t. Therefore entropy can be defined for a reversible change happening at a constant temperature (T), as entropy change (∆S) is equal to heat absorbed divided by the temperature (T).
∆S = q/t
When a system is allowed to change from a given state to another, the heat dq absorbed or evolved during the change depends on the way, the change has taken place. dq depends upon the path taken by the system. When the heat absorbed is at constant pressure then qp = HB – HA therefore qp/T will have a definite value at any given state. Giving positive sign to heat absorbed (q2) and negative sign to heat evolved (q1) by the system, it has been proved that
+q2/T2 = -q1/T1 
Or q1/T1 + q2/T2 = 0
It follows that in a reversible cycle comprising of a series of heat changes, the summation of q/T terms is equal to zero. Thus 
Summation of q/T = 0
For infinitesimal changes, the above equation can be written as 
Summation of dq/dT = 0
Since dq and T are thermodynamic functions whose change is independent of the path of transformation o the system, this function is called entropy. Thus
dS = ∫dq/T or ds = dq/T
it is difficult to define the actual entropy of a system , however, the change in entropy can be defined during a change of state.
Thus entropy change ∆S or dS like ∆E and ∆H is a definite quantity and depends upon the initial and final states of the system. The change in entropy is defined as the integral of all the terms involving heat absorbed (q) divided by the absolute temperature (T) during each infinitesimal change of the process carried out reversibly. When heat is absorbed dq is positive, T is always positive. Thus dS is positive. Hence entropy of the system increases when there is absorption oh heat. When heat is evolved dq is negative. Thus dS are also negative. Hence entropy of the system decreases with the evolution of heat.


UNITS OF ENTROPY
Since entropy is equal to heat energy divided by absolute temperature it is measured in entropy units (eu) which are calories per calories per mole per degree. i.e., Cal.1/mol*1/k.
In this SI system the units are joules per mole per degree i.e. J 1/mol*K. these are represented by EU
1 eu = 4.184 EU
ENTROPY CHANGE IN ISOTHERMAL EXPANSION OF AN IDEAL GAS
Consider an isothermal expansion of an ideal gas taking place in a reversible manner. Then there is no change in internal energy i.e., ∆E = 0. According to first law of thermodynamics,
∆E = q – w
Since ∆E = 0
Then qrev = - w
The work in the expansion of n moles of a gas from V1 to V2 at constant temperature, is given by 
W = -nRT lnV2/V1
Therefore qrev = nRT ln V2/V1
Change in entropy ∆S is given by 
∆S = qrev/T = 1/T nRT ln V2/V1
i.e. , ∆S = nR ln V2/V1
ENTROPY CHANGE ACCOMPANYING CHANGE OF PHASE
Any transformation of a state like solid to liquid, liquid to vapors or solid to vapors is accompanied by change in entropy. This change may be carried at constant temperature reversibly as the two phases are in equilibrium during the change.
For example consider 1 mole of a substance undergoing fusion reversibly. It will absorb molar heat of fusion at temperature equal to its melting point.
Then the entropy change is given by 
∆Sf = ∆Hf/Tf
When ∆Hf is the heat of fusion at its melting point Tf at a constant pressure. When one mole of a liquid is boiled reversibly, it will absorb molar heat of vapourisation at a temperature which is equal to its boiling point.
Then the entropy change is given by
∆Sv = ∆Hv/Tb
When, ∆Hv is the molar heat of vapourisation at its boiling point Tb at constant pressure.
Similarly we can calculate the change in entropy when one mole of a solid changes reversibly from one form to another at its transition temperature.
∆St = ∆Ht/Tt
Where, ∆Ht is the molar heat of transition at its transition temperature at constant pressure.
SPONTANEOUS PROCESS
As already mentioned there are some reactions that occur in nature which are spontaneous e.g: melting of ice, rusting of of iron, while others are non spontaneous like formation of ice at 25°C or the combination of natural gas carbon dioxide and water to form methane and oxygen. It is not always true to tell whether a reaction is spontaneous or non-spontaneous. A mixture of hydrogen can be maintained for a long time without any apparent reaction. We may therefore conclude that this reaction is non-spontaneous. However, if a lighted match or platinum foil is brought in to the mixture, the reaction occurs spontaneously. Thus the formation of liquid water from its elements is spontaneous once it is initiated.
Moreover it is often found that endothermic reactions which are non-spontaneous at room temperature become spontaneous when the temperatures become spontaneous when the temperature is increased. Consider the reaction of calcium carbonate it will give calcium oxide and carbon dioxide. This reaction is non-spontaneous at 25°C and 1 atm pressure. If the pressure is lowered, calcium carbonate decomposed more rapidly and at 0.1 mm Hg, the reaction becomes spontaneous at 50°C. hence it is possible to make this endothermic reaction spontaneous by increasing the temperature and decreasing the pressure.
FREE ENERGY
J. Willard Gibbs later proved that the criteria for spontaneity are the capacity to produce useful work. He proved that at constant temperature and pressure, if a reaction in principle can be harnessed to perform useful work, that reaction is spontaneous. If work has to be supplied from the surroundings to make the reaction occur it cannot be spontaneous. The capacity of spontaneous reaction carried out at constant temperature and pressure to produce useful work can be interpreted in terms of a fundamental property of the substances taking place in the reaction, known as the free energy. free energy of a substances taking part in the reaction, to supply useful work in a reaction. The amount of useful work that can be obtained from a reaction is limited by the difference in free energy between products and reactants.
Some spontaneous natural processes are
1. Heat flows from the hot end of a metal bar to the cold end till the temperature of both ends become equal. Thus a thermal equilibrium is maintained.
2. Water moves freely from a higher level to a lower level until the levels are equalized, mechanical equilibrium is thus obtained.
3. Metallic copper is deposited with the evolution of heat when copper sulphate solution is brought in contact with zinc and the reaction continues till the chemical equilibrium is maintained.