Chemical Thermodynamics

The study of movement of heat energy in a chemical reaction is known a **Thermodynamics** .

System : is The part of the universe which is under thermodynamic consideration . The thermodynamic consideration is always taken at room temperature (25o C = 298 K)
Surrounding : is the part of universe other than the system .
Boundary : separates the system and the surroundings .

## System Configuration

**Open System  :** Transfer of Energy and matter is allowed

**Closed System  :** Transfer of Energy is allowed but matter is not allowed

**Isolated System :**  Transfer of Energy and matter is not possible. (thermostat)

The part of the universe , apart from the system is called as **Surroundings** .

## State

**State** , is the condition of the system . It is defined by using state variables . **State variables** are the properties of the system like temperature , pressure , energy ,etc .

When a state changes from one form to other , we say a **process**  has occurred .

## Process

**Isocoric** Volume remains constant

**Isobaric** Pressure remains constant

**Isothermal** Temperature remains constant

**Adiabatic** There is no heat exchange

**Cyclic** The final and initial state of the process is same (All state variables should be restored)
**Reversible** The driving force is greater than the opposing force by infinitely small difference .

**Extensive Property** These properties depend upon the amount in the system . e.g. Mass , volume , pressure , internal energy , heat capacity , entropy , enthalpy , gibbs free energy .

**Intensive Property** These properties are independent of amount taken in a system . e.g. Density , Viscosity , refractive index , specific heat capacity , resistivity .

## Functions

**State Function :**  The state variables do not depend on the pathway . They only depend on the state of the system . e.g. Potential Energy , Entropy .

**Path Function :**  The state variables do depend on the pathway . e.g. work , heat .

**Thermodynamic Equilibrium :** A system is said to be in equilibrium if the state variables do not change with time .

## Heat and Work

The form of energy exchanged between two bodies at different temperatures is known as Heat energy . The amount of heat transferred is represented by q .

Heat is gained q is positive

Heat is lost q is negative

If a force applied on a body , displaces the body , then work is said to be done .

## Pressure Volume Work

**Isothermal** **Irreversible Process**

**W = - Pex ∆V**

W = -∆nRT

**Isothermal** **Reversible Process**

**W = - 2.303 nRT log10 (V2/V1)**

= -2.303 nRT log10 (P1/P2)

NOTE : Work done = Area under PV curve and Work is a path function .

## First Law of Thermodynamics

The First Law of Thermodynamics states that the energy lost from one part of the system evolves in another form , thus conserving total energy of the universe .

1) Th total energy of an isolated system remains constant .

2) Energy can be converted from one form to another but not destroyed .

3) The total energy of universe is always constant .

4) Whenever quantity of energy of one kind disappears , an exactly equivalent amount of energy of other kind must evolve .

**Mathematical Form**

**∆U = q + W**

**First Law for different Processes**

**Isothermal Process**

**Isochoric Process**

**Isobaric Process**

**Adiabatic Process**

## Enthalpy

**∆H = ∆U + P∆V**

∆H = ∆U + RT∆n

## Enthalpy for Physical Processes

**Enthalpy of Fusion**

**Enthalpy of Freezing**

**Enthalpy of Vaporization**

**Enthalpy of Condensation**

**Enthalpy of Sublimation**

**Enthalpy of ionization**

**Enthalpy of Electron Gain**

**Enthalpy of Atomization**

**Enthalpy of Dilution**

## Hess' Law

Hess' Law states that the change in enthalpy for a reaction is the same whether the reaction is carried out in 1 step or a series of steps . This means that Enthalpy is a State Function .

## Born Haber Cycle

For NaCl , E = -411 kJ

Enthalpy of Sublimation : 109 kJ

Enthalpy of Ionization : 496 kJ

Enthalpy of Atomization : 122 kJ

Enthalpy of Electron Gain : - 348 kJ

Lattice Enthalpy : -790 kJ

## Enthalpy of Solution

Solute - Solute Interaction : The enthalpy of lattice gives us an idea about the solute-solute interaction .

Solvent-Solvent Interaction :

Solute - Solvent Interaction : The Hydration Enthalpy gives us an idea about solute - solvent interaction .

## Enthalpy of Chemical Reaction

Enthalpy of a Chemical Reaction is also called the heat of reaction .

... **∆H = ΣHproducts - ΣHreactants**

Enthalpy of chemical reaction is expressed as joule or kilo joule . The individual enthalpies are expressed as Joule per Mole .

The enthalpy of a substance in its elemental state is 0 . e.g. ∆H(O2) = 0 , ∆H(Cl2) = 0 , ∆H(C) = 0

**Standard Enthalpy**

The enthalpy change that accompanies a chemical reaction in which all the substances are in their standard forms .

**Enthalpy of Formation**

The enthalpy change that accompanies a reaction in which the products are formed in their standard forms from its elements also in the standard form .

**Enthalpy of Combustion**

The enthalpy change that accompanies the complete combustion of one mole of a substance or its raction with oxygen .

## Bond Enthalpy

The enthalpy change needed to break bonds in one mole of gaseous molecules is called as bond enthalpy . An exactly opposite energy is applied to break the bond .

Let BE be the Bond Enthalpy .

... **∆HoREACTION = Σ ∆Horeactants - Σ ∆HoProducts**

## Spontaneous Process

A spontaneous process is a process which occurs irreversibly without any need of external force . A Non-spontaneous Process is a process which does not occur on its own and is reversible .

For a reaction to occur spontaneously , the stability of product should be more than that of reactants . Thus , the energy of products should be less than that of reactants . ... The system should lose energy to perform a spontaneous process . Thus we can formulate :-

**q is -ve** ; reaction is spontanous

**q is +ve** ; reaction is Non-spontaneous

But , this rule is not universally applicable . For e.g. it does not hold true for the melting or fusion of solid to liquid , which is an endothermic reaction but still is a spontaneous reaction , as it occurs on its own at room temperature .

## Entropy

Entropy is the measure of disorderness . The gaseous state is more disordered than liquid and liquid is more disordered than solid , due to their mobility of molecules .

Thus , the entropy of gaseous state is higher than liquid , higher than solid state . This shows that entropy change is directly proportional to the heat provided to it in a reversible manner . Now , at higher temperatures the change in heat won't have a big change in Entropy . At lower temperatures , a change in heat , causes greater change in entropy . This shows that Entropy change is inversely proportional to the temperature at which the system is already present .

... **∆S = qrev/ T**

Here , we cannot calculate the entropy , but we can calculate the change in entropy .

## Second Law of Thermodynamics

The Second Law of thermodynamics States that the spontaneous flow of heat is always unidirectional from higher temperature to lower temperature .
Heat cannot be completely converted into an equivalent amount of work without producing permanent changes either in the system or its surroundings .

The total energy of the universe increases in a spontaneous process .

**∆Suniverse = ∆Ssys + ∆Ssurr**

 Thus , if **∆S is+ve ;** reaction is spontanous ; (i.e. the **∆**S is increasing)

**∆S is -ve ;** reaction is non-spontaneous

Though this law is universally valid , it does not fall under thermodynamics because it involves the observation of surrounding , which is against the basic rule of thermodynamics . Thus , we have the third law of thermodynamics , in which the second law has been modified in terms of system properties only .

## Gibbs Free Energy

Gibbs Energy was introduced to modify the second law of thermodynamics , so that it deals only with the system .

**G = H - TS**

**∆G = ∆H - T∆S**

Consider ∆Ssurr = qrev / T

∆Ssurr = - ∆H / T

Now , ∆Stotal = ∆S + ∆Ssurr

∆Stotal = ∆S - H/T

- ∆Stotal = H/T - ∆S

- T∆Stotal = H - T∆S

-T∆Stotal = H -T∆S

∆G =- T∆Stotal

**G is -ve** ; Reaction is Spontaneous

**G is +ve** ; Reaction is Non-Spontaneous

∆G = ∆Go + RT ln Q {For a condition of the reacting system , other than equilibrium}

∆G = ∆Go + RT ln K {For a reacting system at Equilibrium}

But , ∆G = 0

... ∆Go = - RT ln K = - 2.303 RT log10 K

## Third Law of Thermodynamics

The third law of thermodynamics states that the entropy of a perfectly ordered crystalline substance is zero at absolute zero of temperature . ... S = 0 ; T=0 .

## Derivations

1. Work Done in isothermal irreversible process .
2. Work done in isothermal reversible process
3. Born-Haber Cycle
4. Enthalpy Change
5. Entropy
6. Gibb's Energy