IB DP Chemistry: Topic 5. Energetics/thermochemistry :5.2 Hess’s Law: Study Notes

THERMODYNAMICS

SYSTEM

SURROUNDINGS

TYPES OF SYSTEM

1. Open system  – A system which can exchange matter as well as energy with surroundings.
2. Closed system – A system which can exchange energy and not matter with surroundings.
3. Isolated system –  A system which can exchange neither matter nor energy with surroundings.
4. Homogeneous system – A system consisting of one phase only e.g. pure solid, a liquid or a mixture of gases.
5. Heterogeneous system – It may consists of two or more phases e.g. a solid in contact with liquid etc.

STATE OF SYSTEM

MACROSCOPIC PROPERTIES

EXTENSIVE PROPERTIES

INTENSIVE PROPERTIES

STATE VARIABLES AND STATE FUNCTIONS

INTERNAL ENERGY, INHERENT ENERGY OR HIDDEN ENERGY (IE)

• Translational energy of the molecules, Et  
• Rotational energy, Er
• Vibrational energy, Ev
• Electronic energy, Ee   
• Nuclear energy, En
• Interaction energy of molecules, Ei  

+ve   change is endothermic

– ve   change is exothermic

INTERNAL ENERGY CHANGE (E)

T = Rise in temperature

MODES OF THE TRANSFER OF ENERGY

EXPRESSION FOR PV WORK

The mathematical expression for pressure-volume work is

SIGN CONVENTIONS :

• Heat absorbed by the system is positive  +ve
• Heat evolved by the system is negative   –ve
• Work done on the system is positive  +ve
• Work done by the system is negative –ve

PROCESSES AND THEIR TYPES

1. Process – The operation by which a system changes from one state to another state is called process
2. Reversible process – If the driving force is only infinitesimally greater than the opposing force and process can be reversed at any instant, it is known as reversible process.
3. Irreversible process – It does not take place infinitesimally slow.

THERMODYNAMIC PROCESSES

1. Isothermal process (T = 0) : During each stage of process, the temperature remains constant. If  the process is exothermic heat is given out to surroundings, If the process is endothermic heat is absorbed from surroundings.
2. Adiabatic process (dq=0) : No heat leaves or enter the system, temperature of a system rises in exothermic process, temperature falls in endothermic process.
3. Isobaric process : Pressure remains constant, only volume changes.

volume  decreases

 volume increases

4. Isochoric process  : Volume remains constant but pressure changes.

pressure decreases

  pressure increases

5. Cyclic process :  After undergoing a number of changes, the system returns to its original state. In cyclic process

THERMODYNAMIC EQUILIBRIUM

1. Thermal equilibrium – The temperature of the system remains constant throughout and no heat flows from one part to another part of system.
2. Mechanical equilibrium – The pressure remains constant and no mechanical work is done by one part of system on another part.
3. Chemical equilibrium – The composition of various phases remains the same.

FIRST LAW OF THERMODYNAMICS

1. Law of equivalence of different forms of energies
2. Energy can neither be created nor destroyed but can be transformed from one form to another.
3. Total energy of universe is conserved (fixed, constant)

MATHEMATICAL EXPRESSION OF FIRST LAW

If volume remains constant, no work is done then

DISCUSSION OF EQUATION

(i) when

(ii) when

(iii) when  

If work is done on the system (when  ) heat flows from system to surroundings.

(iv) Cyclic process, E = 0, q = –w

SIGNIFICANCE  OF E

ENTHALPY (H) AND ENTHALPY CHANGE (H)

SIGNIFICANCE OF H

P = 0,

;  (From first law of thermodynamics)

FACTORS AFFECTING THE H

• Physical state of reactants and products
• Quantities of  reactants and products
• Allotropic forms
• Temperature
• Conditions of constant P and  Constant V at a particular temperature.

KIRCHOFF’S EQUATION

Cp = Difference in the heat capacities of products and the reactants at constant pressure.

=Difference in the heat capacities of  products and the reactants at constant volume.

STANDARD ENTHALPY

The enthalpy change at the standard conditions i.e. at 1 atm pressure and 298K temperature is called standard enthalpy of the reaction and is denoted by

RELATION BETWEEN H AND E:

It is given by , where

n = (Number of moles of products – number of moles of reactants) gaseous only.

E AND H FOR MONOATOMIC GAS :

Internal Energy =  per mole and

Enthalpy  

                 

APPLICATIONS OF  FIRST LAW OF THERMODYNAMICS

HESS’S LAW OF CONSTANT HEAT SUMMATION

APPLICATIONS OF HESS’S LAW

• Calculation of heats of reactions
• Determination of heat changes of slow reactions
• Calculation of enthalpies of formation
• Calculation of bond energies

WORK DONE IN ISOTHERMAL REVERSIBLE EXPANSION (MAXIMUM WORK)

WORK DONE IN ADIABATIC REVERSIBLE EXPANSION

or T. P1– = const.

WORK DONE IN ADIABATIC IRREVERSIBLE EXPANSION

      

Pext = 0, work done = 0,  also

If i.e. expansion work or work done by system.  

If  then Wirr is  +ve i.e. compression work or work done on the system.

HEAT CAPACITY OF A SYSTEM

.

Heat capacity at constant volume  

Heat capacity at constant pressure

where are specific heats at constant pressure and constant volume respectively

For monoatomic gas X=0, for diatomic gas X=R and for triatomic gas

LIMITATION OF FIRST LAW OF THERMODYNAMICS

SPONTANEOUS PROCESS

1. Spontaneous processes that need no initiation
   1. Evaporation of water H2O (l)  H2O (g)
   2. Dissolution of sugar  

3. 3. Intermixing of gases
4. Spontaneous processes that need initiation
   1. 
   2. Electrolysis of water  

SECOND LAW OF THERMODYNAMICS

• Clausius :  Heat cannot itself pass from a colder body to a hotter body.
• Kelvin : It is impossible to get a continuous supply of work from a body or engine which can transfer heat from a single heat reservoir.
• Planck : It is impossible to construct a device which will work in a single complete cycle and convert heat into work without producing any change in the surroundings.
• All natural and spontaneous processes take place in one direction and thus are irreversible in nature.
• In a reversible process the entropy of the universe is constant. In an irreversible process the entropy of the universe increases.

Entropy (S)

S = 

STotal = Ssystem + Ssurr > 0

Or   Suniverse >0

S = (Sfinal – Sinitial) = qrev / T

ENTROPY CHANGE FOR AN IDEAL GAS UNDER DIFFERENT CONDITIONS: WITH CHANGE IN P, V AND T

(when T and V are two variables)

 (when T and P are two variables)

For isothermal process

For isobaric process  

For isochoric process  

GIBB’S FREE ENERGY (G)

 and change is given by

Useful work

HELMHOLTZ  FREE ENERGY (WORK FUNCTION) (A)

CRITERIA FOR FEASIBILITY OR SPONTANEITY OF A PROCESS

G = H – TS (at constant T)

STotal = Ssys + Ssurr > 0

Ssurr = 

STotal = Ssys +

TSTotal = TSsys – Hsys

= –(Hsys – TSsys)

= –(G)

1. If   is negative, the process is spontaneous
2. If   is zero, the process is in equilibrium
3. If   is Positive the process does not occur

STANDARD FREE ENERGY CHANGE (AND EQUILIBRIUM CONSTANT (K)

They are related as follows  2.303 RT log K

FREE ENERGY CHANGE AND CELL POTENTIAL

nFEº

VARIATION OF FREE ENERGY WITH TEMPERATURE AND PRESSURE IN A REVERSIBLE PROCESS

CHANGE IN FREE ENERGY FOR ISOTHERMAL PROCESS

CRITERIA OF FEASIBILITY OR SPONTANEITY IN TERMS OF :

1. Entropy :

, the process is reversible and system is in equilibrium when internal energy and volume are kept constant.

the process is irreversible and if , the process is reversible.

2. Internal energy : When entropy and volume kept constant

If , the process is irreversible and if , the process is reversible.

3. Enthalpy (H) : When entropy and pressure are kept constant
   , the process is irreversible and if , the process is reversible.
4. Work function (A) : When temperature and volume are kept constant
   , the process is irreversible and if , the process is reversible.
5. Free energy (G) : When pressure and temperature are kept constant
   , the process is irreversible and if , the process is reversible.

ZEROTH LAW OF THERMODYNAMICS

THIRD LAW OF THERMODYNAMICS

.

CLAPEYRON – CLAUSIUS EQUATION

1. For water (liquid ) = water (vapour) we have

;

2. For water (Solid, Ice) = water (liquid)

;

3. For solid = vapour equilibrium

;

INTEGRATED FORM OF CLAPEYRON – CLAUSIUS EQUATION

log

APPLICATIONS OF CLAPEYRON CLAUSIUS EQUATION

1. Calculation of molar heat of vaporisation
2. Effect of temperature on vapour pressure of a liquid
3. Effect of pressure on boiling point
4. Calculation of molal elevation constant (kb) and molal depression constant (kf) of a solvent.

HEAT ENGINE

EFFICIENCY OF HEAT ENGINE

CARNOT CYCLE

1. Isothermal expansion
2. Adiabatic expansion
3. Isothermal compression
4. Adiabatic compression

EFFICIENCY OF CARNOT CYCLE OR ENGINE

Since     is always less than unity, hence efficiency is always less than unity

CARNOT THEOREM

RESONANCE ENERGY

(Expected value of ) – (Observed value of )

Sol. Calculated value of  

    

CALORIFIC VALUE

TYPES OF REACTIONS AND CORRESPONDING ENTHALPY CHANGES

1. Heat of reaction at constant volume and certain temperature
   It is defined as the change in internal energy () of the system when requisite number of molecules of reactants react to form the products. () =  = heat of reaction at constant volume
2. Heat of reaction at constant pressure and certain temperature
   It is defined as the difference in enthalpies () of products and reactants  heat of reaction at constant pressure
3. Relation between heat of reaction at constant volume () and at constant pressure ()

4. Sign of  and :  Negative sign of or shows that heat is evolved and reaction is exothermic while a positive sign of and shows that heat is absorbed and reaction is endothermic.
5. Factors affecting the heat of reaction
   1. Physical state of the reactants and products
   2. Amount of the reactants
   3. Temperature
   4. Pressure
6. Thermochemical equation

7. Heat of formation () : It is defined as the enthalpy change accompanying the formation of one mole of the compound from its elements.

8. Standard heat of formation  : It is the enthalpy change accompanying the formation of one mole of a compound from its elements. All substances being in their standard states. The condition of standard state is 25ºC and 1 atm pressure.
9. Heat of combustion : It is the change in enthalpy of the system, when 1 gram mole of the substance is completely oxidized

10. Application of  heat of combustion
    1. Calorific value of fuel
    2. Calculation of heat of formation
    3. Constitution of organic compounds
11. Heat of neutralization : It is defined as the enthalpy change () accompanying the neutralization of one gram equivalent of the acid by a base in dilute solution at that temperature.

12. Heat of solution  : The enthalpy change per mole of solute when it is dissolved in large excess of solvent (generally H2O) so that further dilution of the solution produces no heat exchange.

13. Heat of dilution : The enthalpy change when a solution containing one mole of a solute is diluted from one concentration to another.
14. Heat of  hydration : The enthalpy change when one mole of a substance combines with the required number of moles of water to form a specified hydrate.

15. Heat of precipitation : The enthalpy change when one mole of a sparingly soluble substance precipitates on mixing dilute solutions of stable electrolytes is called heat of precipitation.

16. Bond enthalpy : It is defined as the average amount of energy required to break all the bonds of a particular type in one mole of the substance. It is also known as bond energy and expressed in kJ mol–1.

;

;

17. Use of bond enthalpy :
    1. Calculating standard enthalpy of reactions

H =[sum of bond energies of reactants] – [sum of bond energies of products]

2. Calculation of bond energy of some specific bond in the molecule

LAWS OF THERMOCHEMISTRY

1. Lavosier and Laplace law : The heat evolved or absorbed in the course of a chemical reaction is equal to the heat absorbed or evolved when the reaction is reversed.  
2. Hess’s law of constant heat summation

TROUTON’S RULE

The quantity   is also called entropy of vaporization Sv.

ENDOTHERMIC COMPOUNDS