Chapter 6. THERMODYNAMICS

CHAPER – 6 THERMODINAMICS

IMPORTANT TERMS AND DEFINITIONS

System: Refers to the portion of universe which is under observation.
Surroundings: Everything else in the universe except system is called surroundings. The Universe = The System + The Surroundings.

Open System: In a system, when there is exchange of energy and matter taking place with
the surroundings, then it is called an open system.
For Example: Presence of reactants in an open beaker is an example of an open system. Closed System: A system is said to be a closed system when there is no exchange of matter ‘ but exchange of energy is possible.
For example: The presence of reactants in a closed vessel made of conducting material.

Isolated System: In a system, when no exchange of energy or matter takes place with the surroundings, is called isolated system.
For example: The presence of reactants in a thermoflask, or substance in an insulated closed vessel is an example of isolated system.

Homogeneous System: A system is said to be homogeneous when all the constituents present is in the same phase and is uniform throughout the system.
For example: A- mixture of two miscible liquids.
Heterogeneous system: A mixture is said to be heterogeneous when it consists of two or more phases and the composition is not uniform.
For example: A mixture of insoluble solid in water. ’
The state of the system: The state of a thermodynamic system means its macroscopic or bulk properties which can be described by state variables:
Pressure (P), volume (V), temperature (T) and amount (n) etc.
They are also known as state functions.

Isothermal process: When the operation is carried out at constant temperature, the process is said to be isothermal. For isothermal process, dT = 0 Where dT is the change in temperature.

Adiabatic process: It is a process in which no transfer of heat between system and surroundings, takes place.

Isobaric process: When the process is carried out at constant pressure, it is said to be isobaric. i.e. dP = 0

Isochoric process: A process when carried out at constant volume, it is known as isochoric in nature.

Cyclic process: If a system undergoes a series of changes and finally returns to its initial state, it is said to be cyclic process.

Reversible Process: When in a process, a change is brought in such a way that the process could, at any moment, be reversed by an infinitesimal change. The change r is called reversible.

•Internal Energy
It is the sum of all the forms of energies that a system can possess.
In thermodynamics, it is denoted by AM which may change, when
— Heat passes into or out of the system
— Work is done on or by the system
— Matter enters or leaves the system.

Change in Internal Energy by Doing Work
Let us bring the change in the internal energy by doing work.
Let the initial state of the system is state A and Temp. T_A Internal energy = u_A
On doing’some mechanical work the new state is called state B and the temp. T_B. It is found to be
T_B > T_A
u_B is the internal energy after change.
∴ Δu = u_B – u_A

Change in Internal Energy by Transfer of Heat
Internal energy of a system can be changed by the transfer of heat from the surroundings to the system without doing work.
Δu = q
Where q is the heat absorbed by the system. It can be measured in terms of temperature difference.
q is +ve when heat is transferred from the surroundings to the system. q is -ve when heat is transferred from system to surroundings.
When change of state is done both by doing work and transfer of heat.
Δu = q + w
First law of thermodynamics (Law of Conservation of Energy). It states that, energy can neither be created nor be destroyed. The energy of an isolated system is constant.
Δu = q + w.

APPLICATIONS

• Work (Pressure-volume Work)
Let us consider a cylinder which contains one mole of an ideal gas in which a frictionless piston is fitted.

• Work Done in Isothermal and Reversible Expansion of Ideal Gas

 • Isothermal and Free Expansion of an Ideal Gas

For isothermal (T = constant) expansion of an

ideal gas into vacuum ; w = 0 since pex = 0.

Also, Joule determined experimentally that

q = 0; therefore, ∆U = 0

• Enthalpy (H)
It is defined as total heat content of the system. It is equal to the sum of internal energy and pressure-volume work.
Mathematically, H = U + PV
Change in enthalpy: Change in enthalpy is the heat absorbed or evolved by the system at constant pressure.
ΔH = q_p
For exothermic reaction (System loses energy to Surroundings),
ΔH and q_p both are -Ve.
For endothermic reaction (System absorbs energy from the Surroundings).
ΔH and q_p both are +Ve.
Relation between ΔH and Δu.

Let us consider a general reaction A B

Let H_A be the enthalpy of reactant A and H_B be that of the products.

∴ H_A = U_A + PV_A

H_B = U_B + PV_B

 ΔH = H_B - H_A

= (U_B + PV_B) – (U_A + PV_A)

ΔH = ΔU + PΔV (H_B – H_A)

 ΔH = ΔU + PΔV

At constant pressure and temperature using ideal gas law,

PV_A = n_A RT (for reactant A)

PV_B = n_B RT (for reactant B)

Thus,   PV_B – PV_A = n_B RT - n_A RT

= ( n_B – n_A) RT

PΔV = Δn_g RT

∴ ΔH = ΔU + Δn_g RT
• Extensive property
An extensive property is a property whose value depends on the quantity or size of matter present in the system.
For example: Mass, volume, enthalpy etc. are known as extensive property.
• Intensive property
Intensive properties do not depend upon the size of the matter or quantity of the matter present in the system.
For example: temperature, density, pressure etc. are called intensive properties.
• Heat capacity
The increase in temperature is proportional to the heat transferred.
q = coeff. x ΔT
q = CΔT
Where, coefficient C is called the heat capacity.
C is directly proportional to the amount of substance.
C_m = C/n
It is the heat capacity for 1 mole of the substance.

• Molar heat capacity
It is defined as the quantity of heat required to raise the temperature of a substance by 1° (kelvin or Celsius).
• Specific Heat Capacity
It is defined as the heat required to raise the temperature of one unit mass of a substance by 1° (kelvin or Celsius).
q = C x m x ΔT
where m = mass of the substance
ΔT = rise in temperature.
• Relation Between C_p and C_v for an Ideal Gas
At constant volume heat capacity = C_v
At constant pressure heat capacity = C_p
At constant volume q_v= C_vΔT = ΔU
At constant pressure q_p = C_p ΔT = ΔH
For one mole of an ideal gas
ΔH = ΔU + Δ (PV) = ΔU + Δ (RT)
ΔH = ΔU + RΔT
On substituting the values of ΔH and Δu, the equation is modified as

C_p ΔT = C_vΔT + RΔT
or C_p-C_v = R

MEASUREMENT OF ΔU AND ΔH—CALORIMETRY

Determination of ΔU: ΔU is measured in a special type of calorimeter, called bomb calorimeter.

Working with calorimeter. The calorimeter consists of a strong vessel called (bomb) which can withstand very high pressure. It is surrounded by a water bath to ensure that no heat is lost to the surroundings.
Procedure: A known mass of the combustible substance is burnt in the pressure of pure dioxygen in the steel bomb. Heat evolved during the reaction is transferred to the water and its temperature is monitored.

ENTHALPY CHANGE, ∆rH OF A REACTION – REACTION ENTHALPY

• Enthalpy Changes During Phase Transformation
Enthalpy of fusion: Enthalpy of fusion is the heat energy or change in enthalpy when one mole of a solid at its melting point is converted into liquid state.

Enthalpy of vaporisation: It is defined as the heat energy or change in enthalpy when one mole of a liquid at its boiling point changes to gaseous state.

Enthalpy of Sublimation: Enthalpy of sublimation is defined as the change in heat energy or change in enthalpy when one mole of solid directly changes into gaseous state at a temperature below its melting point.

ENTHALPIES FOR DIFFERENT TYPES OF REACTIONS

• Standard Enthalpy of Formation
Enthalpy of formation is defined as the change in enthalpy in the formation of 1 mole of a substance from its constituting elements under standard conditions of temperature at 298K and 1 atm pressure.

ΔH_r^º (298.15 K) and ΔG_r^º (298.15 K)

ΔG_r^º (T)

ΔH_r^º (T) and K_p (298.15 K)

K_p (T₁) and K_p (T₂) where T₁, T₂ ≠ T

ΔH_r^º (T) and ΔG_r^º (298.15 K)

Enthalpy of Combustion: It is defined as the heat energy or change in enthalpy that accompanies the combustion of 1 mole of a substance in excess of air or oxygen.

CO_(g) + ½ O_2(g)  CO_2(g) ΔHº = -283 kJ

• Thermochemical Equation
A balanced chemical equation together with the value of Δ_rH and the physical state of reactants and products is known as thermochemical equation.

Thermochemical equations

•  A typical chemical equation is

   S + O₂  SO₂

• It is called a thermochemical equation when we add information about ΔH…

   S + O₂ SO₂     ΔH = -296.9 kJ

• If we change the equation, then the ΔH also changes…

  SO₂  S + O₂       ΔH = +296.9 kJ

• If the reaction is reversed the sign is reversed
• Also, if numbers in the equation change, so will the amount of energy produced/absorbed:

   2S + 2O₂  2SO₂     ΔH = -593.8 kJ

Conventions regarding thermochemical equations
1. The coefficients in a balanced thermochemical equation refer to the number of moles of reactants and products involved in the reaction.

If the coefficients of the chemical equation are multiplied by some factor, the enthalpy change must also be multiplied by the same factor (ΔH is an extensive property).

H_2(g) + ½ O_2(g)  H₂O_(l)  ΔH = -286 kJ

Multiply by a factor of two:

2H_2(g) +  O_2(g) 2H₂O_(l)  ΔH = 2 x (-286kJ) = -572kJ

Multiply by a factor of one-half:

½ H_2(g) + ¼ O_2(g)  ½ H₂O_(l)  ΔH = ½ x (-286kJ) = -134kJ

• Hess’s Law of Constant Heat Summation
The total amount of heat evolved or absorbed in a reaction is same whether the reaction takes place in one step or in number of steps.

The law stats that the change in enthalpy for a reaction is the same whether the reaction takes place in one or a series of step. The Hess’s law can also be states as the enthalpy change for a chemical reaction is the same regardless of the path by which the reaction occurs.

For example, consider following two paths for the preparation of methylene chloride

Path I:

CH_{4 (g)} + 2 Cl_2(g) CH₂Cl_2(g) + 2HCl_(g)   ΔH₁^º = - 202.3kJ

Path II:

CH_{4 (g)} + Cl_2(g)  CH₃Cl_2(g) + HCl_(g)   ΔH₂^º = - 98.3kJ

CH₃Cl_(g) + Cl_2(g)   CH₂Cl_2(g) + HCl_(g)  ΔH₃^º = - 104.0kJ

Adding two steps

CH_4(g) + 2Cl_2(g)  CH₂Cl_2(g) + 2HCl_(g)  ΔH^º = - 202.3kJ

Thus whether we follow path 1 or path 2 the enthalpy change of the reaction is same.

ΔH₁^º = ΔH₂^º + ΔH₃^º = - 202.3kJ

• Born-Haber Cycle
It is not possible to determine the Lattice enthalpy of ionic compound by direct experiment. Thus, it can be calculated by following steps. The diagrams which show these steps is known as Born-Haber Cycle.

SPONTANEITY

Spontaneous Process: A process which can take place by itself or has a tendency to take place is called spontaneous process.
Spontaneous process need not be instantaneous. Its actual speed can vary from very slow to quite fast.
A few examples of spontaneous process are:
(i) Common salt dissolves in water of its own.
(ii) Carbon monoxide is oxidised to carbon dioxide of its own.
• Entropy (S)
The entropy is a measure of degree of randomness or disorder of a system. Entropy of a substance is minimum in solid state while it is maximum in gaseous state.
The change in entropy in a spontaneous process is expressed as ΔS

ΔS = ΔS_system + ΔS_surroundings

ΔS = Overall change in entropy

ΔS_system = Change in entropy of the system

ΔS_surroundings =Change in entropy of the surroundings

ΔS > 0, + entropy change, reaction is spontaneous

ΔS < 0, - entropy change, reaction is nonspontaneous

Equation for the total change in entropy

• Gibbs Energy and Spontaneity
A new thermodynamic function, the Gibbs energy or Gibbs function G, can be defined as G = H-TS
ΔG = ΔH – TΔS
Gibbs energy change = enthalpy change – temperature x entropy change ΔG gives a criteria for spontaneity at constant pressure and temperature, (i) If ΔG is negative (< 0) the process is spontaneous.
(ii) If ΔG is positive (> 0) the process is non-spontaneous.
• Free Energy Change in Reversible Reaction

qualitative relationship between the change in standard free energy and the equilibrium constant for a given relation

GIBBS ENERGY CHANGE AND EQUILIBRIUM

At equilibrium, i.e., ΔG = 0, the process is neither spontaneous nor non-spontaneous because it is balanced between spontaneous and non-spontaneous behavior. (+ΔH)

So,

ΔG = ΔH – T ΔS = 0

Hence,

ΔH = TΔS or T = ΔH / ΔS

T is the temperature at which the transition from spontaneous to non-spontaneous behaviour happens. T is calculated on the assumption that ΔH and ΔS are temperature independent. In reality, ΔH and ΔS change with temperature. However, for modest temperature changes, the variance in them will not add considerable mistakes.

ΔG and Equilibrium constant 

All of the substances (reactants and products) in a chemical reaction may not be in their normal forms. As a result of the connection, the change in Gibbs energy of a reaction is related to the change in standard Gibbs energy.

ΔG = ΔG° + RT ln Q

where:

ΔG° is the standard Gibbs energy change (change in Gibbs energy when all the substances are in their standard state).

Q is the reaction quotient.

The expression of the reaction quotient is similar to that of the equilibrium constant, but there is one single difference between them, i.e., Equilibrium concentrations or partial pressures of products and reactants are included in the equilibrium constant. Whereas Q is expressed in terms of reactant beginning concentration partial pressures and product final concentrations or pressures.

For Example, consider the below example:

aA +bB ⇢ cC + dD

For the above reaction, the reaction Quotient is given by

When the values of concentration or partial pressure are other than equilibrium values. When the reaction reaches equilibrium, the concentrations and partial pressure reach their equilibrium values and at this stage, Q = K. At equilibrium, ΔG = 0 and Q = K, then the standard Gibbs energy equation becomes,

0 = ΔG° + RT ln K

Hence,

ΔG° = -RT ln K = -2.303RT log10K

This equation gives the relationship between standard Gibbs energy change for the reaction and its equilibrium constant.