Revision Notes on Chemical Thermodynamics:

Basic Terminology:

Terms	Explanation
System	Part of the universe under investigation.
Open System	A system which can exchange both energy and matter with its surroundings.
Closed System	A system which permits passage of energy but not mass, across its boundary.
Isolated system	A system which can neither exchange energy nor matter with its surrounding.
Surroundings	Part of the universe other than system, which can interact with it.
Boundary	Anything which separates system from surrounding.
State variables	The variables which are required to be defined in order to define state of any system i.e. pressure, volume, mass, temperature, surface area, etc.
State Functions	Property of system which depend only on the state of the system and not on the path. Example: Pressure, volume, temperature, internal energy, enthalpy, entropy etc.
Intensive properties	Properties of a system which do not depend on mass of the system i.e. temperature, pressure, density, concentration,
Extensive properties	Properties of a system which depend on mass of the system i.e. volume, energy, enthalpy, entropy etc.
Process	Path along which state of a system changes.
Isothermal process	Process which takes place at constant temperature
Isobaric process	Process which takes place at constant pressure
Isochoric process	Process which takes place at constant volume.
Adiabatic process	Process during which transfer of heat cannot take place between system and surrounding.
Cyclic process	Process in which system comes back to its initial state after undergoing series of changes.
Reversible process	Process during which the system always departs infinitesimally from the state of equilibrium i.e. its direction can be reversed at any moment.
Irriversible Process	This type of process is fast and gets completed in a single step. This process cannot be reversed. All the natural processes are of this type

Heat, energy and work:

Heat (Q):

Energy is exchanged between system and surround in the form of heat when they are at different temperatures.
Heat added to a system is given by a positive sign, whereas heat extracted from a system is given negative sign.
It is an extensive property.
It is not a state function.

Energy:

It is the capacity for doing work.
Energy is an extensive property.
Unit : Joule.

Work (W):

Work = Force × Displacement i.e. dW = Fdx
Work done on the system is given by positive sigh while work done by the system is given negative sign.
Mechanical Work or Pressure-Volume Work: work associated with change in volume of a system against an external pressure.
Work done in reversible process: W=

W = – 2.303 nRT log v₂/v₁ = –2.303 nRT log p₁/p₂

Wok done in isothermal reversible contraction of an ideal gas:
?W = – 2.303 nRT log v₂/v₁ = –2.303 nRT log p₁/p₂
Unit : Joule.

Internal Energy (E or U):

Sum of all the possible types of energy present in the system.
ΔE = heat change for a reaction taking place at constant temperature and volume.
ΔE is a state function.
It is an extensive property.
Value of ΔE is -ve for exothermic reactions while it is +ve for endothermic reactions.

First Law of Thermodynamics:

Energy can neither be created nor destroyed although it can be converted from one form to another.

Energy of an isolated system is constant.

Mathematical Expression

Heat observed by the system = its internal energy + work done by the system.
i.e. q = dE + w

For an infinitesimal process

dq = dE + dw

Where, q is the heat supplied to the system and w is the work done on the system.

For an ideal gas undergoing isothermal change ΔE =0.

so q= -w.

For an isolated system, dq=0

so, dE = - dw

For system involving mechanical work only

ΔE = q - pdV

At constant volume i.e. isochoric process

ΔE = q_v

For Isothermal Process

ΔE = 0

q = - pdV =-W

For adiabatic process

?q = 0

ΔE = W

Enthalpy (H):

H = E+PV

At constant pressure:

dH = dE + pdV

For system involving mechanical work only

dH = Q_P(At constant pressure)

For exothermic reactions:

dH = -ve

For endothermic reactions:

dH = +ve

Relation between dH and dE:

dH = dE + dn_gRT

Where,

dn_g= (Number of moles of gaseous products - Number of moles of gaseous reactants)

Heat capacity:

Amount of heat required to rise temperature of the system by one degree.

C = q / dT

Specific heat capacity: Heat required to raise the temperature of 1 g of a substance by one dgree.

C_s = Heat capacity / Mass in grams

Molar heat capacity: Heat required to raise the temperature of 1 g of a substance by one dgree.

C_m = Heat capacity / Molar mass.

Heat capacity of system at constant volume:

C_v = (dE/dT)_v

Heat capacity of system at constant pressure:

C_p = (dE/dT)_p

C_p – C_v = R

Variation Of Heat Of Reaction With Temperature:

dC_P = (dH₂ - dH₁)/(T₂-T₁) & dC_V= (dE₂ - dE₁)/(T₂-T₁

Bomb Calorimeter:

Heat exchange = Z × ΔT

Z–Heat capacity of calorimeter system

ΔT– Rise in temp.

Heat changes at constant volumes are expressed in ΔE and Heat changes at constant

pressure are expressed in dH.

Enthalpies of Reactions:

Enthalpies	Definitions	Example
Enthalpy of Formation	Enthalpy change when one mole of a given compound is formed from its elements	H₂(g) + 1/2O₂(g) → 2H₂O(l), Δ_fH = –890.36 kJ / mol
Enthalpy of Combustion	Enthalpy change when one mole of a substance is burnt in oxygen.	CH₄ + 2O₂(g) →CO₂ + 2H₂O(l), Δ_combH = –890.36 kJ / mol
Enthalpy of Neutralization	Enthalpy change when one equivalent of an acid is neutralized by a base in dilute solution.	H⁺ (aq) + OH^– (aq) → H₂O(l) Δ_neutH = –13.7 kcal
Enthalpy of Hydration	Enthalpy change when a salt combines with the required number of moles of water to form specific hydrate.	CuSO₄(s) + 5H₂O (l) → CuSO₄5H₂O, Δ_hydH° = –18.69 kcal
Enthalpy of Transition	Enthalpy change when one mole of a substance is transformed from one allotropic form to another allotropic form.	C (graphite) → C(diamond), Δt_ransH° = 1.9 kJ/mol
Enthalpy of Sublimation	Enthalpy change when one mole of a solid substance sublime at constant temp. and 1 bar pressure	CO₂(S) → CO₂(g) Δt_fusH° = 6.00 kJ/mol
Enthalpy of fusion	Enthalpy change when one mole of a solid melts	H₂O(S) → H₂O (l) Δt_subH° = 73.00 kJ/mol

Hess’s Law of constant heat summation:

?The total enthalpy change of a reaction is the same, regardless of whether the reaction is completed in one step or in several steps.

Oxidation of carbon
According to Hess’s law: ΔH = ΔH₁ + ΔH₂

Born–Haber Cycle:

Applying Hess’s law we get

ΔH₁ + 1/2 ΔH₂ + ΔH₃ + ΔH₄ + ΔH₅ = ΔH_f (MX) (Lattice energy)

Lattice energy: The change in enthalpy that occurs when 1 mole of a solid crystalline substance is formed from its gaseous ions.

Second law of thermodynamics

Statement:

It is impossible to take heat from a hot reservoir and convert it completely into work by a cyclic process without transferring a part of it to a cold reservoirs.

Mathematically:

ΔS = q_rev/T

Where,

ΔS is entropy change.

Entropy is the degree of randomness thus it increases with increase in randomness of particles of the system i.e. ΔS is positive for melting of ice.
At equilibrium, ΔS = 0
For a spontaneous process, ΔS > 0
Entropy change in an isothermal reversible expansion of a gas
$\Delta S = 2.303\ nR\textup\ log \frac{V_2}{V_1} = 2.303\ nR\ log\frac{P_1}{P_2}$
Spontaneous Processes: These type of physical and chemical changes occur of its own under specific circumstances or on proper initiations. For example: Flow of liquids from higher to lower level.
$\Delta S_{total}=\Delta S_{system}+\Delta S_{surrounding}>0 = \Delta S_{universe}>0$