Lattice energy is defined as "The amount of energy required to completely remove the constituent ions from its crystal lattice to an infinite distance." It is also referred as lattice enthalpy

(i) Entropy is a measure of the molecular disorderliness (randomness) of a system. dS = dq_rev/T
(ii) The entropy (S) is equal to heat energy exchanged (q) divided by the temperature (T) at which the exchange takes place. Therefore, The SI unit of entropy is JK^-1

The enthalpy change of a reaction either at constant volume or constant pressure is the same whether it takes place in a single or multiple steps provided the initial and final states are same.

(i) spontaneous reaction: A reaction that occurs under the given set of conditions without any external driving force is called a spontaneous reaction.
(ii) Criteria for spontaneity of a process: The spontaneity of any process depends on three different factors.
ΔH = -ve, ΔS = +ve, ΔG = -ve.

(i) State function: A state function is a thermodynamic property of a system, which has a specific value for a given state and does not depend on the path (or manner) by which the particular state is reached.
Example: Pressure (P), Volume (V), Temperature(T)
(ii) Path functions: A path function is a thermodynamic property of the system whose value depends on the path by which the system changes from its initial to final states.
Example: Work (w), Heat (q).

When the system at constant pressure undergoes changes from an initial state with H₁, U₁ and, V₁ to a final state with H₂, U₂ and V₂ the change in enthalpy ΔH, can be calculated as follows:
H = U+PV
In the initial state
H₁ = U₁ +PV₁ ........(1)
In the final state
H₂ = U₂ +PV₂ ........(2)
change in enthalpy is (2) - (1)
(H₂ - H₁) = (U₂ - U₁) + P(V₂ - V₁)
ΔH = ΔU+PΔV
As per first law of thermodynamics,
ΔV = q+w
Equation (3) becomes
ΔH = q+w+PΔV
w = -PΔV
ΔH = qp-PΔV+PΔV
ΔH = qp....(4)
q_p - is the heat absorbed at constant pressure and is p considered as heat content. Consider a closed system of gases which are chemically reacting to form gaseous products at constant temperature and pressure with V_i and V_f as the total volumes of the reactant and product gases respectively, and n _i and n_f as the number of moles of gaseous reactants and products, then,
For reactants (initial state) :
PVi = ni RT ...(5)
For products (final state) :
PVf = nfRT .........(6)
(6) - (5)
P(Vf - Vi) = (nf - ni) RT
PΔV = Δn(g) RT ...........(7)
Substituting in (7) in (3)
ΔH = ΔV +Δn(g) RT ........(8)

Characteristics of internal energy (U) :

• The internal energy of a system is an extensive property.
• The internal energy of a system is a state function.
• The change in internal energy of a system is expressed as ΔU= U_f - U_i
• In a cyclic process,' there is no internal energy change. ΔU_(cyclic)= 0
• If the internal energy of the system in the final state (U_f) is less than the internal energy of the system in its initial state (U_i), then ΔU would be negative.
• ΔU = U_f- Ui = -ve (U_f < U_i)
• If the internal energy of the system in the final state (U_f) is greater than the internal energy of the system in its initial state (U_i), then ΔU would be positive.
• ΔU = U_f - U_i = +ve (U_f > U_i)