Enthalpy (H)

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Enthalpy (H)

The enthalpy (H), is a thermodynamic property of a system, is defined as the sum of the internal energy (U) of a system and the product of pressure and volume of the system. That is,

H = U + PV …………………. (7.8)

It reflects the capacity to do mechanical work and the capacity to release heat by the system. When a process occurs at constant pressure, the heat involved (either released or absorbed) is equal to the change in enthalpy.

Enthalpy is a state function which depends entirely on the state functions T, P and U. Enthalpy is usually expressed as the change in enthalpy (ΔH) for a process between initial and final states at constant pressure.

ΔH = ΔU + PΔV …………………. (7.9)

The change in enthalpy (ΔH) is equal to the heat supplied at the constant pressure to a system (as long as the system does no additional work).

ΔH = q_P

In an endothermic reaction heat is absorbed by the system from the surroundings that is q>0 (positive). Therefore, ΔH is also positive. In an exothermic reaction heat is evolved by the system to the surroundings that is, q<0 (negative). If q is negative, then ΔH will also be negative.

Relation Between Enthalpy ‘H’ and Internal Energy ‘U’

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 ………….. (7.10)

In the final state

H₂ = U₂ + PV₂ …………… (7.11)

change in enthalpy is (7.11) – (7.10)

(H₂ – H₁) = (U₂ – U₁) + P(V₂ – V₁)
ΔH = ΔU + PΔV ……………… (7.12)
As per first law of thermodynamics,
ΔU = q + w
Equation 7.12 becomes
ΔH = q + w + PΔV
w= – PΔV
ΔH = q_p – PΔV + PΔV
ΔH = q_p ……………….. (7.13)

q_p – is the heat absorbed at constant pressure and is 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):

PV_i = n_iRT ……………….. (7.14)

For Products (Final State):

PV_f = n_fRT ………………. (7.15)

(7.15) – (7.14)

P (V_f – V_i) = (n_f – n_i) RT
PΔV= Δn_(g)RT ………………… (7.16)

Substituting in 7.16 in 7.12
ΔH = ΔU + Δn_(g)RT ……………… (7.17)

Enthalpy Changes for Different Types of Reactions and Phase Transitions:

The heat or enthalpy changes accompanying chemical reactions is expressed in different ways depending on the nature of the reaction. These are discussed below.

Standard Heat of Formation

The standard heat of formation of a compound is defined as “the change in enthalpy that takes place when one mole of a compound is formed from its elements, present in their standard states (298 K and 1 bar pressure)”. By convention the standard heat of formation of all elements is assigned a value of zero.

Fe(s) + S(s) → FeS(s)
ΔH_f° = – 100.42 kJ mol^-1
2C(s) + H₂(g) → C₂H₂(g)
ΔH_f° = + 222.33 kJ mol^-1
\(\frac{1}{2}\)Cl₂(g) + \(\frac{1}{2}\)H₂(g) → HCl (g)
ΔH_f° = – 92.4 kJ mol^-1

The standard heats of formation of some compounds are given in Table 7.4.

Standard Heat of Formation of Some Compounds