Enthalpy of A System

Enthalpy of A System

In a process carried at constant volume (say in a sealed tube), the heat content of a system is the same as internal energy (E), as no PV work is done. 

But in a constant-pressure process, the system (a gas) also expends energy in doing PV work. Therefore, the total heat content of a system at constant pressure is equivalent to the internal energy E plus the PV energy. This is called the Enthalpy (Greek en = in; thalpos = heat) of the system and is represented by the symbol H.
Enthalpy (H): is the total heat content of a system at constant pressure is equivalent to the internal energy E plus the PV energy.
Thus enthalpy is defined by the equation:

H = E + PV          (1)

Enthalpy – A Function of State

In the equation (1) above, E, P, V are all state functions. Thus H, the value of which depends on the values of E, P, V must also be a function of state. Hence its value is independent of the path by which the state of the system is changed.

Change in Enthalpy

If ΔH be the difference of enthalpy of a system in the final state (H2) and that in the initial state

ΔH = H2 – H1       (2)
Substituting the values of H2 and H1, as from (1) and (2), we have:
ΔH = (E2 + P2V2) – (E1 + P1V1)
= (E2– E1) + (P2V2 – P1V1)
= ΔE + ΔPV
If P is constant while the gas is expanding, we can write:
ΔH = ΔE + w (w = work)      (3)
According to the First Law,
ΔE = q – w      (4)
where q = heat transferred
From equations (3) and (4):
ΔH = q when change in state occurs at constant pressure
This relationship is usually written as:

ΔH = qp
where subscript p means constant pressure.
Thus ΔH can be measured by measuring the heat of a process occurring at constant pressure.

Units and Sign Conventions of Enthalpy


ΔH = H2 – H1
ΔH is positive if H2 > H1 and the process or reaction will be endothermic.
ΔH is negative if H1 > H2 and the reaction will be exothermic.
In case of a chemical reaction carried in the laboratory in an open vessel:
ΔH = H products – H reactants = qp
The heat of reaction at one atmosphere pressure is usually shown along with the equation. Thus,

The quantity of heat 68.32 kcal on the right hand represents – ΔH of the reaction.
The units of ΔH are kilocalories (kcal) or kilojoules (kJ).

Relation Between ΔH and ΔE

Calorific values of many gaseous fuels are determined in constant volume calorimeters. These values are, therefore, given by the expression:

qv= ΔE
When any fuel is burnt in the open atmosphere, additional energy of expansion, positive or negative, against the atmosphere is also involved. The value of q thus actually realised, i.e., qp = ΔH, may be different from the equation:

ΔH = ΔE + PΔV …(1)
If gases are involved in a reaction, they account for most of the volume change as the volumes
of solids and liquids are negligibly small in comparison.
Suppose we have n1 moles of gases before reaction, and n2 moles of gases after it. Assuming
ideal gas behaviour, we have:
P V2= n2 RT
P V1= n1 RT
P (V2 – V1) = (n2 – n1) RT
Substituting in equation (1) we have,
ΔH = ΔE + Δn RT

Solved Problem

For the reaction:

Calculate ΔH for the reaction.

Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.

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