Enthalpy of A System

– Enthalpy (H) is the total heat content of a system at constant pressure and is equivalent to the internal energy E plus the PV energy.

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 and 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 equation (1) above, E, P, and V are all state functions.

– Thus H, the value of which depends on the values of E, P, and 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 is the difference in enthalpy of a system in the final state (H₂) and that in the initial state (H₁),

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 + PΔV

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 the change in state occurs at constant pressure

– This relationship is usually written as:

ΔH = q_p

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

– Since

ΔH = H₂ – H₁

– When 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 = q_p

– 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

– The calorific values of many gaseous fuels are determined in constant volume calorimeters.

– These values are, therefore, given by the expression:

q_v= 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 realized, i.e., q_p = 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 the reaction, and n₂ moles of gases after it.

– Assuming ideal gas behavior, we have:

P V₂= n₂ RT

P V₁= n₁ RT

∴ P (V₂ – V₁) = (n₂ – n₁) RT

PΔV = Δn RT

– Substituting in equation (1) we have,

ΔH = ΔE + Δn RT

Solved Problem

For the reaction:

Calculate ΔH for the reaction.

Solution:

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