Relation between enthalpy `H' and internal energy `U'

Enthalpy

In chemistry most of the chemical reactions are carried out at constant pressure. To measure heat changes of system at constant pressure, it is useful to define a new thermodynamic state function called Enthalpy `H'.

H is defined as sum of the internal energy `U' of a system and the product of Pressure and Volume of the system.

That is,

H = U + PV

H = U + PV

Characteristics of H

Enthalpy, H depends on three state functions U, P, V and hence it is also a state function. H is independent of the path by which it is reached. Enthalpy is also known by the term `heat content'.

Relation between enthalpy `H' and internal energy `U'

When the system at constant pressure undergoes changes from an initial state with H1, U1, V1, P parameters to a final state with H2, U2, V2, P parameters the chamge in enthalpy ∆H, is given by,

∆H = (H2 - H1) = (U2 - U1) + P(V2 - V1)

∆H = ∆U + P∆V

Considering ∆U = q -w or q - P∆V (assuming P- V work), ∆U + P∆V becomes equal to 'q_p'. 'q_p' is the heat absorbed by the system at constant pressure for increasing the volume from V₁ to V₂. This is so because, -w indicates that work is done by the system. Therefore volume increase against constant pressure is considered.

Eqn. becomes q_p = ∆U + P ∆V

= ∆H

Or ∆H = q_p

`q_p' is the heat absorbed by the system at constant pressure and is considered as the heat content of the system.

Heat effects measured at constant pressure indicate changes in enthalpy of a system and not in changes of internal energy of the system. Using calorimeters operating at constant pressure, the enthalpy change of a process can be measured directly.

Considering a system of gases which are chemically reacting to produce product gases with Vr and Vp as the total volumes of the reactant and product gases respectively, and n_r and n_p as the number of moles of gaseous reactants and products, then using ideal gas law we can write that, at constant temperature and constant pressure,

PVr = nrRT and PVp = npRT.

Then considering reactants as initial state and products as final state of the system,

P(V_p - V_r)  =         RT (n_p - n_r)

P∆V = ∆n_gRT where,

∆n_g refers to the to the difference in the number of moles of product and reactant gases. But, we already know that, ∆H = ∆U + P ∆V

∆H = ∆U + ∆n_gRT

Incertain processes internl energy change ∆U = ∆E also.

Standard enthalpy changes

The standard enthalpy of a reaction is the enthalpy change for a reaction when all the participating substances (elements and compounds) are present in their standard states.

The standard state of a substance at any specified temperature is its pure form at 1 atm pressure. For example standard state of solid iron at 500 K is pure iron at 500 K and 1 atm. Standard conditions are denoted by adding the superscript 0 to the symbol ∆H.

For a reaction, the standard enthalpy change is denoted by ∆_rH⁰. Similarly, the standard enthalpy changes for combustion, formation, etc. are denoted by ∆_cH⁰ and ∆_fH⁰ etc respectively. Generally the reactants are presented in their standard states during the enthalpy change.