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

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'.

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 'qp'. 'qp' 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 qp = ∆U + P ∆V

= ∆H

Or ∆H = qp

`qp' 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 nr and np 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(Vp - Vr)  =         RT (np - nr)

P∆V = ∆ngRT where,

∆ng 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 + ∆ngRT

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.

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11th 12th std standard Class Organic Inorganic Physical Chemistry Higher secondary school College Notes : Relation between enthalpy `H' and internal energy `U' |