Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 25

Δ H f ( NaCl, aq ) = Δ H f ( Na + ,aq ) + Δ H f ( Cl − ,aq ) =− 239.7 − 167.2
=− 406.9 kJ/mol
Δ H f ( H 2 O, aq ) =− 285.8 kJ/mol.

Hence, for the overall reaction,

Δ H r = Δ H f ( NaCl, aq ) + Δ H f ( H 2 O, aq )

− Δ H f ( HCl, aq ) − Δ H f ( NaOH, aq ) =− 56.1 kJ/mol.

The enthalpy of reaction at temperatures other than standard temperature can be
estimated from the following equation, called Kirchoff's law , that is,

T
T o Δ C P d T .

Δ H f (T) = Δ H f (T o ) + (2.29)

2.2.7 C OMBINATION OF F IRST AND S ECOND L AWS
Consider a closed system, which does only PV work of expansion and for which δ q

is given by T d S :

d U = T d S − P d V . (2.30)

We can now define two other state functions called Gibbs free energy , G , and
Helmholtz free energy , A :

G = H − TS ,

(2.31)

A = U − TS .

We can derive the following equations for differential changes in G and A :

d G =− S d T + V d P ,

(2.32)

d A =− S d T + P d V .

From the definition of enthalpy, H , we can also derive the following:

d H = T d S + V d P . (2.33)

Most environmental processes are functions of T and P , and hence Gibbs free energy
is a natural state function for those cases. The above differential equations are the
basis for deriving useful physico-chemical thermodynamic relationships.