Page 137 - Chemical equilibria Volume 4

Determination of the Values Associated with Reactions – Equilibrium Calculations 113
We suppose variations of the standard Gibbs energy of the reaction as a
function of the temperature to be known. Based on relation [4.13], we
deduce the standard enthalpy associate, using the relation:
⎛ Δ g ⎞ 0
d ⎜ r ⎟
Δ h =− T 2 ⎝ T ⎠ [4.14]
0
r
dT
If we consider two temperatures T 1 and T 2 which are not too far apart,
then knowledge of the standard Gibbs energy at those two temperatures
enables us to approximately calculate the standard enthalpy at another
temperature lying between T 1 and T 2, by the relation:

Δ TT ⎛ 0 Δ g g ⎞ 0
Δ h = 1 2 ⎜ r 1 − r 2 ⎟ [4.15]
0
T −
r
2 T 1 ⎝ T 1 T 2 ⎠
4.2.4.2. Calculation of an enthalpy on the basis of the equilibrium
constant

This method is based on the van ’t Hoff equation for the variation of the
equilibrium constants with temperature, which we shall suppose to be
known. From relation [4.3], we deduce the associated enthalpy:

d ln K (I)
0
Δ h =− R [4.16]
r
1
d ⎛⎞
⎜⎟
⎝⎠
T
If we choose two temperatures T 1 and T 2 which are not too far apart, then
we only need to know the equilibrium constant at the two temperatures T 1
and T 2. Then, the standard enthalpy at a temperature between T 1 and T 2 is
given approximately by:

TT K (I)
0
Δ h = R T − T 1 ln K 2 (I) [4.17]
12
r
2
2