The van’t Hoff plot II - Clear Cognitiongenchem.clearcognition.org/GeneralChemistryslideshows/...2 The van’t Hoff plot II In a previous slideshow the Clausius-Calpyron equation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
The van’t Hoff plot II
Constructing the van’t Hoff plot from ThermodynamicData
Use of these materials by others is encouraged provided these notices are not altered.
2
The van’t Hoff plot II
In a previous slideshow the Clausius-Calpyron equation was usedto create a van’t Hoff plot of water vapor pressure. This equation,derivable from Thermodynamics is:
It was noted that the abscissa (x) was the quantity 1/T and theordinate (y) was lnP. Thus, the slope was –∆H
v.
For the case of vapor pressure, the ∆H > 0 always. This is not ingeneral the case for reactions and the equilibrium values forreactions at two different temperatures may not be available, atleast initially. Therefore it is useful to be able to calculate thevan’t Hoff plot given only Thermodynamic data. Conversely, froman experimental van’t Hoff plot one can obtain theThermodynamic data.
ln = –‰ ÷P
1
P2
∆Hv
R‰ ÷ ‰ ÷ 1 1
T2 T
1
3
The van’t Hoff plot II
Starting with the relationship between thermodynamics and theequilibrium constant:
and the relationship of Gibbs’ free energy and the enthalpy andentropy:
∆Gº = ∆H
º – T∆Sº
Taking the ln of the first equation and substituting ∆Hº – T∆Sº for
∆Gº yields:
Thus, –∆Hº/R is the slope and ∆S
º/R is the intercept.
lnK = + ∆S
º
R‰ ÷ ‰ ÷–∆H
º
R
1
T
K = e–∆G
º
RT
4
The van’t Hoff plot II
Usually this equation is used by designating two temperatures, amaximum and minimum, and a calculation of the two values oflnK.
First, a look at the parametric arrangement.
lnK = + ∆S
º
R‰ ÷ ‰ ÷–∆H
º
R
1
T
5
lnK2 = ! +
∆Hº 1 ∆S
º
R T2 R ‰ ÷‰ ÷
lnK1 = ! +
∆Hº 1 ∆S
º
R T1 R ‰ ÷‰ ÷
!
The van’t Hoff plot II
This equation could be used between two temperature to yield anequation similar to the Clausius-Calpyron equation. Todemonstrate this use two temperatures, T
1 and T
2 corresponding to
two values of K, K1 and K
2. Substrating equation 1 from 2:
ln = !∆H
º 1 1
R T2 T
1 ‰ ÷‰ ÷K
1
K2‰ ÷
For the reaction: (l) º (g), this becomes the Clausius-Calpyron equation.
lnK = + ∆S
º
R‰ ÷ ‰ ÷–∆H
º
R
1
T
6
The van’t Hoff plot II
Here is an example:
Draw a van’t Hoff plot for the reaction between 100EC and 500EC:
N2(g) + 3H
2(g) ! 2NH
3(g)
The thermodynamic quantities for the reaction are required.