3Chemical Equilibrium
All the tables and figures (except were noted) taken from:
Snoeyink, V.L . and Jenkins, D., 1980. Water Chemistry, John Wiley &Sons
Benjamin, M.M., 2014. Water Chemistry, Waveland Press Inc.
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3 Chemical Equilibrium
All the tables and figures (except were noted) taken from:
Snoeyink, V.L. and Jenkins, D., 1980. Water Chemistry, John Wiley & Sons
Benjamin, M.M., 2014. Water Chemistry, Waveland Press Inc.
Chemical Equilibrium
This Section will allow us to answer the questions:
- Will this reaction proceed?
- In which direction?
If a reaction is impossible, there is no sense in attempting in it at a water or wastewater process
This, without having to perform an experiment!
Will calcium carbonate tend to precipitate or dissolve in water?
Can I oxidize sulfide with nitrate?
๏ It is faster to do a calculation than a lab experiment!
These calculations come from Thermodynamics
Thermodynamics
๐บ๐บ = ๐ป๐ป โ ๐๐๐๐ Assume closed system G = Gibbs free energy (kcal) conservation of mass T = Absolute temperature (หK) energy can flow across boundaries (energy available for โuseful workโ) Constant T and P
0หC = 273หK 25หC = 298หK โ standard conditions (25หC and 1 atmosphere of pressure)
H = Enthalpy (kcal) ๏ Is the total energy of an element or compound
S = Entropy (kcal/หK) ๏ Internal energy โ degree of internal order/disorder ๏ Highly structured materials (e.g. crystals) โ low entropy ๏ Random systems (e.g. gases) โ high entropy
Thermodynamics
GT = Total free energy
๏ For closed systems (at constant pressure and temperature) the criterion for equilibrium is that the total free energy of the system (GT ) is minimum
๏ Reaction proceeds spontaneously only if GT decreases (โ)
Thermodynamics
Since total free energy is difficult to measure, usually we determine the change in Gibbs free energy (โG)
If โG < 0 โ reaction proceeds spontaneously as written
If โG > 0 โ reaction can not proceed spontaneously as written, but proceeds spontaneously in the opposite direction
If โG = 0 (GT is minimum)โ reaction is at equilibrium and will not proceed in either direction
โ๐บ๐บ = โ๐บ๐บ ๐๐^ + ๐ ๐ ๐๐ ๐๐๐๐
T = Absolute temperature (หK)
โGห = change in free energy at standard conditions
ห โ means at standard conditions
R = 8.31x10-3^ KJ/mol หK = 1.987x10-3Kcal/mol หK
(1 KJ/mol = 4.184 Kcal/mol)
Equation 2
Thermodynamics
At equilibrium โG=0 (change in Gibbs free energy) and equation 2 transforms into:
[๐ถ๐ถ]๐๐[๐ท๐ท]๐๐
[๐ด๐ด]๐๐[๐ต๐ต]๐๐
From equation 1: [๐ถ๐ถ]๐๐[๐ท๐ท]๐๐ ๐พ๐พ = [๐ด๐ด]๐๐[๐ต๐ต]๐๐
Substituting equation 4 into equation 2
Equation 3
Equation 4
โ๐บ๐บ = โ๐ ๐ ๐๐๐๐๐๐๐พ๐พ + ๐ ๐ ๐๐ ๐๐๐๐ Equation 5
[๐ถ๐ถ]๐๐[๐ท๐ท]๐๐
[๐ด๐ด]๐๐[๐ต๐ต]๐๐
Thermodynamics
โ๐บ๐บ ๐๐^ = Gibbs free energy of formation:
(the energy necessary to produce one mole of a substance) By convention:
โ๐บ๐บ ๐๐ ๐๐ (^) = 0 for elements in their most stable form (including H+ )
โ๐บ๐บ ๐๐ ๐๐ (^) = 1 for pure solids
๐๐
Chemical Equilibrium
Thermodynamics
Example 3-1 from Snoeyink (pg 68)
a) Determine the equilibrium constant (K) for the reaction in which water dissociates into H+^ and OH-^ at 25หC.
๐ป๐ป 2 ๐๐ โ ๐ป๐ป+^ + 0๐ป๐ปโ
b) Will this reaction proceed as written when ๐ป๐ป+^ = 10โ6^ ๐๐ and (^) ๐๐๐ป๐ปโ^ = 10โ8๐๐?
Thermodynamics
Exercise 3.1 from Appelo and Postma (pg 47)
A water sample contains 10 ppm of Ca+2^ and 5.5 ppm of F -. Is the sample saturated with respect to fluorite ( CaF 2 )? Assume standard conditions.