2024.9.04
Chemistry at pirika.com > Chemistry > Chemical engineering > Reprint: gas-liquid equilibrium estimation by ASOG. > Chapter 1: Basic equations of solution theory
1.7 Handling of association systems
Low-molecular-weight carboxylic acids, such as acetic acid and propionic acid, are partly associated in the gas phase. The essence of this is the bimolecular hydrogen bonding of carboxyl groups. Normal hydrogen bonds spread in two or three dimensions. However, in the case of carboxyl groups, both the hydrogen attached to a heteroatom (oxygen or nitrogen) and the carbonyl oxygen that accepts the hydrogen are in close proximity, so they form dimers and become stabilised.
In a two-component system consisting of component A containing carboxyl groups and the other component B, the following homogeneous and heterogeneous intermolecular associations are possible.
2A1 ⇆ A2, 2B1⇆ B2 (1-13)
A1+B1 ⇆ AB (1-14)
A1 and B1 indicate the monomers of components A and B, A2 and B2 the dimers of A and B, and AB the hetero-aggregate molecules of A and B.
There are only three of these association reactions for which equilibrium constants are known: formic acid, acetic acid and propionic acid. Since none of the equilibrium constants for the association between different molecules are known, it is practically only necessary to consider 2A1 ⇆ A2.
If the equilibrium constant is KA, the following equation holds.
KA=[A2 ] / [A1 ]2 (1-15)
[ ] indicates concentration.
ある温度、圧力、体積が決まった時に、気相中に何モル（何個）の分子がいるかは１つに決まる。その時には、ダイマーであっても1つの分子と数える。
そこでになる。
When a certain temperature, pressure and volume are determined, the number of moles (how many molecules) in the gas phase is determined to be one. At that point, even dimers are counted as one molecule.
So [A1]+ [A2]=1.
KA=(1-[A1 ])/[A1 ]2 (1-16)
Solving this for A1 yields the following.
[A1 ]=(-1+√(1+4KA ))/2KA (1-17)
If both A and B components have carboxyl groups, then do the same for B.
The equilibrium constant for heterogeneous intermolecular association is then used KAB=2√(KA KB ).
In this way, the concentration is corrected for and the vapour-liquid equilibrium is calculated.
Next section: 1.8 How to obtain activity and activity coefficients
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