The Double Solubility Rule

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The Double Solubility Rule An Experimental
Test
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Meyerhoffers double solubility rule The
solubility of a mixture consisting of a dl pair
of enantiomers that crystallize in the form of a
conglomerate will be twice the solubility of
chiral enantiomer.
Can the double solubility rule be verified?
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Whats the total pressure in each case?
PB
PA
Stopcock closed
Solid A Solid B
Stopcock opened
PAPB
PAPB
Solid A Solid B
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Typical Phase Diagrams in Chiral
Systems A. Compound formation
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2. Solid solution with a maximun or minimum in
melting
ln x (?fusHd /R)1/Tfus(d)-1/Tfus
3. Conglomerate
When x 0.5 then Tfus Tfus dl
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Consider pure crystalline d Pd
Ade-?subH/RT Simlarly for the l form Pl
Ale-?subH/RT Ad Al ?subHd ?subHl
Daltons Law of Partial Pressures PT Pd Pl
Pdl 2Ade-?subH/RT Therefore Pdl/ Pl 2
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In a real dl mixture Pdl Adle-?subHdl/RT Pdl/ Pd
2? 2 Adle-?subHdl/RT/ Ade-?subHd/RT Furthermor
e ?subHdl ?fusHdl ?vapHdl ?subHd
?fusHd ?vapHd and ?vapHd ? ?vapHdl What
about ?fusHdl and ?fusHd ? 2 Adle-?fusHdl/RT/
Ade-?fusHd/RT 2 Adl/ Ade- ?? fusH/RT if
Adl/ Ad 1 then ?? fusH RTln(2) ?? fusH
1.73 kJ mol-1 at T 300 K
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Conglomerates
ln x (?fusHd /R)1/TfusA-1/Tfus
When x 0.5 then Tfus Tfus dl
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Conglomerates T /K, ?fusHA /kJ mol-1
TfusA ?fusHA ?fusHdl Tfus dl Tfus
? ?fusH


(calcd) o-chloromandelic acid 392.5 24.7
20.1 358.5 359.5 3.6 hydrobenzoin
420.5 34.3 31.4 393 393 2.9
1,2-dichloroacenaphthene 375 21.3 20.5
339 340 0.8 phenylhydracrylic acid
391 32.6 29.7 366 366 2.9
ln x (?fusHd /R)1/TfusA-1/Tfus
?? fusH 1.73 kJ mol-1 at T 300 K
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Dimethyl tartrate
Menthol
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Dimethyl diacetyltartrate
2,3-Dibromo-1,4-butanediol