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24. The association constant (K) for 1:1 complexation can be
expressed by Eq. 3
½Cꢀ
½Cꢀ
K Z
Z
(3)
½
Hꢀ½Gꢀ ð½Hꢀ K½CꢀÞð½Gꢀ K½CꢀÞ
0
0
353–367. (i) Bradshaw, J. S.; Huszthy, P.; Redd, J. T.; Zhang,
X. X.; Wang, T.; Hathaway, J. K.; Young, J.; Izatt, R. M. Pure
Appl. Chem. 1995, 67, 691–695. (j) Wang, T.; Bradshaw, J. S.;
Huszthy, P.; Izatt, R. M. Supramol. Chem. 1995, 5, 9–13.
0 0
where [H] and [G] are the initial concentrations of the host
and guest, respectively, and [H], [G] and [C] are the
concentrations of the host, guest and complex at equilibrium,
respectively. By substitution of [C]Z[H] (1KX ) into Eq. 3,
(k) Zhang, X. X.; Izatt, R. M.; Zhu, C. Y.; Bradshaw, J. S.
Supramol. Chem. 1996, 92, 64–69. (l) Samu, E.; Huszthy, P.;
´
Horv a´ th, G.; Sz o¨ ll o˝ sy, A.; Neszm e´ lyi, A. Tetrahedron:
0
f
Xf became the unknown of the quadratic equation (Eq. 4):
ꢀ
ꢁ
1
1
Xf K Z 0
K
2
f
Asymmetry 1999, 10, 3615–3626.
0. Wong, W.-L.; Huang, K.-H.; Teng, P.-F.; Lee, C.-S.; Kwong,
H.-L. Chem. Commun. 2004, 384–385.
½
Hꢀ X C ½Gꢀ K½Hꢀ C
(4)
0
0
0
K
1
1
Therefore,
1. For references on molecular recognition studies of amino
acid derivatives using different crown macrocycles, see:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
Kð½Gꢀ K½Hꢀ C1=KÞG ð½Gꢀ K½Hꢀ C1=KÞ K4½Hꢀ ðK1=KÞ
0
0
0
0
0
Xf Z
(
a) Peacock, S. S.; Walba, D. M.; Gaeta, F. C. A.; Helgeson,
R. C.; Cram, D. J. J. Am. Chem. Soc. 1980, 102, 2043–2052.
b) Tsukube, H.; Uenishi, J.; Higaki, H.; Kikkawa, K. Chem.
2
½Hꢀ
0
(
5)
(
Since
Lett. 1992, 12, 2307–2310. (c) Badis, M.; Tomaszkiewicz, I.;
Joly, J.-P.; Rogalska, E. Langmuir 2004, 20, 6259–6267.
2. (a) Kwong, H.-L.; Lee, W.-S.; Ng, H.-F.; Chiu, W.-H.; Wong,
W.-T. J. Chem. Soc., Dalton Trans. 1998, 6, 1043–1046.
1
2
F Z Sðdobsd Kdave
Þ
(
b) Kwong, H.-L.; Lau, K.-M.; Lee, W.-S.; Wong, W.-T. New
2
J. Chem. 1999, 23, 629–632. (c) Kwong, H.-L.; Lee, W.-S.
Tetrahedron: Asymmetry 1999, 10, 3791–3801. (d) Lee, W.-S.;
Kwong, H.-L.; Chan, H.-L.; Choi, W.-W.; Ng, L.-Y.
Tetrahedron: Asymmetry 2001, 12, 1007–1013.
Z S½dobsd;i KX d Kð1 KX Þd ꢀ
(2)
f;i
f
f;i
c
c
K and d were calculated by minimization of the error function
F using a computer program developed by us.