90 OUTLINES OF PHYSICAL CHEMISTRY
In the upper tetrahedron In the lower tetrahedron
��Face 4—2 — 1 turns to the left „ 4—3—1 „ „ right „ 4—3—2 „ „ left „ 3—2—1 „ „ right
��Face 4 — 2 — 1 turns to the left „ 4—3—1 „ „ right
„ 4—3—2 „ „ left
„ 3—2—1 „ „ right
��In both tetrahedra the effect is again the difference between two dextro- and two hevo-rotations. The effect in each of the tetrahedra is the same and of the same sign ; therefore, the whole is optically active.
A similar examination of fig. 22, 2, shows that it represents a substance equal in optical activity to the fore- going, but of opposite sign. Figs. 22, 3 and 4 represent the inactive modification which cannot be separated into two active forms. The two halves of the molecule have an equal optical effect, but of opposite sign. In fig. 20, 3, for example, we find :
Upper tetrahedron Lower tetrahedron
��Face 3 — 2 — 1 is dextro-rotatory „ 4—2—1 „ law)- „ „ 4— 3—1 „ dextro- „ „ 4—3—2 „ Iubvo- „
��Face 3—2 — 1 is laevo-rotatory „ 4 -2 — 1 „ dextro- „ „ 4—3—1 „ lajvo- „ „ 4 — 3 — 2 „ dextro- „
��It is not necessary to give the theory for the type C 1j2 ,3 — C 4 , 5 , 6 in the same detail. Besides, this case comes under the general rule that a molecule which contains n asymmetric carbon atoms is capable of existing in 2 n active modifications.
The following table demonstrates this rule, a, b, c, &c. represent different atoms or radicals united to the asym- metric carbon atom C. An arrangement of the letters like Gab c d indicates a dextro-rotatory system, whilst a laevo- rotatory system is denoted by the arrangement Cab c d. The table does not take account of the racemic forms.
One Asymmetric Carbon Atom c hj\ "^ W0 (^*) ac ^ ve modifications are possible.
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