Question

Consider the following reaction and statements:
\(\mathrm{[Co(NH_3)_4Br_2]^+ + Br^- \rightarrow [Co(NH_3)_3Br_3] + NH_3}\)
(I) Two isomers are produced if the reactant complex ion is a cis-isomer
(II) Two isomers are produced if the reactant complex ion is a trans-isomer
(III) Only one isomer is produced if the reactant complex ion is a trans-isomer
(IV) Only one isomer is produced if the reactant complex ion is a cis-isomer
The correct statements are

• A. (II) and (IV)
• B. (I) and (II)
• C. (I) and (III)
• D. (III) and (IV)

Hint:

One NH3 is replaced by Br-. Count the distinct fac/mer products obtained by replacing each non-equivalent NH3 in the cis and in the trans reactant.

Answer 1

The Correct Option is C

Place the octahedron on x, y, z axes. The product \(\mathrm{[Co(NH_3)_3Br_3]}\) has two geometrical isomers: fac (three Br on one face) and mer (three Br in a plane through the metal).
cis reactant: Br at +x and +y; NH3 at -x, -y, +z, -z.
Replacing NH3 at -x gives Br at +x, -x, +y: mer. Replacing -y gives Br at +x, +y, -y: mer. Replacing +z gives Br at +x, +y, +z: fac. Replacing -z gives fac.
So the cis reactant gives two isomers (fac and mer): statement (I) is true and (IV) is false.
trans reactant: Br at +x and -x; the four NH3 at +y, -y, +z, -z are all equivalent. Replacing any one gives Br at +x, -x and one more position perpendicular to that axis: always mer.
So the trans reactant gives only one isomer: statement (III) is true and (II) is false.
Correct statements: (I) and (III).
Answer: (3) (I) and (III)