Write the mechanism for the reactions of:

• (Z)-3,6-diethyl-oct-4-ene and bromine
• (E)-3,6-diethyl-oct-4-ene and bromine
Assign the R/S configuration for each of the products and determine the
stereochemical relationship of each set of products.

To understand the mechanism of the reactions and determine the R/S configuration for each product, we need to consider the reaction conditions. The reaction between (Z)-3,6-diethyl-oct-4-ene and bromine will proceed via an anti-addition mechanism, while the reaction between (E)-3,6-diethyl-oct-4-ene and bromine will proceed via a syn-addition mechanism.

1. Mechanism for the reaction of (Z)-3,6-diethyl-oct-4-ene and bromine:
In the presence of bromine, the reaction proceeds as follows:

Step 1: Bromine undergoes homolytic cleavage (Br-Br → 2Br•) to form two bromine radicals.
Step 2: One bromine radical attacks the double bond of (Z)-3,6-diethyl-oct-4-ene, leading to the formation of a bromonium ion intermediate. The attack occurs from the less hindered face, resulting in initial formation of a cyclic bromonium ion (three-membered ring).
Step 3: The second bromine radical attacks one of the carbons in the cyclic bromonium ion, resulting in ring opening and formation of a vicinal dibromide. This second attack occurs from the opposite face compared to the first attack, achieving anti-addition.
Step 4: With elimination of a bromide ion, the final product is obtained.

2. Mechanism for the reaction of (E)-3,6-diethyl-oct-4-ene and bromine:
In the presence of bromine, the reaction proceeds as follows:

Step 1: Bromine undergoes homolytic cleavage (Br-Br → 2Br•) to form two bromine radicals.
Step 2: One bromine radical attacks the double bond of (E)-3,6-diethyl-oct-4-ene, leading to the formation of a cyclic bromonium ion intermediate. The attack occurs from the less hindered face, resulting in initial formation of a cyclic bromonium ion (three-membered ring).
Step 3: The second bromine radical attacks one of the carbons in the cyclic bromonium ion, resulting in ring opening and formation of a vicinal dibromide. This second attack occurs from the same face compared to the first attack, achieving syn-addition.
Step 4: With elimination of a bromide ion, the final product is obtained.

Now, let's determine the R/S configuration for each product and the stereochemical relationship between them.

For (Z)-3,6-diethyl-oct-4-ene and bromine reaction:
The bromine addition to the +Z isomer will lead to the formation of two enantiomeric products. The R and S configurations of the resulting chiral centers will be opposite in the two products. The stereochemical relationship between the products will be diastereomeric.

For (E)-3,6-diethyl-oct-4-ene and bromine reaction:
The bromine addition to the +E isomer will result in the formation of two identical products. Both products will have the same R or S configuration at the newly formed chiral centers. The stereochemical relationship between the products will be syn, and they will be identical stereoisomers.

It is important to note that the specific R/S assignments and stereochemical relationships cannot be determined solely from the given reaction, as they depend on the orientation of the starting material. However, the general trends described above can be applied in most cases.