What will be the total number of possible structural isomers with formula ${\mathrm{C}}_7{\mathrm{H}}_{12}{\mathrm{Br}}_2$ fulfilling the following conditions 
(I) it should contain 6 membered ring 
(II) none of the isomer should contain both bromine atom either on same or adjacent carbon atom
(III) none of the isomer should contain bromine atom on tertiary carbon atom 

To solve this problem, we need to systematically apply the given conditions to determine the total number of structural isomers with the molecular formula C7H12Br2. Here's how we can proceed:

Formula and Initial Structure

The molecular formula is C7H12Br2, which indicates a molecule with 7 carbon atoms, 12 hydrogen atoms, and 2 bromine atoms.

The first condition specifies that the compound should contain a 6-membered ring. So, the molecule must be a cyclohexane derivative. The structure will have a 6-membered carbon ring (C6), and the remaining carbon atom will be attached as a substituent.

Bromine Placement Restrictions

• Condition II: None of the bromine atoms should be on the same or adjacent carbon atoms.
  • This means that the two bromine atoms must not be placed on neighboring carbons (neither on adjacent carbons nor the same carbon).
• Condition III: None of the bromine atoms should be on a tertiary carbon atom.
  • A tertiary carbon is one attached to three other carbon atoms. So, we must avoid placing bromine on tertiary carbons.

Analyzing Possible Isomers

Now, we need to count the number of possible structural isomers satisfying all the conditions. The isomers will differ based on the position of the bromine atoms on the 6-membered cyclohexane ring and the positioning of the additional carbon atom.

Upon applying these conditions and ensuring that we don't violate any of the restrictions, we find that there are 5 possible structural isomers that satisfy all the conditions.

Answer:

The total number of possible structural isomers is 5.