How many dichlorodiphenyl with molecular formula `C_12H_8Cl_2` of each bezene ring containing only one (-Cl) group are possible :

Answer

To determine how many dichlorodiphenyl compounds with the molecular formula \( C_{12}H_8Cl_2 \) can be formed, where each benzene ring contains only one chlorine atom, we can follow these steps:

### Step 1: Understand the Structure
Dichlorodiphenyl refers to a compound that consists of two phenyl (benzene) rings connected by a single bond. Each of these rings can have one chlorine atom attached to it.

### Step 2: Identify the Positions for Chlorine Substitution
In a benzene ring, there are six carbon atoms, and hence six positions where substituents can be placed. If we denote the positions on a benzene ring as 1, 2, 3, 4, 5, and 6, we need to place one chlorine atom on each ring.

### Step 3: Determine the Possible Combinations
Since each benzene ring can have one chlorine atom, we need to consider the different combinations of placing these chlorine atoms on the two rings.

1. **First Benzene Ring**: Choose one of the six positions for the chlorine atom.
2. **Second Benzene Ring**: Choose one of the remaining five positions for the chlorine atom.

### Step 4: Calculate the Total Combinations
However, we must consider that the two benzene rings are identical, meaning that swapping the positions of the chlorine atoms between the two rings does not create a new compound. Therefore, we need to account for this symmetry.

1. The number of ways to choose 1 position from 6 for the first ring is \( 6 \).
2. The number of ways to choose 1 position from the remaining 5 for the second ring is \( 5 \).

Thus, the total combinations without considering symmetry would be:
\[ 6 \times 5 = 30 \]

Since the two rings are identical, we divide by 2 to account for the indistinguishable combinations:
\[ \text{Total distinct compounds} = \frac{30}{2} = 15 \]

### Final Answer
Therefore, the total number of distinct dichlorodiphenyl compounds with the molecular formula \( C_{12}H_8Cl_2 \), where each benzene ring contains only one chlorine atom, is **15**.

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