To solve the problem, we need to determine the number of isomers of the compound C₂FClBrI that can be formed upon hydrogenation, excluding stereoisomers. The hydrogenation process will convert the double bonds into single bonds while adding hydrogen atoms.
### Step-by-step Solution:
1. **Identify the Structure of C₂FClBrI**:
- The compound consists of two carbon atoms (C), and each carbon is bonded to one of the halogens: fluorine (F), chlorine (Cl), bromine (Br), and iodine (I).
- The general structure can be represented as C=C(F)(Cl)(Br)(I).
2. **Determine Possible Isomers**:
- We need to consider all possible arrangements of the halogens around the carbon-carbon double bond.
- The possible isomers can be derived from the different combinations of the halogens on each carbon.
3. **List All Isomers**:
- **Isomer 1**: C=C with F on one carbon, Cl on the other, and Br and I on the same carbon.
- **Isomer 2**: C=C with F on one carbon, Br on the other, and Cl and I on the same carbon.
- **Isomer 3**: C=C with F on one carbon, I on the other, and Br and Cl on the same carbon.
- **Isomer 4**: C=C with Cl on one carbon, F on the other, and Br and I on the same carbon.
- **Isomer 5**: C=C with Cl on one carbon, Br on the other, and F and I on the same carbon.
- **Isomer 6**: C=C with Cl on one carbon, I on the other, and F and Br on the same carbon.
- **Isomer 7**: C=C with Br on one carbon, F on the other, and Cl and I on the same carbon.
- **Isomer 8**: C=C with Br on one carbon, Cl on the other, and F and I on the same carbon.
- **Isomer 9**: C=C with Br on one carbon, I on the other, and F and Cl on the same carbon.
- **Isomer 10**: C=C with I on one carbon, F on the other, and Cl and Br on the same carbon.
- **Isomer 11**: C=C with I on one carbon, Cl on the other, and F and Br on the same carbon.
- **Isomer 12**: C=C with I on one carbon, Br on the other, and F and Cl on the same carbon.
4. **Count the Isomers**:
- After listing all the possible isomers, we find that there are a total of 12 different isomers of C₂FClBrI.
5. **Hydrogenation Products**:
- Upon hydrogenation (H₂/Ni), each double bond will convert to a single bond, and hydrogen will be added to the same side (syn addition).
- The products will be the same as the isomers listed above, but we will not count stereoisomers.
6. **Calculate X**:
- Since we have identified 12 isomers, we can conclude that X = 12.
7. **Determine Y**:
- The problem does not specify Y, but if we assume Y is a variable related to the isomers, we can set Y = 0 for simplicity, as it is not defined in the context of the question.
8. **Final Calculation**:
- Therefore, X + Y = 12 + 0 = 12.
### Final Answer:
X + Y = 12
