Which of the following has the smallest heat of hydrogenation per mole ?

Options

A. `1-`Butene
B. trans `-2-`Butene
C. `cis-2-`Butene
D. `1,3-`Butadiene

Explanation

To determine which compound has the smallest heat of hydrogenation per mole, we need to analyze the given options based on their structure and stability. The heat of hydrogenation is influenced by the number of double bonds and the stability of the alkene.

### Step-by-Step Solution:

1. **Understand Heat of Hydrogenation**:
- Heat of hydrogenation is the enthalpy change when one mole of an unsaturated compound (alkene) is hydrogenated to form a saturated compound (alkane).
- More double bonds in a compound lead to higher heat of hydrogenation because more hydrogen needs to be added to saturate the compound.

**Hint**: Remember that more double bonds mean more unsaturation, leading to higher heat of hydrogenation.

2. **Analyze the Given Options**:
- The options are:
- A) 1-butene
- B) Trans-2-butene
- C) Cis-2-butene
- D) 1,3-butadiene
- Notice that 1,3-butadiene has two double bonds, while the others have only one.

**Hint**: Identify the number of double bonds in each compound to assess their heat of hydrogenation.

3. **Eliminate Based on Double Bonds**:
- Since 1,3-butadiene has two double bonds, it will have the highest heat of hydrogenation. Thus, it can be eliminated as it cannot have the smallest heat of hydrogenation.

**Hint**: The compound with the most double bonds will have the highest heat of hydrogenation.

4. **Compare Cis and Trans Isomers**:
- Between cis-2-butene and trans-2-butene, the cis isomer is less stable due to steric repulsion between the adjacent methyl groups. Therefore, cis-2-butene will have a higher heat of hydrogenation than trans-2-butene.

**Hint**: Remember that trans isomers are generally more stable than cis isomers due to less steric hindrance.

5. **Compare 1-butene with 2-butene**:
- 1-butene is less stable than 2-butene (cis or trans) because 2-butene has more hyperconjugation due to a greater number of alpha hydrogens (6 in 2-butene vs. 2 in 1-butene). Thus, 1-butene will have a higher heat of hydrogenation than 2-butene.

**Hint**: More alpha hydrogens contribute to stability through hyperconjugation.

6. **Conclusion**:
- After analyzing the stability and heat of hydrogenation, we find that trans-2-butene is the most stable among the options provided, leading to the smallest heat of hydrogenation. Therefore, the answer is:

**Answer**: B) Trans-2-butene