The concept of resonance explains various properties of compounds.The molecules with conjugated system of `pi` bonds, are stabilized by resonace and have low heat of hydrogenation.Hyperconjugative stabilization also decreases heat f hydrogenation.In aromic rings a functional group with a lone pair of electron exerts +m effect. Some functional groups like -NO, -NC, -CH=`CH_2` can function both as electron releasing (+m,+R) or electron withdrawing (-m,-R) groups.More extended conjugation provides more stabilization.
The correct heat of hydrogenation order is
(p)1,3-Pentadiene , (q)1,3-Butadiene , (r)2,3-Dimethyl-1,3-butadiene , (s)Propadiene

Options

A. pgtqgtrgts
B. sgtqgtpgtr
C. qgtsgtpgtr
D. sgtpgtqgtr

Explanation

To determine the correct order of heat of hydrogenation for the given compounds (1,3-Pentadiene, 1,3-Butadiene, 2,3-Dimethyl-1,3-butadiene, and Propadiene), we need to analyze the stability of each compound based on resonance and hyperconjugation. The more stable a compound is, the lower its heat of hydrogenation will be, as stability is inversely proportional to heat of hydrogenation.

### Step-by-Step Solution:

1. **Identify the Structures**:
- **1,3-Pentadiene (P)**: CH3-CH=CH-CH=CH2
- **1,3-Butadiene (Q)**: CH2=CH-CH=CH2
- **2,3-Dimethyl-1,3-butadiene (R)**: CH2=C(CH3)-C(CH3)=CH2
- **Propadiene (S)**: CH2=C=CH2

2. **Analyze Stability**:
- **1,3-Pentadiene (P)**: This compound has two double bonds and can exhibit resonance. The presence of the methyl group also contributes to hyperconjugation, providing some stabilization.
- **1,3-Butadiene (Q)**: This compound has two double bonds and exhibits resonance, but it lacks additional substituents for hyperconjugation.
- **2,3-Dimethyl-1,3-butadiene (R)**: This compound has two double bonds and two methyl groups, which significantly enhance hyperconjugation and resonance stabilization.
- **Propadiene (S)**: This compound has a cumulated double bond system and is the least stable due to lack of resonance and hyperconjugation.

3. **Rank the Compounds**:
- **Heat of Hydrogenation**: The compound with the highest heat of hydrogenation is the least stable.
- Propadiene (S) is the least stable → highest heat of hydrogenation.
- 1,3-Butadiene (Q) is more stable than Propadiene but less stable than 1,3-Pentadiene (P).
- 1,3-Pentadiene (P) is more stable than 1,3-Butadiene (Q) due to hyperconjugation from the methyl group.
- 2,3-Dimethyl-1,3-butadiene (R) is the most stable due to maximum hyperconjugation and resonance.

4. **Final Order**:
- The order of heat of hydrogenation from highest to lowest is:
- S (Propadiene) > Q (1,3-Butadiene) > P (1,3-Pentadiene) > R (2,3-Dimethyl-1,3-butadiene)

### Conclusion:
The correct order of heat of hydrogenation is:
**S > Q > P > R**.