Stabilities of alkanes can be compared by converting these compounds to a common product and comparing the amount of the heat given off. One possiblitiy would be to measure the heat of combustion from converting alkenes to `xo_(2)` and `H_(2)O` . The heats of combustion are of large values and measuring small difference in these large numbers is difficult. Alkene of the lowest heat of combustion among isomeric alkenes is of the lowest energy and is most stable.
Th stability of alkenes is often compared by meansuring the ehat of hydrogenation `9` heat given off, `Delta H_(h)^(@)` during catalytic hydrogenation. The heat of hydrogenation is in smal number, which provides more accurate energy difference.
For a compound containing more than one double bond, `Delta_(h)^(@)` is the sum of heat of hydrogenation of individual double bonds. For non `-` conjugated diens, this additive relatioship is found to hold. For conjugated dienes, however, the measured value is slightly lower than expected. Cumulated dienes, which are even less stable than non `-` conjugated dienes.
The more stable is the alkene, lower is the heat of combustion and heat of hydrogenation. More highly substituted double bonds are usually more stable. In case of cyclokanes, compounds having higher angle strin are less stable.
Arrange the following compounds according to their increasing heat of combustion. `I.` `1-`Butene
`II.` ci `-2-`Butene
`III.` trans `-2-`Butene
`IV.` `2-` Methyl propene

Options

A. `(IV)gt(I)lt(II)lt(III)`
B. `(I)lt(II)lt(IV)lt(III)`
C. `(IV)gt(III)lt(II)lt(I)`
D. `(I)lt(II)lt(III)lt(IV)`

Explanation

To determine the increasing heat of combustion of the given alkenes, we need to analyze their stability based on the information provided in the question and the video transcript. The stability of alkenes is influenced by the degree of substitution of the double bond: more substituted alkenes are generally more stable and thus have lower heats of combustion.

### Step-by-Step Solution:

1. **Identify the Compounds**:
- I. 1-Butene (CH2=CH-CH2-CH3)
- II. cis-2-Butene (CH3-CH=CH-CH3 with both methyl groups on the same side)
- III. trans-2-Butene (CH3-CH=CH-CH3 with methyl groups on opposite sides)
- IV. 2-Methylpropene (C(CH3)2=CH2)

2. **Determine the Degree of Substitution**:
- 1-Butene is a monosubstituted alkene (1 substituent).
- cis-2-Butene is a disubstituted alkene (2 substituents).
- trans-2-Butene is also a disubstituted alkene (2 substituents).
- 2-Methylpropene is a trisubstituted alkene (3 substituents).

3. **Rank the Stability**:
- The stability order based on substitution is:
- 2-Methylpropene (most stable, lowest heat of combustion)
- trans-2-Butene (more stable than cis due to less steric strain)
- cis-2-Butene
- 1-Butene (least stable, highest heat of combustion)

4. **Assign the Heats of Combustion**:
- Since more stable alkenes have lower heats of combustion, we can assign the heats of combustion in increasing order:
- 2-Methylpropene (lowest heat of combustion)
- trans-2-Butene
- cis-2-Butene
- 1-Butene (highest heat of combustion)

5. **Final Arrangement**:
- Therefore, the increasing order of heat of combustion is:
- IV (2-Methylpropene) < III (trans-2-Butene) < II (cis-2-Butene) < I (1-Butene)

### Conclusion:
The final arrangement according to increasing heat of combustion is:
**IV < III < II < I**