The decreasing order of the anti-knocking value of octane number of the following is: (I) `CH_(4)` (II) `C_(2)H_(6)` (III) `C_(3)H_(8)` (IV) `C_(4)H_(10)`

Options

A. (a) (I) > (II) > (III) > (IV)
B. (b) (IV) > (III) > (II) > (I)
C. (c) (I) > (III) > (II) > (IV)
D. (d) (IV) > (II) > (III) > (I)

Explanation

To determine the decreasing order of the anti-knocking value (octane number) of the given hydrocarbons (I) `CH₄` (methane), (II) `C₂H₆` (ethane), (III) `C₃H₈` (propane), and (IV) `C₄H₁₀` (butane), we can follow these steps:

### Step 1: Understand the concept of octane number
The octane number is a measure of a fuel's ability to resist knocking during combustion. A higher octane number indicates better resistance to knocking.

### Step 2: Analyze the hydrocarbons
- **(I) `CH₄` (Methane)**: Contains 1 carbon atom. It has the highest octane number among the given options because it is a simple alkane with low molecular complexity.
- **(II) `C₂H₆` (Ethane)**: Contains 2 carbon atoms. It has a lower octane number than methane due to increased molecular complexity and potential for knocking.
- **(III) `C₃H₈` (Propane)**: Contains 3 carbon atoms. It has an even lower octane number than ethane as the number of carbon atoms increases, leading to a higher likelihood of knocking.
- **(IV) `C₄H₁₀` (Butane)**: Contains 4 carbon atoms. It has the lowest octane number among the four because it is more prone to knocking compared to the others.

### Step 3: Establish the order
Based on the analysis:
1. `CH₄` (Methane) - Highest octane number
2. `C₂H₆` (Ethane) - Second highest
3. `C₃H₈` (Propane) - Third highest
4. `C₄H₁₀` (Butane) - Lowest octane number

### Final Order
Thus, the decreasing order of the anti-knocking value (octane number) is:
**`CH₄` > `C₂H₆` > `C₃H₈` > `C₄H₁₀`**

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