Calculate the octane number of gasoline fuel, which contains `25%` n - heptane and `75%` is iso - octane.

Options

A. 25
B. 50
C. 75
D. 100

Answer

To calculate the octane number of a gasoline fuel mixture that contains 25% n-heptane and 75% iso-octane, we can follow these steps:

### Step 1: Understand the Definition of Octane Number
The octane number is a measure of the performance of gasoline fuel during combustion. It is defined as the percentage by volume of iso-octane in a mixture of iso-octane and n-heptane that produces the same knocking characteristics as the fuel being tested.

### Step 2: Identify the Components of the Mixture
In this case, the gasoline fuel consists of:
- 25% n-heptane
- 75% iso-octane

### Step 3: Use the Octane Number of the Components
- The octane number of n-heptane is 0 (as it is the reference fuel).
- The octane number of iso-octane is 100.

### Step 4: Calculate the Octane Number of the Mixture
The octane number of the mixture can be calculated using the formula:
\[ \text{Octane Number} = (\text{Fraction of iso-octane} \times \text{Octane Number of iso-octane}) + (\text{Fraction of n-heptane} \times \text{Octane Number of n-heptane}) \]

Substituting the values:
- Fraction of iso-octane = 0.75 (75%)
- Octane Number of iso-octane = 100
- Fraction of n-heptane = 0.25 (25%)
- Octane Number of n-heptane = 0

Thus,
\[ \text{Octane Number} = (0.75 \times 100) + (0.25 \times 0) \]
\[ \text{Octane Number} = 75 + 0 = 75 \]

### Step 5: Conclusion
The octane number of the gasoline fuel mixture is **75**.

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