Problem 19 - Chemistry: The Central Science in SI Units, Global Edition

Question

What is the octane number of a mixture that is \(35 \%\) heptane and \(65 \%\) isooctane?

Step-by-Step Solution

Answer

The octane number of a mixture that is 35% heptane and 65% isooctane can be calculated using the volume-weighted average formula. The result is an octane number of 65 for the mixture.

Step 1: Understand the octane rating

The octane rating is a measure of a fuel's ability to resist 'knock' or 'pinging' during combustion, caused by the air/fuel mixture detonating prematurely in the engine. In the scale, heptane is given a value of 0 and isooctane is given a rating of 100. This means that isooctane can withstand higher compression than heptane before detonating.

Step 2: Identify the volume percentages of the compounds in the mixture

The exercise states that the mixture is composed of 35% heptane and 65% isooctane. This means that for every 100 litres of fuel, there will be 35 litres of heptane and 65 litres of isooctane.

Step 3: Calculate the octane number of the mixture

The octane number of a mixture can be calculated by taking the volume-weighted average of the octane numbers of each component. This can be done using the formula: \(\text{Octane number} = (\text{% Heptane} \times \text{Heptane's octane number}) + (\text{% Isooctane} \times \text{Isooctane's octane number})\) Substitute the given values into the formula: \(\text{Octane number} = (35\% \times 0) + (65\% \times 100) = 0 + 65 = 65\) So, the octane number of the mixture is 65.

Key Concepts

Heptane

Heptane is a colorless liquid that is part of a group of hydrocarbons known as alkanes. It is a key component used to determine the octane rating of fuels. In engines, a high octane number is desirable as it indicates good resistance to knocking during combustion. Unfortunately, heptane has a poor resistance to knocking. It is assigned an octane rating of 0. This means that when mixed with air in an engine, it detonates or ignites much more readily under compression.

If a fuel mixture contains a high percentage of heptane, it will typically have a lower octane number. This results in increased chances of engine knock, which is harmful to engine performance. Understanding the properties of heptane helps in blending fuels optimally to achieve the required octane numbers for various engine types.

Isooctane

Isooctane is another hydrocarbon, but unlike heptane, it has a very high resistance to knocking. It is often used as a standard reference in the octane rating scale, marked with a 100, symbolizing excellent stability in fuel combustion. When blended with other fuels, its high octane rating can significantly boost the overall octane number.

• High resistance to knocking: This characteristic allows engines to operate smoother and at higher compression ratios.
• Standard for octane rating: Isooctane's performance sets the benchmark for other fuels, helping determine fuel quality.

Its superior ability to withstand compression without auto-ignition makes it a critical component in creating balanced fuel mixtures that optimize engine performance and efficiency.

Fuel Combustion

Fuel combustion refers to the chemical reactions that occur when a fuel, such as gasoline, is ignited to produce energy within an engine. The efficiency and performance of combustion largely depend on the octane number of the fuel used.

A higher octane rating indicates that the fuel can withstand greater pressure before pre-ignition, which results in:

• Better engine performance: High-octane fuels typically enable engines to run more smoothly, increasing power output and efficiency.
• Reduced knocking: This minimizes potential damage to the engine, prolonging its lifespan.

The balance between heptane and isooctane in fuel mixtures directly affects the quality of combustion. By adjusting this balance, fuel manufacturers can produce gasoline that meets the specific requirements of different engines, ensuring optimal performance with minimal impact on engine integrity.