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

Short Answer

Expert verified
The octane number of the mixture is 65.

Step by step solution

01

Understanding the Components

The octane number is a measure of a fuel's ability to resist knocking or pinging during combustion, relative to a standard mixture of isooctane and heptane. Isooctane has an octane number of 100, while heptane has an octane number of 0.
02

Expressing the Mixture as a Formula

To find the octane number of the mixture, we need to calculate the weighted average of the individual octane numbers of heptane and isooctane based on their percentages in the mixture. The formula for the octane number of the mixture is: \[\text{Octane number of mixture} = (\% ext{isooctane} \times \text{Octane number of isooctane}) + (\%\text{heptane} \times \text{Octane number of heptane})\].
03

Substitute the Values

Substitute the given percentages and octane numbers into the formula:\[\text{Octane number of mixture} = (0.65 \times 100) + (0.35 \times 0)\].
04

Calculate the Product

Compute the products for each component:- For isooctane: \(0.65 \times 100 = 65\)- For heptane: \(0.35 \times 0 = 0\).
05

Calculate the Octane Number

Add the results of the products to find the octane number of the mixture:\[\text{Octane number of mixture} = 65 + 0 = 65\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fuel Combustion
Fuel combustion is the process of burning a fuel in the presence of oxygen to release energy. This energy is usually in the form of heat, which can be used to power engines, generate electricity, or heat homes. During combustion, a chemical reaction occurs where the fuel combines with oxygen to produce carbon dioxide, water vapor, and other gases.
A key factor in combustion is how efficiently a fuel can be burned without causing knocking. Knocking is an undesirable outcome of combustion in engines, which creates a metallic sound because of premature combustion in the cylinder. It can cause severe damage to the engine if not managed properly.
To avoid knocking, fuels have an octane number that indicates their ability to resist it. A higher octane number means better resistance to knock, allowing the engine to run smoothly.
  • Knocking is a critical issue because it reduces engine performance and efficiency.
  • The octane number helps users select the correct fuel for their engine, minimizing the risk of knocking.
Isooctane
Isooctane is a type of hydrocarbon that acts as a standard reference fuel in determining the octane number. Its chemical formula is \( C_8H_{18} \), and it is known for its ability to resist knocking exceptionally well. Because of this property, isooctane is assigned an octane number of 100.
In a fuel mixture, having a high percentage of isooctane usually raises the overall octane number, improving the fuel's resistance to knocking. This makes isooctane an essential component in high-performance fuels used in racing cars and high-end vehicles.
  • Isooctane is an important compound for inferring the quality of different fuel mixtures.
  • It serves as the benchmark against which other fuel components are measured.
Heptane
Heptane is a straight-chain alkane hydrocarbon with the chemical formula \( C_7H_{16} \). Unlike isooctane, heptane tends to knock easily during combustion, and thus is assigned an octane number of 0. This reference standard signifies the worst knocking characteristics that fuel can possess.
Heptane is utilized in octane number calculations to ascertain how susceptible a particular fuel is to knocking. When used in fuel mixtures, it typically lowers the octane number, meaning the fuel is more likely to cause knocking.
  • Heptane's low octane rating is crucial for determining the limits of fuel quality.
  • It serves as a contrast to isooctane's superior anti-knocking abilities.
Mixture Calculation
Mixture calculation involves determining the octane number of a fuel mixture based on the proportion and octane numbers of its components, usually isooctane and heptane. The process requires calculating a weighted average of these components.
For instance, to find the octane number of a mixture with 35% heptane and 65% isooctane, we apply the formula:\[\text{Octane number of mixture} = (\% \text{isooctane} \times \text{Octane number of isooctane}) + (\% \text{heptane} \times \text{Octane number of heptane})\]
Plugging in the values, the calculation becomes:\[(0.65 \times 100) + (0.35 \times 0) = 65\]This weighted calculation indicates the mixture's performance in resisting engine knock, providing essential information for refining or choosing the correct fuel for a particular vehicle's requirements.
  • Understanding mixture calculation is vital for creating fuels that meet specific octane benchmarks.
  • Helps ensure compatibility between the fuel and the engine design.

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Most popular questions from this chapter

Give the name or condensed structural formula, as appropriate: (a) 3-phenylpentane (b) 2,3 -dimethylhexane (c) 3,3-dimethyloctane (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}\)

True or false: The weaker a single bond in a molecule, the greater the chance it will be the site of a reaction (compared to stronger single bonds in the molecule).

Imagine a single DNA strand containing a section with the following base sequence: \(5^{\prime}\) -AGTTACTGG-3'. What is the base sequence of the complementary strand?

The protein ribonuclease \(\mathrm{A}\) in its native, or most stable, form is folded into a compact globular shape: (a) Does the native form have a lower or higher free energy than the denatured form, in which the protein is an extended chain? (b) What is the sign of the system's entropy change in going from the denatured to the folded form? (c) In the native form, the molecule has four \(-\mathrm{S}-\mathrm{S}-\) bonds that bridge parts of the chain. What effect do you predict these four linkages to have on the free energy and entropy of the native form relative to the free energy and entropy of a hypothetical folded structure that does not have any \(-\mathrm{S}-\mathrm{S}-\) linkages? Explain. (d) A gentle reducing agent converts the four \(-S-S-\) linkages in ribonuclease \(A\) to eight \(-S-H\) bonds. What effect do you predict this conversion to have on the tertiary structure and entropy of the protein? (e) Which amino acid must be present for \(-\mathrm{SH}\) bonds to exist in ribonuclease A?

Indicate whether each statement is true or false. (a) All carbon atoms in propene are \(s p^{2}\) hybridized. (b) Acetone is another name for propanone. (c) The phenyl group contains six \(s p^{2}\) -hybridized carbons. (d) A hydrocarbon containing only \(s p^{3}\) carbons must be an alkane.

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