Question

In some areas, gasoline is formulated to contain \(15 \%\) ethanol during some seasons. If gasoline releases \(11.4 \mathrm{kcal} / \mathrm{g}\) upon combustion, but ethanol releases only \(7.12 \mathrm{kcal} / \mathrm{g}\), how much less energy in \(\mathrm{kJ} / \mathrm{g}\) is provided by the mixture than by pure gasoline?

Short answer

The total energy released by the mixture is \(9.345 \, \mathrm{kcal} / \mathrm{g}\), and the energy difference between pure gasoline and the mixture in kJ/g is \((11.4 - 9.345) \times 4.184 = 8.59 \, \mathrm{kJ} / \mathrm{g}\).

Step-by-step solution

Calculate total energy for gasoline

The energy released by pure gasoline per gram is given as \(11.4 \, \mathrm{kcal} / \mathrm{g}\). We will keep this value as it is, for future comparison.

Calculate total energy for the mixture

Assuming the weight of the mixture is 1g, then the mass of gasoline is \(85\%\) of 1g (or \(0.85g\)) and the mass of ethanol is \(15\%\) of 1g (or \(0.15g\)). The total energy \(E_{total}\) released by the mixture is the sum of the energy released by the gasoline and the ethanol, which is equal to \(0.85 \times 11.4 + 0.15 \times 7.12\).

Calculate the energy difference

Subtract the energy released by the mixture (\(E_{total}\)) from the energy released by pure gasoline to get the difference in energy.

Convert energy difference from kcal/g to kJ/g

Use the conversion factor 1 kcal = 4.184 kJ to convert the energy difference from kcal/g to kJ/g.

Key concepts

Energy Conversion Chemistry

Understanding the process of energy conversion in chemical reactions, particularly combustion, is crucial for various applications, including fuel usage in vehicles. During combustion, a substance reacts with oxygen, releasing energy in the form of heat. This can be represented in a chemical equation that reflects the conversion of reactants to products alongside the energy output.

Chemical energy stored in bonds of the fuel is converted to thermal energy (heat), which can be measured in units like kilocalories (kcal) or kilojoules (kJ). For instance, gasoline and ethanol release different amounts of energy per gram when burned, as they have different chemical compositions and bond structures. This combustion energy is significant for engine performance and efficiency, as well as environmental impact.

Ethanol-Gasoline Mixture

The use of an ethanol-gasoline mixture as fuel is an example of how different substances can be combined to alter energy content and emissions. Ethanol, often produced from biomass, is considered a renewable resource that can reduce the carbon footprint of fuel. Mixing ethanol with gasoline modifies the energy content of the fuel and, therefore, the overall efficiency of the engine.

In the problem provided, the gasoline is blended with 15% ethanol. This means that for every gram of the mixture, 0.85 grams is gasoline, and 0.15 grams is ethanol. The combustion properties of each component must be considered to determine the total energy output of the mixture. While ethanol-gasoline mixtures can reduce dependence on pure fossil fuels, they may also alter the energy provided to engines, as witnessed by the different caloric content of each component.

Energy Content Comparison

Comparing the energy content of fuels such as pure gasoline and ethanol-gasoline mixtures is vital for understanding how changes in fuel composition affect energy output. The energy content of a fuel, measured per gram, indicates how much heat energy is produced during its complete combustion.

In the provided exercise, pure gasoline releases 11.4 kcal/g, while ethanol releases significantly less at 7.12 kcal/g. Therefore, a mixture of the two will have an energy release that is a weighted average based on their respective proportions and energy contributions. Knowing how to calculate and compare these values informs decision-making regarding alternative fuels, engine design, and emissions control strategies. It's essential for students to master these concepts to better understand the energy efficiency implications of various fuel types.