Question

The automobile fuel called E85 consists of \(85 \%\) ethanol and \(15 \%\) gasoline. \(\mathrm{E} 85\) can be used in so-called "flex-fuel" vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of \(\mathrm{C}_{8} \mathrm{H}_{18}\) ), that the average heat of combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) is \(5400 \mathrm{~kJ} / \mathrm{mol}\), and that gasoline has an average density of \(0.70 \mathrm{~g} / \mathrm{mL}\). The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{mL}\). (a) By using the information given as well as data in Appendix C, compare the energy produced by combustion of \(1.0 \mathrm{~L}\) of gasoline and of \(1.0 \mathrm{~L}\) of ethanol. (b) Assume that the density and heat of combustion of \(\mathrm{E} 85\) can be obtained by using \(85 \%\) of the values for ethanol and \(15 \%\) of the values for gasoline. How much energy could be released by the combustion of \(1.0 \mathrm{~L}\) of E85? (c) How many gallons of E85 would be needed to provide the same energy as 10 gal of gasoline? (d) If gasoline costs \(\$ 3.10\) per gallon in the United States, what is the break-even price per gallon of \(\mathrm{E} 85\) if the same amount of energy is to be delivered?

Short answer

The energy produced by the combustion of 1.0 L of gasoline is 33,156 kJ, while 1.0 L of ethanol produces 23,463 kJ. The combustion of 1.0 L of E85 releases 36,917 kJ of energy. To provide the same energy as 10 gallons of gasoline, approximately 9 gallons of E85 are needed. The break-even price per gallon of E85 is approximately $3.45 if the same amount of energy is to be delivered.

Step-by-step solution

(a) Compare the energy produced by combustion of 1.0 L of gasoline and 1.0 L of ethanol.

First, we need to calculate the energy produced by 1.0 L of gasoline: 1. Convert 1.0 L of gasoline to grams: \(1.0 L \times 0.70 g/mL = 700 g\) 2. Convert grams to moles: \( \frac{700 g}{114 g/mol} \approx 6.14 mol\) (Assuming the average molar mass of octane is \(114 g/mol\)) 3. Calculate the energy produced: \(6.14 mol \times 5400 kJ/mol = 33,156 kJ\) Now, we will calculate the energy produced by 1.0 L of ethanol: 1. Convert 1.0 L of ethanol to grams: \(1.0 L \times 0.79 g/mL = 790 g\) 2. Convert grams to moles: \( \frac{790 g}{46 g/mol} \approx 17.17 mol\) (Assuming the molar mass of ethanol is \(46 g/mol\)) 3. From Appendix C, the heat of combustion of ethanol is equal to \(1367 kJ/mol\). Calculate the energy produced: \(17.17 mol \times 1367 kJ/mol = 23,463 kJ\) Comparing the energy produced by 1.0 L of gasoline and 1.0 L of ethanol, we can see that gasoline produces more energy, with \(33,156 kJ\), while ethanol produces only \(23,463 kJ\).

(b) Calculate the energy produced by combustion of 1.0 L of E85.

First, we need to find the density and heat of combustion of E85: 1. Density of E85: \(0.85 \times 0.79 g/mL + 0.15 \times 0.70 g/mL \approx 0.778 g/mL\) 2. Heat of combustion of E85: \(0.85 \times 1367 kJ/mol + 0.15 \times 5400 kJ/mol \approx 2244.5 kJ/mol\) Now, let's calculate the energy produced by 1.0 L of E85: 1. Convert 1.0 L of E85 to grams: \(1.0 L \times 0.778 g/mL = 778 g\) 2. Convert grams to moles: \( \frac{778 g}{47.26 g/mol} \approx 16.45 mol\) (Assuming the average molar mass of E85 is \(47.26 g/mol\): \(0.85(46) + 0.15(114)\) ) 3. Calculate the energy produced: \(16.45 mol \times 2244.5 kJ/mol = 36,917 kJ\) The energy produced by the combustion of 1.0 L of E85 is \(36,917 kJ\).

(c) Determine how many gallons of E85 would be needed to provide the same energy as 10 gallons of gasoline.

First, let's find the energy produced by 10 gallons of gasoline: 1. Convert gallons to liters: \(10 gal \times 3.785L/gal = 37.85 L\) 2. Calculate the energy produced by 37.85 L of gasoline: \(37.85 L \times 33,156 kJ/L = 1,255,768 kJ\) Now, let's find the volume of E85 needed to produce the same amount of energy as 10 gallons of gasoline: 1. Calculate the volume of E85 needed: \( \frac{1,255,768 kJ}{36,917 kJ/L} \approx 34.01 L\) 2. Convert liters to gallons: \(34.01 L \times \frac{1 gal}{3.785 L} \approx 8.99 gal\) Approximately 9 gallons of E85 are needed to produce the same amount of energy as 10 gallons of gasoline.

(d) Calculate the break-even price per gallon of E85 if the same amount of energy is to be delivered.

1. Find the total energy cost for 10 gallons of gasoline: \(10 gal \times \$3.10/gal = \$31.00\) 2. Calculate the break-even price per gallon of E85: \( \frac{\$31.00}{8.99 gal} \approx \$3.45/gal\) The break-even price per gallon of E85 is approximately \$3.45 if the same amount of energy is to be delivered.

Key concepts

Combustion Energy

When discussing fuels, combustion energy refers to the amount of energy released when a fuel is burned completely. This is an important concept as it determines how much work can be extracted from a given quantity of fuel, such as gasoline or ethanol.
Combustion energy is often measured in kilojoules per mole (kJ/mol), which signifies how much energy is released per mole of fuel. For example, octane, a significant component of gasoline, has an average heat of combustion of 5400 kJ/mol.
Understanding combustion energy is crucial for comparing different fuels.

• Gasoline has a higher combustion energy compared to ethanol.
• Combustion energy informs decisions about fuel efficiency and performance.

These comparisons are essential, especially in the context of E85 fuel, which combines both ethanol and gasoline to create a flex-fuel option that's both efficient and more environmentally friendly.

Ethanol and Gasoline Mixture

E85 is a type of biofuel that consists of 85% ethanol and 15% gasoline. This mixture is designed to maximize the use of ethanol, which is a renewable energy source, while still maintaining enough gasoline to ensure proper engine performance.
The mixture ratio affects the fuel's properties, such as its density and combustion energy. Different mixtures can be used depending on availability and pricing but E85 is one of the most common forms for flex-fuel vehicles.
Combining ethanol and gasoline leads to certain advantages:

• Reduces greenhouse gas emissions compared to pure gasoline.
• Sustainable as it is partly made from renewable sources.
• Offers comparable energy efficiency with modified engines.

These benefits make ethanol-gasoline mixtures an appealing choice for both environmental and economic reasons, particularly in the ever-evolving automotive industry.

Flex-fuel Vehicles

Flex-fuel vehicles are designed to run on more than one type of fuel, often a mixture of gasoline and ethanol. With E85 being one such mixture, these vehicles can adjust their fuel intake depending on what's available.
The adaptability of flex-fuel vehicles lies in their engine technology. They can automatically recognize the ethanol-to-gasoline ratio and adjust combustion processes accordingly. As a result, they can efficiently utilize different fuel mixtures without compromising on performance.
Key features of flex-fuel vehicles include:

• Versatility in fuel choice adapts to varying fuel availability.
• Environmental advantages due to lower emissions.
• Potentially reduced fuel costs if ethanol is cheaper than gasoline.

Overall, flex-fuel vehicles represent a step towards a more flexible, environmentally conscious form of transportation. By utilizing mixtures like E85, they offer a viable alternative to traditional gasoline-powered vehicles.