The combustion of one mole of liquid octane, CH3(CH2)6CH3, produces 5470 kJ of heat. Calculate how much heat is produced if 1.000 gallon of octane is combusted.

Verified step by step guidance

Determine the density of octane, which is typically about 0.703 g/mL. This will help in converting the volume of octane (in gallons) to mass (in grams).

Convert the volume of octane from gallons to liters, knowing that 1 gallon is approximately 3.785 liters, and then to milliliters (1 liter = 1000 mL).

Calculate the mass of octane in grams using the volume in milliliters and the density (mass = density × volume).

Convert the mass of octane to moles using the molar mass of octane (C8H18), which is about 114 g/mol (mass in grams / molar mass).

Multiply the number of moles of octane by the heat produced per mole (5470 kJ/mole) to find the total heat produced when the given amount of octane is combusted.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Combustion Reaction

A combustion reaction is a chemical process in which a substance (usually a hydrocarbon) reacts with oxygen to produce carbon dioxide, water, and energy in the form of heat. In this case, the combustion of octane releases a significant amount of energy, quantified as 5470 kJ per mole of octane burned.

Molar Mass and Density

To calculate the heat produced from a specific volume of octane, it is essential to know its molar mass and density. The molar mass of octane (C8H18) is approximately 114.22 g/mol, and its density is about 0.703 g/mL. This information allows us to convert the volume of octane (in gallons) to mass (in grams) and then to moles.

Heat Calculation

The total heat produced from the combustion of octane can be calculated using the formula: total heat = (moles of octane) x (heat produced per mole). After determining the number of moles from the mass of octane, multiplying by the heat released per mole provides the total energy output from the combustion process.

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