(a) If an automobile travels 350 km with a gas mileage of 9.0 km/L, how many kilograms of CO2 are produced? Assume that the gasoline is composed of octane, C8H181l2, whose density is 0.692 g/mL. (b) Repeat the calculation for a truck that has a gas mileage of 2 km/L.

Verified step by step guidance

Calculate the total volume of gasoline used by the automobile by dividing the distance traveled (350 km) by the gas mileage (9.0 km/L). This gives the volume in liters.

Convert the volume of gasoline from liters to milliliters, knowing that 1 L = 1000 mL.

Use the density of octane (0.692 g/mL) to find the mass of gasoline in grams by multiplying the volume in milliliters by the density.

Convert the mass of gasoline from grams to moles using the molar mass of octane (C8H18). The molar mass is calculated by adding the atomic masses of carbon and hydrogen in the formula C8H18.

Use the stoichiometry of the combustion reaction of octane to determine the moles of CO2 produced. The balanced equation for the combustion of octane is: 2 C8H18 + 25 O2 → 16 CO2 + 18 H2O. From this, calculate the moles of CO2 produced per mole of octane, and then convert the moles of CO2 to mass in kilograms using the molar mass of CO2 (44.01 g/mol).

Key Concepts

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

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the calculation of reactants and products in chemical reactions. It allows us to determine the amount of substances consumed and produced in a reaction based on balanced chemical equations. In this context, stoichiometry is essential for calculating the amount of CO2 produced from the combustion of octane, as it involves understanding the mole ratios between octane and carbon dioxide.

Density and Volume Calculations

Density is defined as mass per unit volume and is a critical concept for converting between mass and volume in chemical calculations. In this problem, the density of octane is used to convert the volume of gasoline consumed (based on gas mileage) into mass, which is necessary for determining the total amount of CO2 produced. Understanding how to manipulate density equations is vital for accurate calculations.

Combustion Reactions

Combustion reactions are exothermic reactions that occur when a substance reacts with oxygen, typically producing heat, light, water, and carbon dioxide. For octane, the balanced combustion reaction shows how many moles of CO2 are produced per mole of octane burned. This concept is crucial for calculating the total CO2 emissions from the fuel consumed by the automobile and truck in the given scenarios.

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