Question

(a) If an automobile travels \(350 \mathrm{~km}\) with a gas mileage of 9.0 \(\mathrm{km} / \mathrm{L}\), how many kilograms of \(\mathrm{CO}_{2}\) are produced? Assume that the gasoline is composed of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) whose density is \(0.692 \mathrm{~g} / \mathrm{mL}\). (b) Repeat the calculation for a truck that has a gas mileage of \(2 \mathrm{~km} / \mathrm{L}\).

Short answer

The automobile produces approximately 84.4 kg of CO₂, while the truck produces approximately 378 kg of CO₂.

Step-by-step solution

Find the amount of gasoline consumed by the automobile

Divide the distance driven (350 km) by the gas mileage (9 km/L) to determine the amount of gasoline consumed: Gasoline_consumed = 350 km / 9.0 km/L = 38.89 L (approx.)

Calculate the mass of gasoline consumed by the automobile

Given the density of octane as 0.692 g/mL, we can convert the amount of gasoline consumed to mass: Gas_mass_car = Gasoline_consumed * 0.692 g/mL * 1000 mL/L = 26900 g (approx.)

Determine the stoichiometry of the combustion reaction of octane

The balanced equation for the combustion of octane is: C8H18(l) + 12.5 O2(g) -> 8 CO2(g) + 9 H2O(l) For each mole of octane combusted, 8 moles of CO2 are produced.

Calculate the molar mass of octane and CO2

Molar mass of octane (C8H18) = (8 * 12.01 g/mol) + (18 * 1.01 g/mol) = 114.23 g/mol Molar mass of CO2 = (1 * 12.01 g/mol) + (2 * 16.00 g/mol) = 44.01 g/mol

Calculate the mass of CO2 produced by the automobile

Use stoichiometry to find the mass of CO2 produced from the mass of octane burnt: Mass_CO2_car = (Gas_mass_car /114.23 g/mol) * 8 mol CO2/1 mol C8H18 * 44.01 g/mol = 84400 g or 84.4 kg of CO2 (approx.) b) Calculating the amount of CO2 produced by the truck

Find the amount of gasoline consumed by the truck

Divide the distance driven (350 km) by the gas mileage (2 km/L) to determine the amount of gasoline consumed by the truck. Gasoline_consumed_truck = 350 km / 2.0 km/L = 175 L

Calculate the mass of gasoline consumed by the truck

Using the density of octane (0.692 g/mL), we can convert the amount of gasoline consumed by the truck: Gas_mass_truck = Gasoline_consumed_truck * 0.692 g/mL * 1000 mL/L = 121000 g (approx.)

Use the stoichiometry of the combustion reaction to determine the mass of CO2 produced by the truck

Using the stoichiometry from the previous part, we calculate the mass of CO2 produced by the truck: Mass_CO2_truck = (Gas_mass_truck /114.23 g/mol) * 8 mol CO2/1 mol C8H18 * 44.01 g/mol = 378000 g or 378 kg of CO2 (approx.) The automobile produces approximately 84.4 kg of CO2, while the truck produces approximately 378 kg of CO2.

Key concepts

Combustion Reaction

A combustion reaction is a chemical process where a substance combines with oxygen and releases energy in the form of heat and light. It is a type of exothermic reaction, meaning it releases more energy than it consumes. These reactions are key to understanding how fuel sources like gasoline power engines. A classic example of combustion is the burning of hydrocarbons, such as octane, which is a component of gasoline.

In the context of our exercise, the combustion of octane can be represented by the balanced chemical equation:

• \(C_{8}H_{18}(l) + 12.5\,O_{2}(g) \rightarrow 8\,CO_{2}(g) + 9\,H_{2}O(l)\)

This equation shows that one molecule of octane reacts with 12.5 molecules of oxygen to produce 8 molecules of carbon dioxide and 9 molecules of water.

Understanding this stoichiometric relationship is crucial as it allows us to calculate how much carbon dioxide is produced from a given amount of gasoline.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is a fundamental property used to relate a chemical substance's mass to the number of particles or moles it contains. The molar mass is an essential part of stoichiometry calculations, especially in chemical reactions.

For octane (\(C_{8}H_{18}\)), its molar mass can be calculated by adding up the atomic masses of all the atoms in its molecular formula:

• Carbon (C) atomic mass = 12.01 g/mol
• Hydrogen (H) atomic mass = 1.01 g/mol
• Octane, \(C_{8}H_{18}\), consists of 8 carbon atoms and 18 hydrogen atoms.

Thus, the molar mass of octane is:\[(8 \times 12.01) + (18 \times 1.01) = 114.23\,g/mol\]Similarly, the molar mass of carbon dioxide (\(CO_{2}\)) is given by:\[(1 \times 12.01) + (2 \times 16.00) = 44.01\,g/mol\]In our exercise, we use molar mass to convert the mass of octane into moles, allowing us to use stoichiometry to determine how much CO2 is produced.

Gasoline Consumption

Gasoline consumption is often measured in terms of fuel efficiency, usually expressed as kilometers per liter (km/L) or miles per gallon (mpg). It indicates how far a vehicle can travel on a specific volume of fuel. Understanding gasoline consumption is crucial not only for environmental concerns but also for economic reasons, as lower consumption typically means reduced fuel costs and fewer emissions.

In our given problem, the automobile has a fuel efficiency of 9 km/L, while the truck's efficiency is 2 km/L. This means the car will travel 9 km for every liter of gasoline it burns, whereas the truck will travel only 2 km per liter.

To determine how much gasoline has been consumed during a trip, we divide the total distance traveled by the vehicle's fuel efficiency. For instance, the car traveling 350 km at 9 km/L consumes about 38.89 liters of gasoline. Similarly, the truck traveling the same distance, but with a lower efficiency of 2 km/L, consumes about 175 liters of gasoline.

Octane

Octane is a hydrocarbon and one of the primary constituents of gasoline. Its chemical formula is \(C_{8}H_{18}\), consisting of 8 carbon atoms bonded in a chain, surrounded by 18 hydrogen atoms. Its structure makes it highly combustible, thereby releasing significant energy when burned, which is why it's an essential component of fuel for internal combustion engines.

The performance of gasoline is often rated by its octane number, which measures its ability to resist knocking during combustion. Knocking is a condition where the fuel-air mixture in an engine's cylinders ignites prematurely, causing a decrease in efficiency and potentially harming the engine. However, in our specific exercise, we focus on octane seen through the lens of its combustion in the controlled environment of an engine.

By combusting octane, vehicles effectively convert chemical energy into the mechanical energy needed to power the engine, illustrating the importance of stoichiometric calculations in predicting the amounts of reactants and products involved in this process.