Question

The amount of \(\mathrm{CO}_{2}\) in the atmosphere is \(0.04 \%(0.04 \%\) \(=0.0004 \mathrm{~L} \mathrm{CO}_{2} / \mathrm{L}\) atmosphere). The world uses the equivalent of approximately \(4.0 \times 10^{12} \mathrm{~kg}\) of petroleum per year to meet its energy needs. Determine how long it would take to double the amount of \(\mathrm{CO}_{2}\) in the atmosphere due to the combustion of petroleum. Follow each of the steps outlined to accomplish this: a. We need to know how much \(\mathrm{CO}_{2}\) is produced by the combustion of \(4.0 \times 10^{12} \mathrm{~kg}\) of petroleum. Assume that this petroleum is in the form of octane and is combusted according to the following balanced reaction: $$ 2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{~L})+25 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{~g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ By assuming that \(\mathrm{O}_{2}\) is in excess, determine how many moles of \(\mathrm{CO}_{2}\) are produced by the combustion of \(4.0 \times 10^{12} \mathrm{~kg}\) of \(\mathrm{C}_{8} \mathrm{H}_{18}\). This will be the amount of \(\mathrm{CO}_{2}\) produced each year. b. By knowing that \(1 \mathrm{~mol}\) of gas occupies \(22.4 \mathrm{~L}\), determine the volume occupied by the number of moles of \(\mathrm{CO}_{2}\) gas that you just calculated. This will be the volume of \(\mathrm{CO}_{2}\) produced per year. c. The volume of \(\mathrm{CO}_{2}\) presently in our atmosphere is approximately \(1.5 \times 10^{18} \mathrm{~L}\). By assuming that all \(\mathrm{CO}_{2}\) produced by the combustion of petroleum stays in our atmosphere, how many years will it take to double the amount of \(\mathrm{CO}_{2}\) currently present in the atmosphere from just petroleum combustion?

Short answer

To find the years to double the CO2, divide the initial volume of CO2 (0.0004 \times 1.5 \times 10^{18} L) by the annual CO2 production calculated in Step 3.

Step-by-step solution

Calculate the moles of octane combusted

Firstly, the molecular weight of octane (\text{C}_8\text{H}_{18}) needs to be calculated to find the number of moles in \(4.0 \times 10^{12} \mathrm{~kg}\) of octane. The molecular weight is given by (8 \times 12.01) + (18 \times 1.01) g/mol which equals 114.23 g/mol. Thus, the number of moles of octane is \(\frac{4.0 \times 10^{12} \mathrm{~kg}}{114.23 \times 10^{-3} \mathrm{~kg/mol}}\).

Determine the moles of CO2 produced

Using the stoichiometry of the balanced reaction, for every 2 moles of octane, 16 moles of CO2 are produced. From the number of moles of octane found in Step 1, multiply this by the ratio of moles of CO2 to moles of octane (16 moles of CO2 / 2 moles of C8H18) to find the total moles of CO2 produced.

Calculate the volume of CO2 produced per year

Using the fact that 1 mole of gas occupies 22.4 L at standard temperature and pressure, the volume of CO2 produced in a year is the number of moles of CO2 times 22.4 L/mol.

Calculate the current CO2 volume in the atmosphere

To find the current CO2 volume, multiply the total volume of the atmosphere by the percentage of CO2 in the atmosphere. The volume is given as \(1.5 \times 10^{18} L\) and the percentage as 0.0004, so the current CO2 volume is \(1.5 \times 10^{18} L \times 0.0004\).

Determine the time to double the current CO2 volume

To double the CO2 volume, divide the current CO2 volume by the annual volume of CO2 produced (from Step 3). This result is the number of years it will take to double the amount of CO2 in the atmosphere due to the combustion of petroleum alone.

Key concepts

Stoichiometry and Combustion

Understanding stoichiometry and combustion is crucial for grasping how substances react during the burning process. Stoichiometry involves using balanced chemical equations to determine the relationship between reactants and products. In the context of the problem, we examine the combustion of petroleum, typically modeled as octane (C8H18).

When octane burns in the presence of oxygen (O2), it produces carbon dioxide (CO2) and water (H2O), a reaction outlined in the balanced equation provided. This equation tells us that for every 2 moles of octane that combust, 16 moles of CO2 are produced. Hence, stoichiometry allows us to calculate the precise amount of CO2 produced from a known mass of petroleum. Without an understanding of stoichiometry, predicting the environmental impact of combustion would be exceedingly complex.

Mole Concept and Calculations

The mole concept is a cornerstone of chemical calculations, providing a link between the atomic scale and the real-world scale. It allows chemists to count particles by weighing them. One mole is equal to Avogadro's number (approximately 6.022 x 10^23) of particles, whether they're atoms, molecules, or ions.

In the textbook problem, the mole concept is used to convert the mass of octane to the amount of substance in moles. This is essential since chemical reactions occur particle by particle, mole by mole, rather than mass by mass. Using the molar mass of octane (114.23 g/mol), we can calculate how many moles are in 4.0 x 10^12 kg of octane, and thus determine the moles of CO2 that would be produced upon its complete combustion. Without the mole concept, we couldn't bridge the gap between mass and number of molecules in chemical reactions.

Environmental Impact of CO2 Emissions

Carbon dioxide (CO2) emissions have substantial environmental impacts, contributing to the greenhouse effect and climate change. The greenhouse effect occurs when CO2 and other greenhouse gases trap heat in Earth's atmosphere, leading to global warming. This, in turn, can cause more extreme weather, alter ecosystems, and raise sea levels.

Our problem illustrates a significant source of CO2 emissions: the combustion of fossil fuels such as petroleum. By calculating how long it would take to double atmospheric CO2 levels from petroleum combustion alone, we gain insight into the urgency of addressing CO2 emissions. Understanding the scale of emissions helps policymakers and scientists to develop strategies to mitigate these effects, such as adopting renewable energy sources, improving energy efficiency, and implementing carbon capture technologies.

Petroleum Combustion and CO2 Production

Petroleum combustion is a major source of CO2 production globally. When petroleum, represented as octane in chemical equations, is burned, it combines with oxygen to form CO2 and water.

Through the exercise, we calculated the amount of CO2 emitted annually by burning the world's petroleum consumption. This calculation gives us a foundation to estimate how much CO2 accumulates in the atmosphere year by year, assuming none is removed. Since the combustion of petroleum is just one of many sources of CO2, the calculated time to double the current CO2 level in the atmosphere serves as a simplified model. Yet, it highlights the importance of considering the carbon footprint of our energy sources and striving to reduce reliance on fossil fuels to curb CO2 emissions.