The world burns approximately 3.7 ×10^12 kg of fossil fuel per year. Use the combustion of octan

The world burns approximately 3.7 ×10^12 kg of fossil fuel...

The world burns approximately $3.7 \times 10^{12} \mathrm{kg}$ of fossil fuel per year. Use the combustion of octane as the representative reaction and determine the mass of carbon dioxide (the most significant greenhouse gas) formed per year. The current concentration of carbon dioxide in the atmosphere is approximately 399 ppm (by volume). By what percentage does the concentration increase each year due to fossil fuel combustion? Approximate the average properties of the entire atmosphere by assuming that the atmosphere extends from sea level to 15 $\mathrm{km}$ and that it has an average pressure of 381 torr and average temperature of 275 $\mathrm{K}$ . Assume Earth is a perfect sphere with a radius of 6371 $\mathrm{km}$ .

The world burns approximately $3.7 \times 10^{12} \mathrm{kg}$ of fossil fuel per
year. Use the combustion of octane as the representative reaction and determine the mass of carbon dioxide (the most significant greenhouse gas) formed per year. The current concentration of carbon dioxide in the atmosphere is approximately 399 ppm (by volume). By what percentage does the concentration increase each year due to fossil fuel combustion? Approximate the average properties of the entire atmosphere by assuming that the atmosphere extends from sea level to 15 $\mathrm{km}$ and that it has an average pressure of 381 torr and average temperature of 275 $\mathrm{K}$ . Assume Earth is a perfect sphere with a radius of 6371 $\mathrm{km}$ .

Key Concepts

Atmospheric Volume and Spherical Geometry

Estimating the volume of the Earth's atmosphere requires applying geometrical formulas to a spherical Earth, typically using the known radius and the altitude up to which the atmosphere extends. This concept allows one to approximate the total mass or volume of the atmosphere, which is important when determining the relative increase in the concentration of carbon dioxide due to emissions.

Ideal Gas Law and Atmospheric Properties

The ideal gas law (PV = nRT) is used to relate the pressure, volume, temperature, and number of moles of a gas. This concept is crucial when estimating the density of air or the total number of moles present in the atmosphere, based on average pressure and temperature values. It provides a framework to convert atmospheric pressure and volume into a quantifiable mass or number of moles, which is needed for comparing the mass of CO2 added by combustion to the total atmospheric mass.

Parts Per Million (ppm) and Concentration Increase

The ppm unit is used to express very dilute concentrations of substances, such as carbon dioxide in the atmosphere. This concept involves understanding that ppm is a ratio representing the number of CO2 molecules per million molecules of air. It is crucial for calculating the percentage increase in atmospheric CO2 concentration by comparing the mass (or mole) addition from fossil fuel combustion to the existing atmospheric content.

Combustion Reaction Stoichiometry

This concept involves writing and balancing the chemical equation for the combustion of a fuel, which allows one to determine the mole ratios between reactants and products. Understanding the stoichiometry is essential to calculate the amount of carbon dioxide produced from a given amount of fossil fuel, using the balanced equation to relate the moles of fuel consumed to the moles of CO2 generated.

Fossil Fuel Carbon Content and Conversion

Fossil fuels are carbon-rich, and their combustion converts the carbon into carbon dioxide. This concept entails determining the fraction of the fossil fuel's mass that is carbon and then using stoichiometric relationships from the combustion process to compute the resulting mass of carbon dioxide. It is a key step in linking the mass of fossil fuel burned to the mass of greenhouse gas emitted.

Transcript

00:01 In this question, we're first going to calculate the mass co2 formed per year, combustion reaction.

00:34 And we can calculate the moles of c8h18, which is equal to 3 .5 times 10 to the 12th kilograms.

00:48 And word to grams, one kilogram is equivalent to 1 ,000 grams over 114 .0 grams per mole would be the molar mass of c8h18, and we get 3 .07 times 10 to the 13 moles of c8h18.

01:12 And using our sterechometry here, 3 .07 times 10 to the 13 moles.

01:18 Of c8h18, one mole as c8h18 is equivalent to eight moles of co2 from a balanced combustion equation up above.

01:30 One mole of co2 is a molar mass of 44 .0 grams of co2, and we find that the mass of co2 is equal to 1 .08 times 10 to the 16 grams of co2.

01:44 So that's the first part of our question, is the mass of co2, is 1 .0 .2.

01:49 0 .08 times 10 to the 16th grams.

01:53 For part two of this question, we're asked to calculate the percent increase of carbon dioxide per year.

02:05 We'll first calculate the volume of the atmosphere, which will be equal to 4 thirds pi, r2 cubed minus r1 cubed.

02:26 We'll start with r1 cubed.

02:28 This is the radius at sea level, and we're told that the atmosphere extends up 15 kilometers.

02:39 So this is the radius at sea level plus 15 kilometers.

02:45 So we can plug these numbers in to calculate the volume of the atmosphere.

02:49 4 thirds pi, 6386 kilometers cubed minus 633 .3 .6 kilometers cubed minus 633.

02:59 71 kilometers cubed and we find that this is equal to 7 .665 times 10 to the 9th kilometers cubed.

03:11 Now let's convert this into liters 7 .665 times 10 to the 9th kilometers cubed times one kilometer.

03:23 It's equivalent to 1 ,000 meters.

03:26 That would be cubed times 1 meter cubed is 1 ,000 liters and this would equal 7 .665 times 10 to the 21 liters...

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