The world burns approximately 3.5 * 1012 kg of fossil fuel...

The world burns approximately 3.5 * 1012 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 394 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 km and that it has an average pressure of 381 torr and average temperature of 275 K. Assume Earth is a perfect sphere with a radius of 6371 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 The first thing we want to do in this problem is write the equation for the combustion of octane.

00:09 So that's 2c8h18 plus 2502 forms 16 co2 and 18 h2.

00:26 And so now we want to determine our moles of octane so we can determine our moles of co2.

00:35 So we have 3 .5 times 10 to the 12 kilograms of octane.

00:45 We first multiply by 1 ,000 grams per kilogram.

00:52 Then by the molar mass of octane, 11 .23 grams per mole.

01:03 And then this is moles of octane, and we want moles of carbon dioxide.

01:10 And so we know that there's two moles of octane for 16 moles of co2.

01:22 And so this gives us our moles of co2 as 2 .45119 times 10 to the 14th moles of co2.

01:36 Now we can use the ideal gas law, pv equals nrt, in order to find the volume of that carbon dioxide.

01:47 So we rearrange this to solve for volume.

01:51 V equals nrt over p.

01:54 And then we can plug in all of our values.

01:56 So we have 2 .45 -119 times 10 to the 14th moles.

02:04 Our r value is 0 .082 -057 liter atmospheres per mole kelvin.

02:15 Our temperature is 275 kelvin.

02:20 Our pressure is 381 millimeters of mercury.

02:26 I'm going to divide that by 760 in order to get our pressure in atmospheres.

02:33 Doing all of that gives us a volume of co2 as 1 .103 times 10 to the 16th liters.

02:42 So that is our volume of co2.

02:46 Now we need to find the volume of the atmosphere in order to determine what the parts per million of this co2 is...

Please give Ace some feedback