The world burns approximately 3.5 ×10^12 kg of fossil fuel per year. Use the combustion of octa

The world burns approximately 3.5 ×10^12 kg of fossil fuel...

The world burns approximately $3.5 \times 10^{12} \mathrm{~kg}$ 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 $387 \mathrm{ppm}$ (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

Parts per Million (ppm) Concentration

The parts per million concentration is a unit of measure that expresses the ratio of a particular gas to the total composition of the atmosphere on a volumetric or mole basis. It is particularly significant in environmental studies because even small ppm changes in CO2 can indicate substantial changes in absolute quantities, which can be linked to global warming trends.

Atmospheric Modeling

Atmospheric modeling applies physical and chemical principles to estimate the properties of the Earth’s atmosphere, such as its total mass, pressure distributions, and temperature averages. This modeling is crucial for determining the baseline amount of each constituent gas, such as CO2, and understanding how additional emissions alter the overall atmospheric composition.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, establishes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is key for estimating the total moles of gases present in the atmosphere, which allows for the conversion of global-scale seemingly microscopic concentration values (like parts per million) into absolute quantities, enabling further analysis of concentration changes.

Greenhouse Gas Emissions

Understanding greenhouse gas emissions involves quantifying the amount of gases, such as carbon dioxide, released into the atmosphere from various sources like fossil fuel combustion. This concept is crucial for assessing the environmental impact and potential contributions to climate change, as even small changes in atmospheric CO2 concentrations can significantly affect the Earth’s energy balance.

Stoichiometry of Combustion Reactions

This concept involves using balanced chemical equations to determine the quantitative relationships between reactants and products in a combustion reaction, such as the reaction of a hydrocarbon like octane with oxygen to produce carbon dioxide and water. It is essential for calculating the amount of carbon dioxide produced from a known quantity of fuel by accounting for the moles of reactants and products, and then converting to mass using the molecular weight of CO2.

Transcript

00:01 In this question we want to determine the percentage increase and we're going to determine this using this formula that is the percentage increase is equal to the parts per million increase divided by the parts per million initial multiplied by a hundred over one.

00:21 So looking at this formula all we have to do here is to determine our changes in concentration and would multiply by a hundred after looking at their ratio to determine the percentage.

00:32 Percentage increase.

00:34 So for us to do this, the first step that we're going to do is to calculate the amount of co2 from 3 .5 grams, 3 .5 times 10 to the power 12 kages of octane.

00:44 So the reaction is c8 h18 plus o2 to produce co2 and h2o.

00:55 So if we are to balance this out, this is going to be 16 and we're going to have 18 moles of h2o.

01:02 2 moles of octane and 2 5 moles of o2 so what we can do here is to convert rather if before we do the conversions what we have to look at here is if we are to compare the octane against the co2 we can tell that the ratio the mole ratio is 2 is 2 16 which is 1 is 2 8 so if we determine the actual number of moles of octane we can get the corresponding number of moles of co2 by looking at this ratio.

01:42 Now the number of moles of a substance, we know number of moles is equal to mass divided by the molar mass.

01:50 So right now we want to determine the number of moles of co2 and this is equal to the mass divided by the mr of co2.

02:01 Another way to do this is to look at the number of moles of octane, and we look at how they are relating with the number of moles of co2, number of moles of co2.

02:15 So to determine the number of moles of co2, we have to multiply this by 8, since these are in the ratio of 1 is to 8.

02:23 So all we can do right now is to just calculate the number of moles of octane and multiply that by 8 to determine the number of moles of co2.

02:32 So looking at this, the number of moles of octane, we're still using this main form.

02:36 Formula that is the number of moles rather let's say the number of moles of co2 this is going to be 8 multiplied by the number of moles of octane the mass of octane that we have we have 3 .5 times 10 to the power 12 cages and we have to multiply by 10 to the power 3 to convert this into claims because the molar units the molar mass units they are given in grams per more so now that we have the mass in grams we can divide by the molar mass of octane which is 114 .23.

03:11 Here we are going to get the number of moles of co2 and these are 2 .45 multiplied by 10 to the power 14 moles of co2.

03:21 So to get the parts per million in volume we need to convert the number of moles of co2 to the volume and for us to do that we can assume ideal gas behavior.

03:34 If we assume ideal gas behavior we have pv being equal to nrt.

03:40 Now using this formula for us to determine the volume v, this is going to be equal to nrt divided by the pressure.

03:47 The number of moles you've already calculated and these are 2 .45 multiplied by 10 to the power 1 4, multiplied by an r, 0 .08206 multiplied by the temperature of 275, divided by the pressure which is in atmosphere 0 .5.

04:08 So the volume here is going to be 1 .1 times 10 to the power 16 liters of co2...

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