Taking the mass of the atmosphere to be 6.0E15 metric tons, what mass of carbon must
be burned in order to increase the average carbon dioxide level in the atmosphere
by 110ppm by volume (in metric tons)?
To calculate the mass of carbon that must be burned to increase the average carbon dioxide level in the atmosphere by 110 parts per million (ppm) by volume, we need to consider the molecular ratio of carbon dioxide (CO2).
1. First, we need to calculate the total volume of the atmosphere. Given the mass of the atmosphere is 6.0E15 metric tons, we need to convert it to volume.
To do this, we need to know the density of the atmosphere. Assuming a density of 1.225 kg/m^3, we can calculate the volume using the formula:
Volume = Mass / Density
Converting the mass to kilograms: 6.0E15 × 10^6 metric tons = 6.0E15 × 10^9 kilograms
Volume = 6.0E15 × 10^9 / 1.225 = 4.898E24 m^3
2. Next, we need to calculate the initial mass of carbon dioxide (CO2) in the atmosphere before the increase. Given a 1 ppm volume ratio of CO2 to the atmosphere corresponds to 1.96 Gt (gigatons), we can calculate the initial mass of CO2 as follows:
Initial CO2 Mass = 110 ppm × 1.96 Gt
Converting ppm to a fraction: 110 ppm = 110/1,000,000 = 0.00011
Initial CO2 Mass = 0.00011 × 1.96 Gt = 0.0002156 Gt
Converting gigatons to metric tons: 0.0002156 Gt × 10^9 = 215.6 metric tons
3. Finally, we can calculate the mass of carbon that must be burned to increase the CO2 level by 110 ppm. Since each CO2 molecule consists of 1 carbon atom and 2 oxygen atoms, we can determine the mass of carbon needed using the molecular mass ratio:
Molecular mass of CO2 = 12.01 g/mol (carbon) + 2 × 16.00 g/mol (oxygen) = 44.01 g/mol
For simplicity, we'll convert the molecular mass to metric tons by dividing by 10^6:
Molar mass of carbon = 12.01 g/mol / 10^6 = 1.201E-5 metric tons/mol
Now, we can calculate the mass of carbon required:
Mass of Carbon = Initial CO2 Mass / (Molar mass of carbon / Molecular mass of CO2)
Mass of Carbon = 215.6 metric tons / (1.201E-5 metric tons/mol / 44.01 g/mol)
Converting metric tons to kilograms: 215.6 × 10^3 kg
Mass of Carbon = 215.6 × 10^3 kg / (1.201E-5 × 44.01 × 10^-3 kg/mol)
Calculating: Mass of Carbon ≈ 4.677E12 kg
Therefore, the mass of carbon that must be burned to increase the average carbon dioxide level in the atmosphere by 110 ppm by volume is approximately 4.677 trillion kilograms.