Taking the mass of the atmosphere to be 4.6E15 metric tons, what mass of carbon must be burned in order to increase the average carbon dioxide level in the atmosphere by 130ppm by volume (in metric tons)?
To determine the mass of carbon that must be burned to increase the average carbon dioxide (CO2) level in the atmosphere by 130 parts per million (ppm) by volume, you will need to consider the following steps:
Step 1: Calculate the total volume of the atmosphere.
Given that the mass of the atmosphere is 4.6 x 10^15 metric tons, we need to convert this mass into a volume. To do this, we can use the average density of the Earth's atmosphere, which is about 1.225 kg/m^3. Since 1 metric ton is equal to 1000 kg, we have:
Mass of the atmosphere = 4.6 x 10^15 metric tons
= 4.6 x 10^18 kg (by converting metric tons to kg)
To find the volume of the atmosphere, we can use the formula:
Volume = Mass / Density
Volume = 4.6 x 10^18 kg / 1.225 kg/m^3
Step 2: Calculate the volume increase due to 130 ppm increase in CO2 concentration.
To determine the volume increase of CO2 required to achieve a 130 ppm increase in concentration, we need to calculate the volume of the atmosphere multiplied by 130 ppm. Assuming the volume remains constant when adding CO2, we have:
Volume increase = Volume of the atmosphere x (130 ppm / 1,000,000)
Step 3: Convert the volume increase to mass using the molar mass of CO2.
The molar mass of CO2 is approximately 44 grams/mole. To convert the volume increase into mass, we use the ideal gas law equation: PV = nRT. Since we are working with a constant volume, the equation becomes: P = nRT/V. Rearranging to solve for n (the number of moles), we have: n = PV/RT.
Step 4: Finally, convert moles to metric tons. Multiply the number of moles by the molar mass of CO2 and convert grams to metric tons.
By following these steps, you can calculate the mass of carbon that must be burned to increase the average carbon dioxide level in the atmosphere by 130 ppm by volume.