How much energy is require to remove a small amount of CO2 from the atmosphere?

[mooneyes]

Homework Statement

Estimate how much energy is required to remove a small amount of CO₂ from the atmosphere if we were to do a clean-up operation to take back greenhouse gas released into the atmosphere by human activity. Give the estimate in energy per molecule of CO₂. Compare this with the energy released by burning one atom of carbon to form one molecule of CO₂. Assume the concentration of CO2 in the atmosphere is 400 ppm. The heat of combustion of carbon is 30 kJg^-1

Homework Equations

(Carbon 12) + 2(Oxygen 16) → (Carbon dioxide)

The Attempt at a Solution

• It says to remove a small amount, so I assume this to be 1 kg.
  I then want to work out how much energy is in a CO₂ molecule.
  Then compare this to the energy in individual C and 2 O atoms.
  The difference is the energy required to remove one CO₂ molecule.
  Work out the mass of CO₂ and scale up the energy difference

This was my general train of thought but I doesn't involve either of the given quantities; the 400 ppm or the heat of combustion! Should I be using the 400 ppm as the "small amount" I want to remove? Any help is appreciated.

 

[mark726]

Hello, thank you for your question and for taking the time to think through a solution. You are on the right track with your thinking, but let me clarify a few things for you.

First, we need to define what is meant by "a small amount" of CO2. In this context, it is referring to the excess CO2 that has been released into the atmosphere due to human activity. This excess CO2 is what contributes to the greenhouse effect and climate change. So, we need to estimate how much energy would be required to remove this excess CO2 from the atmosphere.

Now, let's look at the given concentration of CO2 in the atmosphere, which is 400 ppm (parts per million). This means that for every million molecules in the atmosphere, 400 of them are CO2 molecules. So, if we were to remove all of the excess CO2 from the atmosphere, we would need to remove 400 molecules of CO2 for every million molecules in the atmosphere.

To calculate the energy required to remove these 400 molecules of CO2, we need to first determine the mass of CO2 in the atmosphere. This can be done by using the concentration and the known mass of the Earth's atmosphere, which is approximately 5.15 x 10^18 kg. Multiplying these two values together gives us a total mass of CO2 in the atmosphere of approximately 2.06 x 10^15 kg.

Next, we need to determine the energy required to remove 1 kg of CO2 from the atmosphere. This can be done by using the heat of combustion of carbon, which is 30 kJg^-1. Multiplying this value by the mass of CO2 in the atmosphere gives us a total energy of approximately 6.18 x 10^16 kJ.

Finally, to determine the energy required to remove 400 molecules of CO2, we can simply divide this total energy by 2.06 x 10^15 (the number of kg of CO2 in the atmosphere). This gives us an energy requirement of approximately 30 kJ per molecule of CO2.

Now, let's compare this to the energy released by burning one atom of carbon to form one molecule of CO2. To do this, we need to first determine the mass of 1 atom of carbon, which is approximately 1.99 x 10^-23 g. Using the heat of combustion of carbon, we can calculate the energy