To determine which fuel contributes the least to global warming in terms of energy obtained per gram of carbon dioxide produced, we can calculate the energy obtained per gram of carbon dioxide produced for each fuel.
First, let's establish the equation for the combustion of each fuel:
1. For coal (carbon):
C + O2 → CO2
2. For natural gas (methane):
CH4 + 2O2 → CO2 + 2H2O
3. For petroleum (octane):
C8H18 + (12.5)O2 → 8CO2 + 9H2O
To calculate the energy obtained per gram of carbon dioxide produced, we need to consider the energy released during combustion and the molar mass of carbon dioxide.
For coal (carbon):
- Energy released during combustion of coal: 32 kJ/g
- Molar mass of carbon dioxide (CO2): 44 g/mol
We can convert the given energy per gram of carbon (32 kJ/g) to kJ/mol by using the molar mass of carbon (12 g/mol) and then the molar mass of carbon dioxide:
32 kJ/g * (1 mol/12 g) * (44 g/mol) = 117.33 kJ/mol
Therefore, for coal, the energy obtained per gram of carbon dioxide produced is 117.33 kJ/mol.
Now we can repeat this process for natural gas and petroleum:
For natural gas (CH4):
- Energy released during combustion of natural gas: 49 kJ/g
- Molar mass of carbon dioxide (CO2): 44 g/mol
49 kJ/g * (1 mol/16 g) * (44 g/mol) = 154 kJ/mol
Therefore, for natural gas, the energy obtained per gram of carbon dioxide produced is 154 kJ/mol.
For petroleum (C8H18):
- Energy released during combustion of petroleum: 48 kJ/g
- Molar mass of carbon dioxide (CO2): 44 g/mol
48 kJ/g * (1 mol/114 g) * (44 g/mol) = 17.19 kJ/mol
Therefore, for petroleum, the energy obtained per gram of carbon dioxide produced is 17.19 kJ/mol.
By comparing the values, we find that petroleum (C8H18) contributes the least to global warming in terms of energy obtained per gram of carbon dioxide produced.