Problem 32 - Chemistry: An Atoms-Focused Approach

Question

Most of the \(\mathrm{CO}_{2}\) emitted by industrial sources comes from the combustion of fossil fuels, but some is also produced by cement manufacturing and the conversion of limestone \(\left(\mathrm{CaCO}_{3}\right)\) to lime \((\mathrm{CaO}):\) $$\mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$ How many tons of \(\mathrm{CO}_{2}\) are produced per ton of lime?

Step-by-Step Solution

Answer

Answer: For every ton of lime (CaO) produced, 0.7860 tons of CO2 are emitted.

Step 1: Write down the balanced chemical equation

The given balanced chemical equation is: $$\mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$

Step 2: Calculate the molar masses of the involved substances

We need the molar masses of CaCO3, CaO, and CO2. Molar mass of CaCO3: Ca(40.08) + C(12.01) + 3O(16.00) = 100.09 g/mol Molar mass of CaO: Ca(40.08) + O(16.00) = 56.08 g/mol Molar mass of CO2: C(12.01) + 2O(16.00) = 44.01 g/mol

Step 3: Set up a conversion factor from tons of lime to tons of CO2

Since from the balanced chemical equation we see that 1 mol of CaCO3 produces 1 mol of CO2, we can set up the conversion factor as follows: $$\frac{\text{Moles of CO}_{2}}{\text{Moles of CaCO}_{3}} = \frac{44.01 \,\text{g/mol}}{100.09\, \text{g/mol}}$$

Step 4: Convert g/mol to tons/mol

We will convert the masses in our conversion factor to tons to make our final calculation easier: $$\frac{\text{Moles of CO}_{2}}{\text{Moles of CaCO}_{3}} = \frac{44.01\, \text{g/mol} \times \frac{1\, \text{ton}}{10^6\, \text{g}}}{100.09\, \text{g/mol} \times \frac{1\, \text{ton}}{10^6\, \text{g}}}$$

Step 5: Calculate the tons of CO2 produced per ton of CaCO3

Now, with our conversion factor set in tons, we can solve for the tons of CO2 produced per ton of CaCO3: $$\frac{\text{Tons of CO}_{2}}{\text{Tons of CaCO}_{3}} = \frac{44.01\, \text{ton/mol}}{100.09\, \text{ton/mol}} = 0.4395$$

Step 6: Multiply by the conversion from CaCO3 to CaO

Lastly, we have to take into account that 1 mol of CaCO3 corresponds to 1 mol of CaO, thus: $$\frac{\text{Tons of CO}_{2}}{\text{Tons of CaO}} = 0.4395 \times \frac{\text{Tons of CaCO}_{3}}{\text{Tons of CaO}} = 0.4395 \times \frac{100.09\, \text{ton/mol}}{56.08\, \text{ton/mol}} = 0.7860$$

Step 7: Conclusion

Therefore, for every ton of lime (CaO) produced, 0.7860 tons of CO2 are emitted.

Key Concepts

Molar Mass Calculation

Molar mass calculation is a fundamental part of understanding chemical reactions. It involves determining the mass of one mole of a given substance. To calculate the molar mass, you simply add up the masses of each atom in a compound while considering their respective quantities. For example, in limestone which is chemically known as calcium carbonate (CaCO₃), you need to consider the masses of calcium (Ca), carbon (C), and three oxygen atoms (O).

• The atomic mass of calcium is approximately 40.08 g/mol.
• The atomic mass of carbon is around 12.01 g/mol.
• Each oxygen atom is approximately 16.00 g/mol, and you multiply this by 3 since there are three oxygen atoms in the compound.

Thus, the molar mass of CaCO₃ sums up to 100.09 g/mol. This value is crucial because it helps in converting quantities between moles and grams, as seen in our exercise solution. Understanding and correctly calculating molar mass allows us to accurately determine material requirements and emissions in chemical reactions.

Limestone Decomposition

Limestone decomposition is an important chemical process, especially in industries like cement manufacturing. The chemical formula for limestone is CaCO₃ (calcium carbonate). When it decomposes, it breaks down into lime (CaO) and carbon dioxide (CO₂). This reaction can be simplified as follows:\[ \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g)\]This equation shows that from one mole of limestone, one mole of lime and one mole of carbon dioxide are generated. Further, the decomposition requires heat, often achieved in kilns in industrial settings. This reaction is pivotal in the cement industry to produce lime, which is a key component for cement, and it also contributes to CO₂ emissions, making it an environmental concern. Understanding limestone decomposition not only assists in material planning but also helps in managing environmental impacts through better industrial practices.

Carbon Dioxide Emissions

Carbon dioxide emissions from chemical reactions are significant contributors to atmospheric pollution, especially in industrial processes. In the case of limestone decomposition in cement production, for every ton of CaO produced, approximately 0.786 tons of CO₂ are emitted. This is calculated by comparing the molar masses of CO₂ and the resulting lime to establish an emission factor per ton of product.
The creation of CO₂ in this process is unavoidable due to the inherent chemical reaction. However, understanding the magnitude of these emissions can drive innovation towards reducing the environmental footprint of industrial operations. This could involve implementing carbon capture and storage (CCS) technologies, improving energy efficiency, and using alternative raw materials. Understanding how chemical equations translate to real-world emissions is a vital step toward environmental sustainability.