Problem 38 - Chemistry: An Atoms-Focused Approach

Question

Capturing \(\mathrm{CO}_{2}\) Carbon dioxide can be removed from a gas stream by reacting it with potassium carbonate in the presence of water: $$\mathrm{CO}_{2}(g)+\mathrm{K}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{KHCO}_{3}(s)$$ If a resting human exhales \(36 \mathrm{mg} \mathrm{CO}_{2}\) in one breath, then how much potassium carbonate would be required to capture it all?

Step-by-Step Solution

Answer

Answer: Approximately 0.113 grams of potassium carbonate are required to capture all the carbon dioxide exhaled in one breath by a resting human.

Step 1: Convert the mass of CO₂ to moles

To convert the mass of carbon dioxide to moles, we will use the molar mass of carbon dioxide, which is 44.01 g/mol. In one breath, a resting human exhales 36 mg of carbon dioxide which is equal to 0.036 g. Hence, moles of CO₂ = mass of CO₂ / molar mass of CO₂ moles of CO₂ = 0.036 g / 44.01 g/mol ≈ 8.18 × 10⁻⁴ mol

Step 2: Determine the stoichiometric ratio

From the balanced chemical equation, we can see that the stoichiometric ratio of \(\mathrm{CO}_{2}\) to \(\mathrm{K}_{2} \mathrm{CO}_{3}\) is 1:1. That means that one mole of carbon dioxide reacts with one mole of potassium carbonate.

Step 3: Calculate the amount of K₂CO₃ needed in moles

Since the stoichiometric ratio between the \(\mathrm{CO}_{2}\) and \(\mathrm{K}_{2} \mathrm{CO}_{3}\) is 1:1, we can directly use the moles of \(\mathrm{CO}_{2}\) to find the moles of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) needed. So, the moles of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) needed = moles of CO₂ ≈ 8.18 × 10⁻⁴ mol

Step 4: Convert the moles of K₂CO₃ to grams

To convert the moles of potassium carbonate to grams, we will use the molar mass of potassium carbonate, which is 138.205 g/mol. mass of K₂CO₃ = moles of K₂CO₃ × molar mass of K₂CO₃ mass of K₂CO₃ = 8.18 × 10⁻⁴ mol × 138.205 g/mol ≈ 0.113 g So, approximately 0.113 grams of potassium carbonate are required to capture all the carbon dioxide exhaled in one breath by a resting human.

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into different substances through the breaking and forming of bonds. In the carbon dioxide capture scenario, the chemical reaction is between carbon dioxide (\(\mathrm{CO}_{2}\)) with potassium carbonate (\(\mathrm{K}_{2} \mathrm{CO}_{3}\)) and water (\(\mathrm{H}_{2} \mathrm{O}\)). This reaction produces potassium bicarbonate (\(\mathrm{KHCO}_{3}\)).

A balanced chemical equation represents this reaction as follows:

\[ \mathrm{CO}_{2}(g) + \mathrm{K}_{2} \mathrm{CO}_{3}(s) + \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2\mathrm{KHCO}_{3}(s) \]

In the context of carbon capture, understanding the reactants and products helps in determining how effectively carbon dioxide can be removed from gas streams. This reaction illustrates the practical application of chemical reactions in reducing the concentration of \(\mathrm{CO}_{2}\), which is a significant greenhouse gas.

Stoichiometry

Stoichiometry is the section of chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It is often based on the principle of conservation of mass, where the mass of the reactants equals the mass of the products.

In a chemical equation, stoichiometric coefficients express the ratio of moles of each substance involved in the reaction. In the example of carbon capture:

• The balanced equation tells us that 1 mole of \(\mathrm{CO}_{2}\) reacts with 1 mole of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) to form 2 moles of \(\mathrm{KHCO}_{3}\).
• This 1:1 ratio is crucial for calculating how much \(\mathrm{K}_{2} \mathrm{CO}_{3}\) is needed to react with a certain amount of \(\mathrm{CO}_{2}\).

By understanding stoichiometry, we can precisely calculate the amounts of all substances involved to ensure the reaction proceeds efficiently.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is fundamental in converting between the mass of a compound and the number of moles.

In the carbon dioxide capture equation, knowing the molar mass of each component is essential to accurately perform conversions:

• The molar mass of \(\mathrm{CO}_{2}\) is 44.01 g/mol.
• For \(\mathrm{K}_{2} \mathrm{CO}_{3}\), the molar mass is 138.205 g/mol.

By converting 36 mg of \(\mathrm{CO}_{2}\) to grams (0.036 g), we use its molar mass to find the number of moles. This step is crucial in stoichiometric calculations to determine how much \(\mathrm{K}_{2} \mathrm{CO}_{3}\) is required for the reaction.

Gas Absorption

Gas absorption is a process that involves the capture and removal of gas molecules from a mixture by using a liquid or solid absorbent. In this context, carbon dioxide capture is achieved by absorption onto a solid, potassium carbonate.

The chemical absorption process integrates the concept of chemistry with physical gas removal techniques to efficiently capture \(\mathrm{CO}_{2}\) from gas streams. Potassium carbonate acts as the absorbent, reacting with \(\mathrm{CO}_{2}\) to form potassium bicarbonate, which stays within the system.

This method is particularly effective because it turns gaseous carbon dioxide into a different solid form, which can be easily managed. Understanding gas absorption is pivotal in creating practical solutions to tackle emissions of greenhouse gases and improve air purification processes.