Carbon dioxide in air can be removed by an aqueous metal hydroxide solution such as \(\mathrm{LiOH}\) and \(\mathrm{Ba}(\mathrm{OH})_{2} .\) (a) Write equations for the reactions. (Carbon dioxide reacts with water to form carbonic acid.) (b) Calculate the mass of \(\mathrm{CO}_{2}\) that can be removed by \(5.00 \times 10^{2} \mathrm{~mL}\) of a \(0.800 \mathrm{M} \mathrm{LiOH}\) and a \(0.800 M \mathrm{Ba}(\mathrm{OH})_{2}\) solution. (c) Which solution would you choose for use in a space capsule and which for use in a submarine?

Understanding balanced chemical reactions is fundamental in chemistry, especially when dealing with carbon dioxide removal. It's essential because it ensures the law of conservation of mass is respected, meaning matter is neither created nor destroyed in a chemical reaction. For the reaction of carbon dioxide with metal hydroxides, we can examine the two provided reactions:

For lithium hydroxide (), the reaction with carbon dioxide () yields lithium carbonate () and water (), balanced as follows: (1) . For barium hydroxide (), the balanced reaction with carbon dioxide is: (2) . In the first equation, it's evident that for every molecule of carbon dioxide, two molecules of lithium hydroxide are required, while the second reaction showcases a one-to-one ratio between carbon dioxide and barium hydroxide. Balancing these equations correctly is crucial for the subsequent steps of stoichiometric calculations.

Molarity is a measure of the concentration of a solute in a solution, expressed as moles per liter. It is used in various calculations related to solutions and plays a critical role in chemistry, especially when determining how much reactant is available for a given reaction. For instance, the molarity of the solutions in the exercise is given as . To perform precise chemical calculations, you need to understand how to convert the volume of a solution into the number of moles of solute it contains. This conversion is straightforward: (moles of solute) = (volume of solution in liters) × (molarity of the solution). With the provided volume of , you calculate the moles of the solute ( or ) by multiplying by the molarity, allowing us to proceed with stoichiometric calculations. Grasping molarity and solution calculations is essential for mastering chemistry.

Stoichiometry is the tool that lets us quantify the relationship between reactants and products in a chemical reaction. It bridges the concepts of balanced reactions and molarity by using the mole ratio from the balanced equations to relate the amounts of each substance involved. In the case of carbon dioxide removal, stoichiometry allows us to predict the amount of carbon dioxide that can be removed given a certain amount of hydroxide solution.

From the balanced equations, we extract the stoichiometric coefficients and relate them to the moles calculated from the molarity. Then, by using the molar mass of carbon dioxide (), we can determine the mass of removed. It's the nuances of stoichiometry—understanding mole-to-mole conversions and the practical use of molar masses—that ensure precision in chemistry. Accurately applying stoichiometry can mean the difference between theoretical and real-world expectations, ensuring efficiency in processes such as carbon dioxide removal in controlled environments like space capsules or submarines.