Question

Alkali metal hydroxides are sometimes used to "serub" excess carbon dioxide from the air in closed spaces (such as submarines and spacecraft). For example, lithium hydroxide reacts with carbon dioxide according to the unbalanced chemical equation $$ \mathrm{LiOH}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{Li}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g) $$ Suppose a lithium hydroxide canister contains \(155 \mathrm{~g}\) of \(\mathrm{LiOH}(s)\). What mass of \(\mathrm{CO}_{2}(g)\) will the canister be able to absorb? If it is found that after 24 hours of use the canister has absorbed \(102 \mathrm{~g}\) of carbon dioxide, what percentage of its capacity has been reached?

Short answer

The canister of lithium hydroxide can absorb approximately 142.576 g of carbon dioxide. After 24 hours, 102 g of CO₂ has been absorbed, which corresponds to approximately 71.55% of its capacity.

Step-by-step solution

Balance the chemical equation

First, we balance the chemical equation to find the stoichiometric ratio between LiOH and CO₂. The balanced equation is: $$ 2\mathrm{LiOH}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{Li}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2}\mathrm{O}(g) $$

Determine the stoichiometric ratio

From the balanced equation, 2 moles of LiOH react with 1 mole of CO₂. We need to find the mass of CO₂ that reacts with 155g of LiOH. To do this, we will use the molar masses of LiOH and CO₂. Molar mass of LiOH = Molecular weight of Li + Molecular weight of O + Molecular weight of H Molar mass of LiOH = 6.939 g/mol + 15.999 g/mol + 1.008 g/mol = 23.946 g/mol Molar mass of CO₂ = Molecular weight of C + 2(Molecular weight of O) Molar mass of CO₂ = 12.011 g/mol + 2(15.999 g/mol) = 44.009 g/mol

Calculate the mass of CO₂

First, find the moles of LiOH in 155g of LiOH using the molar mass found in step 2. Moles of LiOH = Mass of LiOH / Molar Mass of LiOH Moles of LiOH = 155 g/23.946 g/mol ≈ 6.477 moles Since 2 moles of LiOH react with 1 mole of CO₂, we can calculate the moles of CO₂ with the stoichiometric ratio. Moles of CO₂ = 0.5 * Moles of LiOH = 0.5 * 6.477 = 3.2385 moles Finally, calculate the mass of CO₂ using the molar mass found in step 2. Mass of CO₂ = Moles of CO₂ * Molar Mass of CO₂ Mass of CO₂ = 3.2385 moles * 44.009 g/mol ≈ 142.576 g

Calculate the percentage of the capacity reached

The canister has absorbed 102g of CO₂ after 24 hours. Now, we will determine the percentage of the capacity reached. Percentage = (Mass of CO₂ absorbed / Total Mass of CO₂ the canister can absorb) * 100% Percentage = (102 g / 142.576 g) * 100% Percentage ≈ 71.55% Thus, after 24 hours of use, the canister has reached approximately 71.55% of its capacity to absorb CO₂.

Key concepts

Understanding Chemical Reactions

Chemical reactions are the heart of chemistry. They occur when substances interact to form new products. In the context of our exercise, lithium hydroxide (LiOH) reacts with carbon dioxide (CO2) to produce lithium carbonate (Li2CO3) and water (H2O). Understanding chemical reactions involves knowing the reactants, products, and the law of conservation of mass, which states that the total mass of reactants must equal the total mass of products. The reaction must be balanced, meaning the number of atoms for each element must be the same on both sides of the equation.

The Role of Molar Mass

Molar mass is a fundamental concept in stoichiometry and represents the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It's calculated by adding the atomic masses of each element found in a compound. In our exercise, the molar mass of LiOH is crucial to determining how much CO2 the LiOH can absorb, as it allows us to convert between mass in grams and amount in moles, connecting the macroscopic scale with the molecular scale.

Balancing Chemical Equations

When dealing with chemical reactions, it's important to balance the equation to adhere to the law of conservation of mass. Balancing involves adjusting the coefficients in front of substances in the reaction to ensure the same number of each type of atom on both sides. In the lithium hydroxide and carbon dioxide reaction, we balance by ensuring that there are two lithium (Li) atoms, two oxygen (O) atoms, and one carbon (C) atom on each side. This step sets the foundation for correct stoichiometric calculations.

Gas Absorption in Chemistry

Gas absorption is a process where one substance captures and contains another substance. In closed environments like submarines or spacecraft, alkali metal hydroxides are used to absorb CO2 from the air. The exercise demonstrates a practical application of chemical reactions and stoichiometry in removing excess CO2 to maintain a breathable atmosphere.

Alkali Metal Hydroxides in Reactions

Alkali metal hydroxides, such as lithium hydroxide (LiOH), are strong bases commonly used in various chemical processes, including gas absorption. They're highly reactive and readily form salts and water when reacting with acids, in this case, carbon dioxide, which behaves like an acidic oxide. Knowledge of the properties of alkali metal hydroxides is essential for predicting the outcomes of their reactions with other substances.

Stoichiometric Calculations for Practical Use

Stoichiometry is the quantitative relationship between the amounts of reactants used and products formed in a chemical reaction. It involves using the balanced equation to find ratios of moles of reactants and products. In the given problem, stoichiometric calculations enable us to determine the mass of CO2 that can be absorbed by a specific mass of LiOH. These calculations are not just theoretical but have real-world applications, such as determining the efficiency of a gas absorption system.