Question

Calcium oxide can be used to "scrub" carbon dioxide from air. $$ \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s) $$ What mass of \(\mathrm{CO}_{2}\) could be absorbed by \(1.25 \mathrm{~g}\) of \(\mathrm{CaO}\) ? What volume would this \(\mathrm{CO}_{2}\) occupy at STP?

Short answer

The mass of CO2 that can be absorbed by 1.25 grams of CaO is 0.981 grams. The volume occupied by the CO2 at STP (Standard Temperature and Pressure) is 0.499 liters.

Step-by-step solution

Write down the given information and find the molar masses

We are given that we have 1.25 grams of CaO. First, we need to find the molar mass of CaO and CO2 to convert the mass of compounds into moles. Molar mass of CaO = Molar mass of Ca + Molar mass of O = 40.08 (Ca) + 16.00 (O) = 56.08 g/mol Molar mass of CO2 = Molar mass of C + 2x Molar mass of O = 12.01 (C) + 2 x 16.00 (O) = 44.01 g/mol Now, let's find the moles of CaO present and use the stoichiometry of the balanced chemical equation to find the moles of CO2.

Convert mass of CaO to moles

Using the molar mass of CaO, we can convert the mass of CaO into moles. Moles of CaO = \(\frac{1.25\text{ g}}{56.08\text{ g/mol}}\) = 0.0223 mol

Find the moles of CO2 using the stoichiometry of the balanced reaction

In the balanced chemical equation, the mole ratio of CaO to CO2 is 1:1. Therefore, the moles of CO2 absorbed by CaO will be equal to the moles of CaO. Moles of CO2 = Moles of CaO = 0.0223 mol

Convert moles of CO2 to mass

Now, we will convert moles of CO2 into mass using the molar mass of CO2. Mass of CO2 = Moles of CO2 x Molar mass of CO2 = 0.0223 mol x 44.01 g/mol = 0.981 g So, the mass of CO2 that can be absorbed by 1.25 grams of CaO is 0.981 grams.

Find the volume occupied by the CO2 at STP

We know that at STP (Standard Temperature and Pressure: 0°C or 273.15K and 1 atm), 1 mole of an ideal gas occupies 22.4 L. We have 0.0223 moles of CO2, so the volume of CO2 at STP can be calculated as follows: Volume of CO2 = Moles of CO2 x Volume occupied by 1 mole at STP = 0.0223 mol x 22.4 L/mol = 0.499 L Therefore, the volume occupied by CO2 at STP is 0.499 liters.

Key concepts

Understanding Chemical Reactions

At its core, a chemical reaction is a process where substances, known as reactants, transform into new substances, called products. It follows a specific stoichiometric ratio, which is based on the law of conservation of mass - the idea that matter cannot be created or destroyed in a chemical reaction. In our exercise, calcium oxide (CaO) reacts with carbon dioxide (CO₂) to form calcium carbonate (CaCO₃). This process, often used in scrubbing CO₂ from the air, showcases a one-to-one molar ratio. For students, visualizing reactions like this can be made simpler through balanced chemical equations, as shown in the exercise. It's crucial to understand that for every mole of CaO used, one mole of CO₂ is absorbed, providing a clear and quantifiable relationship between reactants and products.

When working with this concept, notice how the original problem directly applies the stoichiometric ratio, where the first step in any stoichiometric problem is to ensure you have a balanced equation. It confirms that in terms of moles, the amount of reactant used will determine the amount of product produced. This simple yet powerful understanding forms the basis of many quantitative analyses in chemistry.

The Role of Molar Mass in Stoichiometry

The concept of molar mass is a gateway to understanding the quantitative aspect of chemical reactions. It represents the mass of one mole of a substance and is typically expressed in grams per mole (g/mol). Knowing the molar mass allows chemists to convert between mass and moles, which are essential when dealing with chemical quantities. For example, in the provided exercise, the molar masses of calcium oxide and carbon dioxide are calculated from the atomic masses of their respective elements, and these values are utilized to determine the mass of CO₂ that can be absorbed by a given amount of CaO.

Why is Molar Mass Important?

The molar mass acts as a conversion factor in stoichiometry. It makes the comparison of substances on a mole-to-mole basis possible, which is critical because chemical reactions occur according to mole ratios, not mass ratios. This understanding helps break down complex reactions into manageable calculations by allowing students to convert the mass of a substance to the amount of substance in moles, thereby enabling the use of stoichiometry to predict the outcomes of reactions quantitatively.

Standard Temperature and Pressure (STP) in Calculations

When it comes to gases, the conditions under which they are measured can significantly impact their volume. This brings us to the concept of Standard Temperature and Pressure (STP), which is a common reference point used in chemistry. At STP, defined as 0°C (273.15K) and 1 atmosphere of pressure, one mole of any ideal gas occupies 22.4 liters. This standardization facilitates the comparison and calculation of gas volumes across different reactions and conditions.

In our textbook exercise, once the mass of CO₂ generated is obtained, it's vital to determine what volume this gas would occupy at STP. This volume can be calculated by multiplying the moles of CO₂ by the volume that one mole of gas occupies at STP, yielding a precise and easily understood result. For students learning this concept, it's important to recognize that this standard serves as a simplifying assumption for solving problems involving gases, and it is crucial for predicting how much space a certain amount of gas will take up in the everyday laboratory or industrial conditions.