Question

What volume of \(\mathrm{CO}_{2}\) measured at STP is produced when \(27.5 \mathrm{g}\) of \(\mathrm{CaCO}_{3}\) is decomposed? $$ \mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$

Short answer

The volume of CO₂ produced when 27.5 g of CaCO₃ is decomposed at STP is approximately 6.16 L.

Step-by-step solution

Calculate the moles of CaCO₃.

First, we need to convert the mass of CaCO₃ into moles. In order to do this, we will find the molar mass of CaCO₃. The molar mass of Ca is 40.08 g/mol, C is 12.01 g/mol, and O is 16.00 g/mol. Molar mass of CaCO₃ = Ca + C + 3 * O = 40.08 + 12.01 + (3 * 16.00) = 100.09 g/mol Now we can convert the mass of 27.5 g CaCO₃ into moles: Moles of CaCO₃ = mass / molar mass = 27.5 g / 100.09 g/mol ≈ 0.275 moles

Determine the moles of CO₂ produced.

According to the balanced reaction, 1 mole of CaCO₃ produces 1 mole of CO₂. So, the moles of CO₂ produced will be equal to the moles of CaCO₃. Moles of CO₂ = 0.275 moles

Calculate the volume of CO₂ at STP.

At STP (Standard Temperature and Pressure: 0°C and 1 atm), 1 mole of any gas occupies 22.4 liters. So, the volume of CO₂ produced at STP can be calculated using the following formula: Volume of CO₂ = moles of CO₂ * volume occupied by 1 mole of CO₂ at STP Volume of CO₂ = 0.275 moles * 22.4 L/mol ≈ 6.16 L So, the volume of CO₂ produced when 27.5 g of CaCO₃ is decomposed at STP is approximately 6.16 L.

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is crucial when solving chemistry problems involving stoichiometry and reactions. The molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms present in a molecule.

For instance, the molar mass of calcium carbonate (CaCO₃) is found by adding the molar masses of calcium (Ca), carbon (C), and oxygen (O). Since (CaCO₃) includes one atom of calcium, one of carbon, and three of oxygen, the calculation becomes a simple addition: 40.08 g/mol (Ca) + 12.01 g/mol (C) + 3 × 16.00 g/mol (O), resulting in 100.09 g/mol for (CaCO₃). This step is fundamental in stoichiometry as it enables us to convert grams to moles, which is a necessary conversion when dealing with chemical reactions.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the substances as they participate in various chemical reactions. It involves using balanced chemical equations to calculate the quantities of reactants and products.

In the example, stoichiometry is exemplified by the decomposition of calcium carbonate into calcium oxide and carbon dioxide. To predict the amount of carbon dioxide produced from a given mass of calcium carbonate, one must first convert the mass of calcium carbonate to moles using the molar mass. Then, the stoichiometry of the chemical equation (CaCO₃ → CaO + CO₂) is used to understand that each mole of calcium carbonate yields one mole of carbon dioxide upon decomposition. This direct mole-to-mole relationship simplifies the stoichiometric calculation and allows us to swiftly determine the moles of CO₂ produced.

Gas Laws

The behavior of gases is governed by gas laws which are a set of generalized principles that predict how gases will respond to changes in temperature, pressure, and volume. The gas laws are vital for solving problems involving gases, as seen when calculating the volume of a gas produced in a chemical reaction.

At standard temperature and pressure (STP), defined as 0°C (273 K) and 1 atm, the volume occupied by one mole of any gas is 22.4 liters according to the ideal gas law. This is a simplification because real gases don't always behave like ideal gases; however, it is close enough for many calculations, including molar volume calculations at STP.

By knowing the moles of CO₂ produced and the volume one mole occupies at STP, the total volume of CO₂ can easily be calculated. This particular aspect of the gas laws allows students to connect the dots between the amount of substance (in moles) produced or consumed in a reaction and the physical space (in liters) that the gas will occupy under standard conditions.