Question

If \(10.11 \mathrm{~g}\) of limestone decomposes by heat to give \(8.51 \mathrm{~g}\) of solid calcium oxide and carbon dioxide gas, what is the mass of carbon dioxide produced?

Short answer

1.60 g of carbon dioxide is produced.

Step-by-step solution

Identify the Initial Mass

The initial mass given in this problem is the mass of limestone, which is 10.11 g.

Calculate the Final Mass of Calcium Oxide

The problem states that after the decomposition of limestone, we have 8.51 g of solid calcium oxide formed.

Apply the Law of Conservation of Mass

According to the law of conservation of mass, the mass of reactants must equal the mass of products in a chemical reaction. Here, limestone decomposes into calcium oxide and carbon dioxide.

Set up the Equation for Mass Conservation

Let the mass of carbon dioxide produced be \( m_{CO_2} \). Based on the conservation of mass, we have:\[ 10.11 ext{ g limestone} = 8.51 ext{ g CaO} + m_{CO_2} \]

Solve for the Mass of Carbon Dioxide

Rearrange the equation to solve for the mass of carbon dioxide:\[ m_{CO_2} = 10.11 ext{ g} - 8.51 ext{ g} \] The calculation gives:\[ m_{CO_2} = 1.60 ext{ g} \]

Key concepts

Law of Conservation of Mass

The law of conservation of mass is a fundamental principle in chemistry. It states that mass cannot be created or destroyed in a chemical reaction. This means that the total mass of reactants before the reaction must equal the total mass of the products after the reaction. In our example, this principle is applied by balancing the mass of limestone, calcium oxide, and carbon dioxide. The limestone decomposes completely into 8.51 grams of calcium oxide and some carbon dioxide. By using the law of conservation of mass, we deduce the mass of the carbon dioxide by taking the difference between the initial and final masses. This ensures that the total mass before decomposition equals the total mass after decomposition.

Decomposition Reactions

Decomposition reactions are a type of chemical reaction where a single compound breaks down into two or more simpler substances. These reactions often require external conditions like heat or light to proceed. In the case of limestone, heating causes it to decompose into calcium oxide and carbon dioxide.
Limestone, primarily calcium carbonate (\( \text{CaCO}_3 \)) breaks down upon heating to form calcium oxide (\( \text{CaO} \)) and carbon dioxide (\( \text{CO}_2 \)). We can represent it as:

• \( \text{CaCO}_3 \to \text{CaO} + \text{CO}_2 \)

Understanding decomposition reactions is critical since they are used in various industrial processes, such as producing materials like cement from limestone.

Chemical Reactions

Chemical reactions involve the transformation of substances through breaking and forming bonds, resulting in the creation of new products. Each reaction is signified by a balanced equation illustrating the reactants turning into products through specific pathways.
In a chemical equation, reactants appear on the left, and products on the right, linked by an arrow indicating the direction of the transformation. In our exercise, the reaction is:

• \( \text{CaCO}_3 \to \text{CaO} + \text{CO}_2 \)

It's crucial that the number of atoms of each element is equal on both sides of the equation, adhering to the law of conservation of mass. This ensures that no atoms are lost or gained in the reaction itself, merely rearranged into different products.