Question

Upon heating, calcium carbonate $\left({\mathrm{CaCO}}_3\right)$ decomposes to calcium oxide $(\mathrm{CaO})$ and carbon dioxide $\left({\mathrm{CO}}_2\right)$ a. Determine the theoretical yield of ${\mathrm{CO}}_2$ if 235.0 $\mathrm{g}$ of ${\mathrm{CaCO}}_3$ is heated. b. What is the percent yield of ${\mathrm{CO}}_2$ if 97.5 $\mathrm{g}$ of ${\mathrm{CO}}_2$ is collected?

Short answer

a) The theoretical yield of CO2 is $103.3g$. b) The percent yield of CO2 is $94.4\mathrm{\%}$.

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation for the decomposition of calcium carbonate is: $$CaC{O}_3(s)\to CaO(s)+C{O}_2(g)$$

Convert the given mass of reactant (CaCO3) to moles

To perform stoichiometry calculations, we need to convert the mass of calcium carbonate (235.0 g) to moles using its molar mass (100.09 g/mol). We can do this as follows: moles of CaCO3 = mass of CaCO3 / molar mass of CaCO3 moles of CaCO3 = $\frac{235.0g}{100.09g/mol}=2.347mol$

Determine the mole ratio between the reactant (CaCO3) and the product (CO2)

From the balanced chemical equation, we can see that the mole ratio between CaCO3 and CO2 is 1:1. This means that one mole of CaCO3 will produce one mole of CO2.

Calculate the theoretical yield of CO2 in moles and then convert to grams

The theoretical yield of CO2 can be calculated using the mole ratio from the balanced chemical equation. Since 1 mole of CaCO3 produces 1 mole of CO2, we can write: moles of CO2 = moles of CaCO3 × (1 mol CO2 / 1 mol CaCO3) moles of CO2 = 2.347 mol × (1 mol CO2 / 1 mol CaCO3) = 2.347 mol CO2 Now, we need to convert the moles of CO2 to grams using its molar mass (44.01 g/mol): mass of CO2 = moles of CO2 × molar mass of CO2 mass of CO2 = 2.347 mol × 44.01 g/mol = 103.3 g So, the theoretical yield of CO2 is 103.3 g.

Calculate the percent yield

The percent yield is the actual yield (97.5 g) divided by the theoretical yield (103.3 g), multiplied by 100: percent yield = $\frac{actualyield}{theoreticalyield}\times 100$ percent yield = $\frac{97.5g}{103.3g}\times 100=94.4\mathrm{\%}$ The percent yield of CO2 is 94.4%. In summary: a) The theoretical yield of CO2 is 103.3 g. b) The percent yield of CO2 is 94.4%.

Key concepts

Theoretical Yield

Theoretical yield refers to the maximum amount of product that can be produced in a chemical reaction based on the amount of limiting reactant available. It's a vital concept in stoichiometry, helping predict the outcomes of chemical processes.

In the case of calcium carbonate decomposing, we use the balanced reaction and its stoichiometry to determine that for every mole of ${\mathrm{CaCO}}_3$ we would theoretically get a mole of ${\mathrm{CO}}_2$. By calculating the moles of the starting substance and applying the mole ratio from the balanced equation, we can predict the maximum amount of carbon dioxide produced. Knowing the theoretical yield is critical in industrial chemistry to optimize reactions and to compare against actual results.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, indicating what percentage of the theoretical yield was actually obtained.

It is calculated by taking the actual yield (the amount of product actually collected) and dividing it by the theoretical yield, then multiplying by 100 to get a percentage. In essence, it's a metric of how well the reaction proceeded according to plan. If the percent yield is less than 100%, it can be due to incomplete reactions, side reactions, loss of product during recovery, or measurement errors. In our calcium carbonate example, the percent yield tells us that 94.4% of the theoretical carbon dioxide was produced - this is quite efficient, indicating that the reaction went fairly well.

Chemical Reaction

A chemical reaction is a process in which one or more substances, the reactants, are converted to one or more different substances, known as the products. Chemical reactions are described by chemical equations, which give the substances involved and their quantities.

For instance, $CaC{O}_3(s)\to CaO(s)+C{O}_2(g)$ is the equation for the decomposition of calcium carbonate when heated. The substances on the left side of the arrow are the reactants, and the substances on the right are the products. The balanced equation also tells us the stoichiometry of the reaction, which is essential for calculations like determining theoretical and percent yields.

Mole Concept

The mole concept is fundamental to understanding chemical reactions quantitatively. It provides a way to measure quantities of substances based on the number of particles, like atoms or molecules, they contain.

One mole is defined as the amount of substance containing as many particles as there are atoms in 12 grams of carbon-12. This number, Avogadro's number, is approximately $6.022\times {10}^{23}$ particles per mole. In calculations, the mole concept allows chemists to convert between mass and number of particles (or moles). For example, to find out how much $C{O}_2$ can be produced from 235.0 grams of $CaC{O}_3$, we convert grams to moles using the substance's molar mass and then use stoichiometry to relate it to the product.