Question

Lime, \(\mathrm{CaO},\) can be produced in two steps as shown in the equations below. If the percentage yield of the first step is \(83.5 \%\) and the percentage yield of the second step is \(71.4 \%\), what is the expected overall percentage yield for producing \(\mathrm{CaO}\) from \(\mathrm{CaCl}_{2} ?\) $$ \begin{aligned} \mathrm{CaCl}_{2}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CaCO}_{3}(s)+2 \mathrm{HCl}(a q) \\ \mathrm{CaCO}_{3}(s) \stackrel{\text { heat }}{\longrightarrow} \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \end{aligned} $$

Short answer

The expected overall percentage yield for producing CaO from CaCl2 is 59.609%.

Step-by-step solution

Calculate the overall yield for the first step

To find the overall yield after the first step, use the given percentage yield. If the percentage yield for the first step is 83.5%, this means that for every 100% of the expected amount of CaCO3, we only get 83.5% of it in reality. The yield can be expressed as a decimal (83.5% = 0.835) for further calculations.

Calculate the overall yield for the second step

Similarly, calculate the overall yield after the second step using the given percentage yield of 71.4%. Convert the percentage yield to a decimal (71.4% = 0.714) for further calculations. Only 71.4% of the CaCO3 obtained from the first step will be converted to CaO.

Determine the overall percentage yield

To find the expected overall percentage yield of CaO production from CaCl2, multiply the decimal yields of both steps. The overall yield is the product of the yields from the first and second steps. Hence, the overall percentage yield is 0.835 * 0.714 * 100 = 59.609%.

Key concepts

Chemical Reaction Yield

The yield of a chemical reaction is a measure of how much product is obtained compared to the maximum amount possible, known as the theoretical yield. In practical scenarios, not all reactions proceed to completion due to various reasons such as side reactions, incomplete reactions, or practical losses during the process. This is where the percentage yield comes into play. It is calculated by taking the actual yield from an experiment and dividing it by the theoretical yield, then multiplying by 100 to get a percentage.

The percentage yield is crucial for understanding the efficiency of a reaction, and it's represented by the following formula:
\[\begin{equation}\text{Percentage Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\end{equation}\]
For instance, in the provided exercise, the yields of two steps in a chemical process to produce lime are given, and they must be considered sequentially to calculate the overall yield of the process. Let's take a closer look:

• First Step Yield: This involves reacting \(\mathrm{CaCl}_{2}\) in aqueous solution with carbon dioxide and water to form \(\mathrm{CaCO}_{3}\) and hydrochloric acid. The percent yield is given as 83.5%, which means that only 83.5% of the \(\mathrm{CaCO}_{3}\) expected is actually formed.
• Second Step Yield: This involves heating the obtained \(\mathrm{CaCO}_{3}\) to decompose it into lime (\(\mathrm{CaO}\)) and carbon dioxide gas. The reaction has a 71.4% yield, meaning 71.4% of the \(\mathrm{CaCO}_{3}\) from the first step actually turns into \(\mathrm{CaO}\).

By understanding the concept of chemical reaction yield and its application in sequential steps, students can better grasp the real-world applicability and limitations of reactions in industrial and laboratory settings.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of moles, where all the atoms present in the reactants must be accounted for in the products. Stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given reaction.

To conduct stoichiometric calculations, you need to:

• Write a balanced chemical equation to ensure that the number of atoms for each element is the same on both sides of the reaction.
• Use the molar ratios derived from the coefficients of the balanced equation to determine the relationship between the amounts of reactants and products.

The exercise demonstrates the application of stoichiometry in sequential reactions to produce \(\mathrm{CaO}\). The stoichiometric coefficients in the given reactions are critical to understanding the molar ratios needed for calculating theoretical yields, which in turn are necessary for computing percentage yields. It’s important for students to be attentive to these stoichiometric relationships when performing yield calculations to ensure accuracy in their predictions.

Limiting Reagent

The limiting reagent in a chemical reaction is the substance that is completely consumed first and thus limits the amount of product that can be formed. It dictates the maximum amount of product possible (theoretical yield) and is determined by comparing the mole ratios of the reactants present to the mole ratios required by the balanced chemical equation.

In practice, when performing a reaction, one often starts with a known amount of reactants. The first step in finding the limiting reagent is to calculate the moles of each reactant. Next, use stoichiometry to determine which reactant will produce the least amount of product – this is your limiting reagent.

• If starting with \(\mathrm{CaCl}_{2}\), it might be the limiting reagent in the reaction towards \(\mathrm{CaCO}_{3}\), depending on the other reagents' molar quantities.
• Similarly, the initial amount of \(\mathrm{CaCO}_{3}\) will dictate the maximum amount of \(\mathrm{CaO}\) that can be formed in the second step.

Understanding which reagent is limiting is crucial for correct yield predictions and is particularly relevant in industry, where cost and efficiency optimization are key. The provided exercise assumes 100% theoretical yield for simplicity but in a real scenario, identifying the limiting reagent would be a critical part of yield calculation.