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What mass of lime, \(\mathrm{CaO},\) can be obtained by heating \(125 \mathrm{kg}\) of limestone that is \(95.0 \%\) by mass \(\mathrm{CaCO}_{3} ?\) $$\mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$

Short Answer

Expert verified
66.512 kg of lime (CaO) can be obtained.

Step by step solution

01

Calculate the Mass of Pure Calcium Carbonate

The limestone is not pure and contains only 95% calcium carbonate (CaCO₃). To find the mass of pure CaCO₃, calculate: \( \text{mass of CaCO₃} = 125 \text{ kg} \times 0.95 = 118.75 \text{ kg} \).
02

Convert Mass to Moles of Calcium Carbonate

We need to convert the mass of CaCO₃ to moles. The molar mass of CaCO₃ is 100.1 g/mol. First, convert the mass from kg to grams: \( 118.75 \text{ kg} = 118750 \text{ g} \). Then, calculate the moles: \( \text{moles of CaCO₃} = \frac{118750 \text{ g}}{100.1 \text{ g/mol}} \approx 1186.81 \text{ moles} \).
03

Use Stoichiometry to Find Moles of Calcium Oxide

According to the reaction \( \text{CaCO}_{3} \rightarrow \text{CaO} + \text{CO}_{2} \), 1 mole of CaCO₃ produces 1 mole of CaO. Therefore, the moles of CaO produced is equal to the moles of CaCO₃, which is 1186.81 moles.
04

Convert Moles of Calcium Oxide to Mass

To find the mass of CaO, use its molar mass of 56.08 g/mol. Calculate: \( \text{mass of CaO} = 1186.81 \text{ moles} \times 56.08 \text{ g/mol} \approx 66512 \text{ g} \). Convert grams to kilograms: \( 66512 \text{ g} = 66.512 \text{ kg} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Limestone Decomposition
Limestone is a common sedimentary rock primarily composed of calcium carbonate (\( \text{CaCO}_{3} \)). When limestone undergoes decomposition, it is subjected to high temperatures. This process of heating limestone is known as calcination, which results in the decomposition of \( \text{CaCO}_{3} \) into two new products: calcium oxide (\( \text{CaO} \)), commonly referred to as lime, and carbon dioxide (\( \text{CO}_{2} \)).
The thermal decomposition can be represented by the chemical equation:\[ \text{CaCO}_{3}(\text{s}) \rightarrow \text{CaO}(\text{s}) + \text{CO}_{2}(\text{g}) \]This reaction is crucial in various industrial processes, including the manufacture of cement and lime. It requires temperatures typically over 800°C. The reaction is endothermic, meaning it absorbs heat energy to proceed.
Understanding the decomposing process of limestone is not just about the reaction itself, but also understanding the conditions under which it occurs and its applications.
Calcium Carbonate
Calcium carbonate is an essential compound found in natural forms such as chalk, limestone, and marble. It is a white, odorless, and tasteless substance that has significant uses in industries like construction, pharmaceuticals, and even food production.
Calcium carbonate has the chemical formula \( \text{CaCO}_{3} \). In its pure form, it possesses a molar mass of approximately 100.1 g/mol.
  • As chalk, it is used as a blackboard chalk and in sports to prevent slipping.
  • In the medical field, it acts as a calcium supplement and an antacid to relieve heartburn, acid indigestion, and upset stomach.
  • In construction, it forms the primary ingredient of cement and lime.
In stoichiometric calculations involving calcium carbonate, it's important to realize its role in the equation. Here, we start from the known mass percentage to determine the amount of substance available for the reaction. The purity percentage is crucial in determining the effective mass that will participate in the stoichiometry of thermal decomposition.
Stoichiometric Calculations
Stoichiometric calculations play a fundamental role in chemistry. They are used to calculate the relative quantities of reactants and products in chemical reactions. When handling exercises like the decomposition of limestone, these calculations are integral in quantifying the expected amounts of products formed.
In the context of limestone decomposition, stoichiometry involves calculating how much calcium oxide (\( \text{CaO} \)) can be produced from a given mass of calcium carbonate (\( \text{CaCO}_{3} \)). The process starts with converting the mass of \( \text{CaCO}_{3} \) into moles using its molar mass:\[ \text{moles of } \text{CaCO}_{3} = \frac{\text{mass of } \text{CaCO}_{3}}{\text{molar mass}} \]For the equation \( \text{CaCO}_{3} \rightarrow \text{CaO} + \text{CO}_{2} \), the stoichiometry indicates a 1:1 mole ratio between \( \text{CaCO}_{3} \) and \( \text{CaO} \). This means the amount of moles of \( \text{CaCO}_{3} \) directly corresponds to the amount of \( \text{CaO} \) produced.Finally, we convert the moles of \( \text{CaO} \) back to mass using its molar mass:\[ \text{mass of } \text{CaO} = \text{moles of } \text{CaO} \times \text{molar mass of } \text{CaO} \]Mastering stoichiometric calculations ensures the ability to predict and quantify chemical reactions accurately.

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Most popular questions from this chapter

Potassium perchlorate is prepared by the following sequence of reactions: $$\mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{KCl}(\mathrm{aq})+\mathrm{KClO}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$$ $$\begin{aligned}3 \mathrm{KClO}(\mathrm{aq}) & \rightarrow 2 \mathrm{KCl}(\mathrm{aq})+\mathrm{KClO}_{3}(\mathrm{aq}) \\\4 \mathrm{KClO}_{3}(\mathrm{aq}) & \rightarrow 3 \mathrm{KClO}_{4}(\mathrm{aq})+\mathrm{KCl}(\mathrm{aq})\end{aligned}$$ What mass of \(\mathrm{Cl}_{2}(\mathrm{g})\) is required to produce \(234 \mathrm{kg}\) of \(\mathrm{KClO}_{4} ?\)

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