Question

Assume that limestone, \(\mathrm{CaCO}_{3}\), is used to remove \(90 . \%\) of the sulfur from 4.0 metric tons of coal containing \(2.0 \% \mathrm{~S} .\) The product is \(\mathrm{CaSO}_{4}\) $$\mathrm{CaCO}_{3}(\mathrm{~s})+\mathrm{SO}_{3}(\mathrm{~g}) \longrightarrow \mathrm{CaSO}_{4}(\mathrm{~s})+\mathrm{CO}_{2}(\mathrm{~g})$$ Calculate the mass of limestone required. Express your answer in metric tons.

Short answer

The mass of limestone required is approximately 0.225 metric tons.

Step-by-step solution

Determine Sulfur in Coal

Calculate the amount of sulfur in 4.0 metric tons of coal. Since the coal contains 2.0% sulfur, we find: \( \text{Sulfur mass} = 4.0 \text{ metric tons} \times 0.02 = 0.08 \text{ metric tons.} \)

Calculate Sulfur Removed

Since 90% of the sulfur is removed, calculate the amount of sulfur that is removed: \( \text{Removed sulfur} = 0.08 \times 0.90 = 0.072 \text{ metric tons.} \)

Moles of Sulfur Removed

Convert the mass of sulfur removed to moles. The molar mass of sulfur (S) is approximately 32.07 g/mol. Convert metric tons to grams: \( 0.072 \text{ metric tons} \times 10^6 = 72000 \text{ g.} \)\[ \text{Moles of S} = \frac{72000}{32.07} \approx 2245.06 \text{ moles.} \]

Moles of Limestone Required

From the balanced chemical equation, 1 mole of \( \mathrm{CaCO}_{3} \) reacts with 1 mole of \( \mathrm{SO}_{3} \). Thus, the moles of limestone needed are equal to the moles of sulfur removed: 2245.06 moles.

Mass of Limestone Required

Calculate the mass of limestone required using its molar mass \( \text{(CaCO}_3)\) which is approximately 100.09 g/mol:\[ \text{Mass of } \mathrm{CaCO}_{3} = 2245.06 \text{ moles} \times 100.09 \text{ g/mol} \approx 224960.8 \text{ g.} \]Convert grams to metric tons: \( 224960.8 \text{ g} \div 10^6 = 0.225 \text{ metric tons.} \)

Key concepts

Chemical reactions

Chemical reactions are processes in which substances, known as reactants, transform into different substances, called products. They involve the breaking and forming of chemical bonds, leading to a rearrangement of atoms. In our exercise, we observe a classic chemical reaction: limestone ( CaCO_{3} ) reacting with sulfur trioxide ( SO_{3} ) to form calcium sulfate ( CaSO_{4} ) and carbon dioxide ( CO_{2} ).

• The balanced equation demonstrates stoichiometry, indicating the ratio of reactants to products.
• Balanced reactions ensure that the number of atoms for each element is the same on both sides of the equation.
• Stoichiometric coefficients provide important ratio information that helps in calculating amounts of reactants or products.

Understanding this reaction is crucial in industrial applications, like sulfur removal in coal combustion, where specific reactants are needed to produce desired products efficiently.

Limestone

Limestone is a naturally occurring mineral, primarily composed of calcium carbonate ( CaCO_{3} ). It is an abundant rock widely used in construction and industrial processes. In this particular exercise, limestone serves an essential role in a chemical reaction for sulfur removal.

• Limestone's chemical properties are leveraged for its reactivity with sulfur-related compounds.
• In this process, it reacts with sulfur trioxide to form gypsum, CaSO_{4} , a useful byproduct.
• Environmental applications include reducing acid rain by removing sulfur pollutants.

This transformation of limestone contributes to a reduction in atmospheric pollutants, showcasing its role in promoting environmental sustainability.

Sulfur removal

Sulfur removal is a critical process in preventing pollution and protecting the environment. This exercise illustrates how limestone can effectively remove sulfur from coal combustion emissions.

• Sulfur, often present in coal as sulfur compounds, forms sulfur dioxide during combustion.
• If sulfur is not removed, it contributes to acid rain and respiratory problems.
• By reacting with limestone, sulfur is converted into stable calcium sulfate, which minimizes harmful emissions.

The reaction helps in ensuring cleaner air by reducing sulfur oxides, benefiting both the ecosystem and human health.

Coal combustion

Coal combustion is the process of burning coal to produce energy. Despite its efficiency, it can result in the emission of pollutants, such as sulfur dioxide. This exercise involves the removal of sulfur resulting from coal combustion through a chemical reaction.

• Combustion turns coal's chemical energy into thermal energy for electricity generation.
• This process releases sulfur dioxide, contributing to environmental issues.
• Using processes like the one in this exercise, emissions are controlled, reducing the environmental impact.

Understanding coal combustion's environmental challenges still highlights the need for developing cleaner energy sources and improving current emission reduction technologies.

Molar mass calculation

Molar mass calculation is a fundamental step in stoichiometry, crucial for converting between mass and moles in chemical equations. In this exercise, determining the molar mass of substances like sulfur and limestone is key to finding how much limestone is needed.

• Molar mass is calculated by summing the atomic masses of all atoms in a molecule.
• It allows for the conversion from mass (in grams or metric tons) to moles, using the formula: \[\text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass}}\]
• For example, the molar mass of sulfur is approximately 32.07 g/mol, and for limestone (CaCO_{3}) it's around 100.09 g/mol.

This calculation is essential for ensuring precise and effective chemical reactions, crucial in industrial applications like emission control.