Problem 13 - Chemistry and Chemical Reactivity

Question

Sulfur dioxide, a pollutant produced by burning coal and oil in power plants, can be removed by reaction with calcium carbonate. \(2 \mathrm{SO}_{2}(\mathrm{g})+2 \mathrm{CaCO}_{3}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CaSO}_{4}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g})\) (a) What mass of \(\mathrm{CaCO}_{3}\) is required to remove \(155 \mathrm{g}\) of \(\mathrm{SO}_{2} ?\) (b) What mass of \(\mathrm{CaSO}_{4}\) is formed when \(155 \mathrm{g}\) of \(\mathrm{SO}_{2}\) is consumed completely?

Step-by-Step Solution

Answer

242.22 g of \(\mathrm{CaCO}_3\) is required. 329.48 g of \(\mathrm{CaSO}_4\) is formed.

Step 1: Calculate moles of SO2

First, calculate the number of moles of \(\mathrm{SO}_2\) using its molar mass. The molar mass of \(\mathrm{SO}_2\) is 64.07 g/mol. The formula for moles is \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). Thus, \(\text{moles of } \mathrm{SO}_2 = \frac{155\, \text{g}}{64.07\, \text{g/mol}} = 2.42\, \text{mol}\).

Step 2: Use Stoichiometry to Find Moles of CaCO3

According to the balanced chemical equation, 2 moles of \(\mathrm{SO}_2\) react with 2 moles of \(\mathrm{CaCO}_3\). Therefore, the moles of \(\mathrm{CaCO}_3\) required are equal to the moles of \(\mathrm{SO}_2\). Thus, \(2.42\, \text{mol of } \mathrm{CaCO}_3\) are needed.

Step 3: Calculate Mass of CaCO3 Required

The molar mass of \(\mathrm{CaCO}_3\) is 100.09 g/mol. Multiply the moles of \(\mathrm{CaCO}_3\) by its molar mass to find the required mass: \(2.42 \text{ mol} \times 100.09 \text{ g/mol} = 242.22 \text{ g of } \mathrm{CaCO}_3\).

Step 4: Use Stoichiometry to Find Moles of CaSO4

From the balanced equation, 2 moles of \(\mathrm{SO}_2\) produce 2 moles of \(\mathrm{CaSO}_4\). Therefore, the moles of \(\mathrm{CaSO}_4\) formed are equal to the moles of \(\mathrm{SO}_2\) consumed, which is \(2.42\, \text{mol}\).

Step 5: Calculate Mass of CaSO4 Formed

The molar mass of \(\mathrm{CaSO}_4\) is 136.14 g/mol. Multiply the moles of \(\mathrm{CaSO}_4\) by its molar mass to find the mass formed: \(2.42 \text{ mol} \times 136.14 \text{ g/mol} = 329.48 \text{ g of } \mathrm{CaSO}_4\).

Key Concepts

Chemical Reactions

A chemical reaction involves a process where reactants are transformed into products. In the case of sulfur dioxide pollution control, sulfur dioxide gas (\(\text{SO}_2\)) reacts with calcium carbonate (\(\text{CaCO}_3\)), a solid, in the presence of oxygen (\(\text{O}_2\)) to form calcium sulfate (\(\text{CaSO}_4\)) and carbon dioxide (\(\text{CO}_2\)).

• Reactants: These are the starting materials, here being \(\text{SO}_2\), \(\text{CaCO}_3\), and \(\text{O}_2\).
• Products: These are the substances formed as a result of the reaction, in this case, \(\text{CaSO}_4\) and \(\text{CO}_2\).

Understanding this transformation allows us to predict the amounts of reactants needed, as well as the quantities of products formed. This is crucial in controlling sulfur dioxide emissions.

Molar Mass

Molar mass is the mass of one mole of any given substance. It allows for the conversion between mass and moles, facilitating stoichiometric calculations. Each element in a compound contributes to its molar mass, which is expressed in grams per mole (g/mol). For instance:

• The molar mass of \(\text{SO}_2\) is calculated from the atomic masses of sulfur (approximately 32.07 g/mol) and oxygen (approximately 16.00 g/mol).
• The molar mass of \(\text{CaCO}_3\) involves calcium, carbon, and three oxygen atoms.

Using molar mass:1. To find moles of \(\text{SO}_2\), divide the mass by its molar mass: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).2. Moles can then be applied in stoichiometric calculations to determine quantities of other reactants or products.

Sulfur Dioxide Pollution

Sulfur dioxide (\(\text{SO}_2\)) is a significant air pollutant, primarily released through burning fossil fuels such as coal and oil. When released into the atmosphere, \(\text{SO}_2\) contributes to environmental issues like acid rain and respiratory problems in humans. Strategies to mitigate sulfur dioxide pollution include:

• Chemical reactions, such as the one with \(\text{CaCO}_3\), to remove \(\text{SO}_2\) before it escapes into the atmosphere.
• Scrubber systems in industrial plants to clean flue gases.

These methods convert \(\text{SO}_2\) into less harmful substances, aiding in the reduction of the pollutant's impact on the environment.

Balancing Chemical Equations

Balancing chemical equations is crucial for describing chemical reactions accurately. Each chemical equation must have the same number of each type of atom on both sides of the equation. This principle stems from the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.When balancing equations:

• Identify the number of atoms of each element on both sides of the reaction.
• Add coefficients to balance each element.

For example, in the reaction between \(\text{SO}_2\) and \(\text{CaCO}_3\), coefficients are added to ensure that gas, solid reactants, and resultant products are in perfect harmony. This ensures that calculations for the amounts of substances involved in the reaction, such as \(\text{CaCO}_3\) and \(\text{CaSO}_4\), are precise and reliable.