Question

A particular coal contains \(2.5 \%\) sulfur by mass. When this coal is burned at a power plant, the sulfur is con- verted into sulfur dioxide gas, which is a pollutant. To reduce sulfur dioxide emissions, calcium oxide (lime) is used. The sulfur dioxide reacts with calcium oxide to form solid calcium sulfite. (a) Write the balanced chemical equation for the reaction. (b) If the coal is burned in a power plant that uses 2000 tons of coal per day, what mass of calcium oxide is required daily to eliminate the sulfur dioxide? (c) How many grams of calcium sulfite are produced daily by this power plant?

Short answer

The balanced chemical equation for the reaction between sulfur dioxide and calcium oxide is: CaO + SO₂ → CaSO₃. To eliminate the sulfur dioxide, the power plant needs 43,750,000 g (43.75 tons) of calcium oxide per day. As a byproduct, 93,750,000 g (93.75 tons) of calcium sulfite is produced daily.

Step-by-step solution

Balanced Chemical Equation

First, we need to write the balanced chemical equation for the reaction between sulfur dioxide (SO₂) and calcium oxide (CaO). The product of the reaction is calcium sulfite (CaSO₃). The balanced chemical equation is: CaO + SO₂ → CaSO₃

Mass of Sulfur

Next, we should determine the mass of sulfur in the given amount of coal. The coal is burned in a power plant that uses 2000 tons (or 2000 * 1000 kg) of coal per day. The problem states that the coal contains 2.5% sulfur by mass. To find the mass of sulfur, we multiply the mass of coal by the mass percentage of sulfur: Mass of sulfur = (Mass of coal) * (Mass percentage of sulfur / 100) Mass of sulfur = (2000 * 1000 kg) * (2.5 / 100) = 50000 kg

Mass of Calcium Oxide

Now we need to determine the mass of calcium oxide (CaO) required to eliminate the sulfur dioxide. From the balanced chemical equation, 1 mole of CaO reacts with 1 mole of SO₂. First, we need to convert the mass of sulfur to moles of sulfur dioxide: Moles of SO₂ = (Mass of sulfur x 1000) / Molar mass of SO₂ Moles of SO₂ = (50000 x 1000) / 64 = 781250 moles (rounded to the nearest whole number) Since 1 mole of CaO reacts with 1 mole of SO₂, the moles of CaO required are equal to the moles of SO₂. The mass of calcium oxide can be calculated by multiplying the number of moles by the molar mass: Mass of calcium oxide = Moles of CaO x Molar mass of CaO Mass of calcium oxide = 781250 moles x 56 = 43750000 g

Mass of Calcium Sulfite

Finally, we need to calculate the mass of calcium sulfite (CaSO₃) produced daily. Since the equation is balanced, one mole of CaSO₃ is produced for each mole of SO₂ reacted. Moles of CaSO₃ = Moles of SO₂ = 781250 moles Now, we can calculate the mass of calcium sulfite: Mass of calcium sulfite = Moles of CaSO₃ x Molar mass of CaSO₃ Mass of calcium sulfite = 781250 moles x 120 = 93750000 g To summarize, the power plant needs 43,750,000 g (43.75 tons) of calcium oxide per day to eliminate the sulfur dioxide, and it will produce 93,750,000 g (93.75 tons) of calcium sulfite daily as a byproduct.

Key concepts

Balanced Chemical Equation

Understanding a balanced chemical equation is fundamental in analyzing a chemical reaction. It's an expression that represents the identities and quantities of substances involved. In a balanced equation, the number of atoms for each element and the total charge are the same on both sides of the reaction, adhering to the Law of Conservation of Mass.

Involving the reaction between sulfur dioxide and calcium oxide, the balanced chemical equation is: \[\text{CaO} + \text{SO}_2 \rightarrow \text{CaSO}_3\]. This equation tells us that one mole of calcium oxide reacts with one mole of sulfur dioxide to produce one mole of calcium sulfite, showcasing the stoichiometric relationship between reactants and products.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe. It allows for the quantification of substances involved in chemical reactions. One mole, approximately 6.022 \(\times\) 10\(^{23}\) entities (Avogadro's number), is the amount of a substance that contains as many particles as there are atoms in 12 grams of carbon-12.

By determining the mass of sulfur present in coal and converting it to moles, we can calculate the amount of reactant needed and product formed. For example, 50,000 kilograms of sulfur can be translated into moles of sulfur dioxide, using its molar mass (64 g/mol), to find the corresponding moles of calcium oxide and calcium sulfite in the reaction.

Chemical Reaction Quantification

Quantifying a chemical reaction involves calculations using mole ratios derived from a balanced chemical equation. It answers questions like 'How much of each reactant do you need?' or 'How much of a product is formed?'.

When a power plant burns coal containing sulfur, stoichiometric calculations reveal the mass of calcium oxide needed to eliminate sulfur dioxide emissions. By using mole-to-mass conversions and the balanced equation, we determine that 43,750,000 grams of calcium oxide must be used daily. Moreover, the stoichiometry allows us to figure out that the reaction would result in the production of 93,750,000 grams of calcium sulfite daily, managing the environmental impact by quantifying the required reactants and the resultant products.