Problem 105 - Chemistry: The Central Science

Question

A particular coal contains \(2.5 \%\) sulfur by mass. When this coal is burned at a power plant, the sulfur is converted 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?

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction between sulfur dioxide (SO2) and calcium oxide (CaO) to form calcium sulfite (CaSO3) is given by: \(SO2 + CaO \rightarrow CaSO3\). The power plant needs 87.5 tons of calcium oxide daily to eliminate sulfur dioxide emissions, and 187.5 tons of calcium sulfite are produced daily in the power plant.

Step 1: Write the balanced chemical equation for the reaction

First, let's write the balanced chemical equation for the reaction between sulfur dioxide (SO2) and calcium oxide (CaO) to form calcium sulfite (CaSO3). \(SO2 + CaO \rightarrow CaSO3\) This equation is already balanced: one mole of sulfur dioxide reacts with one mole of calcium oxide to produce one mole of calcium sulfite.

Step 2: Calculate the mass of sulfur in the coal

We are given that the coal contains \(2.5 \%\) sulfur by mass. If the power plant uses 2000 tons of coal per day, we can calculate the mass of sulfur in the coal by taking \(2.5 \%\) of 2000 tons. Mass of sulfur = (Percentage of sulfur × Total mass of coal) / 100 Mass of sulfur = (2.5 × 2000) / 100 = 50 tons So, 50 tons of sulfur is present in the 2000 tons of coal.

Step 3: Convert the mass of sulfur to mass of sulfur dioxide

When the coal is burned, the sulfur is converted into sulfur dioxide (SO2). To determine the amount of sulfur dioxide produced, we will convert the mass of sulfur into the mass of SO2 using their molar masses. 1 mol S = 32 g (Molar mass of sulfur) 1 mol SO2 = 64 g (Molar mass of sulfur dioxide) Using the molar ratios, we can calculate the mass of sulfur dioxide produced. Mass of SO2 = (Mass of S × Molar mass of SO2) / Molar mass of S Mass of SO2 = (50 tons × 64 g/mol) / 32 g/mol = 100 tons So, 100 tons of sulfur dioxide is produced daily when the coal is burned.

Step 4: Calculate the mass of calcium oxide required

Since one mole of sulfur dioxide reacts with one mole of calcium oxide to form one mole of calcium sulfite, we can directly calculate the mass of calcium oxide needed by the power plant. 1 mol SO2 = 64 g (Molar mass of sulfur dioxide) 1 mol CaO = 56 g (Molar mass of calcium oxide) Using the molar ratios, we can calculate the mass of calcium oxide required. Mass of CaO = (Mass of SO2 × Molar mass of CaO) / Molar mass of SO2 Mass of CaO = (100 tons × 56 g/mol) / 64 g/mol = 87.5 tons So, the power plant needs 87.5 tons of calcium oxide daily to eliminate sulfur dioxide emissions.

Step 5: Calculate the mass of calcium sulfite produced

Since one mole of sulfur dioxide reacts with one mole of calcium oxide to form one mole of calcium sulfite, we can directly calculate the mass of calcium sulfite produced daily. 1 mol SO2 = 64 g (Molar mass of sulfur dioxide) 1 mol CaSO3 = 120 g (Molar mass of calcium sulfite) Using the molar ratios, we can calculate the mass of calcium sulfite produced. Mass of CaSO3 = (Mass of SO2 × Molar mass of CaSO3) / Molar mass of SO2 Mass of CaSO3 = (100 tons × 120 g/mol) / 64 g/mol = 187.5 tons So, 187.5 tons of calcium sulfite are produced daily in the power plant.