A coal burning plant that burns 4 metric tons of coal containing 2% sulfur (S) requires 1 metric ton of wet limestone (calcium carbonate) to remove 90% of the sulfur. The process prevents most of the sulfur from being emitted as sulfur dioxide to the air by producing calcium sulfate.
a. show the chemical reaction
b. Calculate percentage of limestone converted to calcium sulfate?
a. The chemical reaction can be represented as follows:
4CaCO3 + 2SO2 -> 2CaSO4 + 4CO2 + 2O2
b. To calculate the percentage of limestone converted to calcium sulfate, we need to use stoichiometry. First, determine the molar masses of the compounds involved:
Molar mass of CaCO3 = 40 + 12 + (3 x 16) = 100 g/mol
Molar mass of CaSO4 = 40 + 32 + (4 x 16) = 136 g/mol
Since 4 metric tons of coal are burned, which contains 2% sulfur, we have:
Mass of sulfur = 4 metric tons x 2% = 80 kg
Now, we need to determine the moles of sulfur dioxide (SO2) produced:
Moles of SO2 = (mass of sulfur) / molar mass of S = 80 kg / 32 g/mol = 2500 mol
According to the chemical reaction, every 2 moles of SO2 require 4 moles of CaCO3 to produce 2 moles of CaSO4. Therefore, the moles of CaCO3 required are half of the moles of SO2:
Moles of CaCO3 = (2/4) x moles of SO2 = 0.5 x 2500 mol = 1250 mol
Now, we can calculate the mass of CaCO3 required:
Mass of CaCO3 = Moles of CaCO3 x molar mass of CaCO3
= 1250 mol x 100 g/mol
= 125,000 g = 125 metric tons
Since 1 metric ton of wet limestone is required, we can calculate the percentage conversion:
Percentage of limestone converted to calcium sulfate = (mass of CaSO4 produced / mass of CaCO3 used) x 100%
= ((2 x Moles of CaSO4) / Moles of CaCO3) x (molar mass of CaSO4 / molar mass of CaCO3) x 100%
= ((2 x moles of SO2) / (0.5 x moles of SO2)) x (136 g/mol / 100 g/mol) x 100%
= 2 x 1.36 x 100%
= 272%
Therefore, the percentage of limestone converted to calcium sulfate is 272%.
a. The chemical reaction in this process involves the combustion of coal and the reaction of limestone with sulfur dioxide.
The combustion of coal can be represented as:
C + O2 -> CO2
The reaction of limestone with sulfur dioxide can be represented as:
CaCO3 + 2SO2 + O2 -> CaSO4 + 2CO2
b. To calculate the percentage of limestone converted to calcium sulfate, we need to calculate the amount of sulfur dioxide (SO2) produced and compare it to the initial amount of limestone (CaCO3).
First, calculate the amount of sulfur dioxide produced:
4 metric tons of coal * 2% sulfur = 0.08 metric tons of sulfur
Since 90% of the sulfur is removed, 10% of the sulfur remains:
0.08 metric tons of sulfur * 0.1 = 0.008 metric tons of sulfur dioxide produced
Next, calculate the amount of limestone initially required:
1 metric ton of wet limestone
Finally, calculate the percentage of limestone converted to calcium sulfate:
(0.008 metric tons of sulfur dioxide produced / 1 metric ton of wet limestone) * 100%
= 0.8%
Therefore, approximately 0.8% of the limestone is converted to calcium sulfate.