Calcium oxide, or lime, is produced by the thermal decomposition of limestone in the reaction CaCO3(s) arrow CaO(s) + CO2(g). What mass of lime can be produced from 2001.2 kg of limestone?
To find the mass of lime produced from a given mass of limestone, we need to use stoichiometry and the concept of molar mass. Here's how you can solve this problem step by step:
Step 1: Write and balance the chemical equation:
CaCO3(s) → CaO(s) + CO2(g)
Step 2: Find the molar mass:
The molar masses of CaCO3, CaO, and CO2 are:
CaCO3: 40.08 g/mol (Ca) + 12.01 g/mol (C) + 3(16.00 g/mol) (O) = 100.09 g/mol
CaO: 40.08 g/mol (Ca) + 16.00 g/mol (O) = 56.08 g/mol
Step 3: Convert the given mass of limestone to moles:
Given mass of limestone = 2001.2 kg
Convert kg to g: 2001.2 kg × 1000 g/kg = 2,001,200 g
Now, use the molar mass of CaCO3 to convert grams to moles:
Moles of CaCO3 = 2,001,200 g ÷ 100.09 g/mol = 20,000.79 mol
Step 4: Use stoichiometry to find the moles of CaO produced:
From the balanced equation, we can see that 1 mol of CaCO3 produces 1 mol of CaO.
Therefore, the moles of CaO produced will be equal to the moles of CaCO3.
Moles of CaO produced = 20,000.79 mol
Step 5: Convert moles of CaO to grams:
Mass of CaO = Moles of CaO × Molar mass of CaO
Mass of CaO = 20,000.79 mol × 56.08 g/mol
Mass of CaO = 1,120,485.25 g
So, the mass of lime (CaO) that can be produced from 2001.2 kg of limestone is approximately 1,120,485.25 grams or 1120.49 kg.