Calculate the mass of calcium carbonate which decomposes to produce:
50g of calcium oxide and
5g of carbon dioxide
To calculate the mass of calcium carbonate that decomposes to produce 50g of calcium oxide and 5g of carbon dioxide, we need to use the law of conservation of mass.
The law of conservation of mass states that in a chemical reaction, the total mass of the reactants is equal to the total mass of the products.
Let's assume the mass of calcium carbonate that decomposes is "x".
The balanced chemical equation for the decomposition of calcium carbonate is:
CaCO3 → CaO + CO2
From the equation, we know that the molar ratio of CaCO3 to CaO is 1:1, and the molar ratio of CaCO3 to CO2 is 1:1. Therefore, the molar masses of CaCO3, CaO, and CO2 will help us convert between moles and grams.
The molar mass of CaCO3 is
40.08 g/mol (Ca) + 12.01 g/mol (C) + 3(16.00 g/mol) (O) = 100.09 g/mol
So, the moles of CaCO3 decomposed can be calculated as:
moles of CaCO3 = mass of CaCO3 / molar mass of CaCO3
moles of CaCO3 = x / 100.09
According to the chemical equation, the molar ratio of CaCO3 to CaO is 1:1. Therefore, the moles of CaO produced will also be x / 100.09.
The molar mass of CaO is
40.08 g/mol (Ca) + 16.00 g/mol (O) = 56.08 g/mol
So, the mass of CaO produced can be calculated as:
mass of CaO = moles of CaO produced × molar mass of CaO
mass of CaO = (x / 100.09) × 56.08
Similarly, the molar ratio of CaCO3 to CO2 is 1:1 in the reaction. Therefore, the moles of CO2 produced will also be x / 100.09.
The molar mass of CO2 is
12.01 g/mol (C) + 2(16.00 g/mol) (O) = 44.01 g/mol
So, the mass of CO2 produced can be calculated as:
mass of CO2 = moles of CO2 produced × molar mass of CO2
mass of CO2 = (x / 100.09) × 44.01
Now, we can set up an equation based on the given information:
mass of CaO (50g) + mass of CO2 (5g) = mass of CaCO3 (x) × 100.09 / 100 + mass of CaCO3 (x) × 44.01 / 100
Simplifying the equation:
50g + 5g = (100.09 + 44.01) x / 100
55g = 144.1x / 100
5500 = 144.1x
x = 5500 / 144.1
x ≈ 38.17g
Therefore, approximately 38.17g of calcium carbonate decomposes to produce 50g of calcium oxide and 5g of carbon dioxide.