An ore sample with a mass of 670 kg contains 27.7% magnesium carbonate .If all of the magnesium carbonate in this ore sample is decomposed to form carbon dioxide ,describe how to determine what mass of carbon dioxide is evolved during the process.
magnesium carbonate is MgCO3
So, each molecule will produce a molecule of CO2
27% of 670kg is 180.9kg
each mole of MgCO3 has a mass of 84.3g, so we have 2145.9 moles of MgCO3.
That will produce 2145.9 moles of CO2, each with a mass of 44g.
To determine the mass of carbon dioxide (CO2) evolved during the process, you can follow these steps:
Step 1: Calculate the mass of magnesium carbonate (MgCO3) in the ore sample.
Given that the ore sample has a mass of 670 kg and contains 27.7% magnesium carbonate, you can calculate the mass of magnesium carbonate as follows:
Mass of MgCO3 = 27.7% of 670 kg
Step 2: Determine the molar mass of MgCO3.
Molar mass of MgCO3 = atomic mass of Mg + atomic mass of C + (3 * atomic mass of O)
Step 3: Convert the mass of MgCO3 to moles.
To convert the mass of magnesium carbonate, use the equation:
moles = mass / molar mass
Step 4: Use stoichiometry to find the ratio of moles of MgCO3 to moles of CO2.
The balanced chemical equation for the decomposition of magnesium carbonate is:
MgCO3(s) -> MgO(s) + CO2(g)
The stoichiometric ratio between MgCO3 and CO2 is 1:1. This means that for every 1 mole of MgCO3 decomposed, 1 mole of CO2 is produced.
Step 5: Convert moles of MgCO3 to moles of CO2.
Since the stoichiometric ratio is 1:1, the moles of MgCO3 obtained in step 3 will be equal to the moles of CO2 produced.
Step 6: Convert moles of CO2 to mass of CO2.
To convert moles of CO2 to mass, use the equation:
mass = molar mass * moles
By following these steps, you can determine the mass of carbon dioxide evolved during the process of decomposing the magnesium carbonate in the ore sample.
To determine the mass of carbon dioxide evolved during the decomposition of magnesium carbonate, you need to follow these steps:
1. Calculate the mass of magnesium carbonate in the ore sample:
- Multiply the mass of the ore sample (670 kg) by the percentage of magnesium carbonate (27.7%):
Mass of magnesium carbonate = 670 kg × 27.7% = 185.59 kg
2. Determine the molar mass of magnesium carbonate:
- The molecular formula of magnesium carbonate is MgCO₃.
- The atomic mass of magnesium (Mg) is 24.31 g/mol.
- The atomic mass of carbon (C) is 12.01 g/mol.
- The atomic mass of oxygen (O) is 16.00 g/mol.
- The molar mass of magnesium carbonate is the sum of the atomic masses of its constituents:
Molar mass of MgCO₃ = (1 × molar mass of Mg) + (1 × molar mass of C) + (3 × molar mass of O)
Molar mass of MgCO₃ = (1 × 24.31 g/mol) + (1 × 12.01 g/mol) + (3 × 16.00 g/mol)
Molar mass of MgCO₃ = 84.32 g/mol
3. Calculate the moles of magnesium carbonate:
- Divide the mass of magnesium carbonate (185.59 kg) by its molar mass (84.32 g/mol):
Moles of MgCO₃ = Mass of MgCO₃ / Molar mass of MgCO₃
Moles of MgCO₃ = 185.59 kg / 84.32 g/mol
4. Use the stoichiometry of the reaction to determine the moles of carbon dioxide:
- The balanced equation for the decomposition of magnesium carbonate is:
MgCO₃(s) → MgO(s) + CO₂(g)
From the equation, we can see that 1 mole of magnesium carbonate produces 1 mole of carbon dioxide.
Therefore, the moles of carbon dioxide produced will be the same as the moles of magnesium carbonate.
5. Convert the moles of carbon dioxide to mass:
- Multiply the moles of carbon dioxide by the molar mass of carbon dioxide:
Mass of carbon dioxide = Moles of CO₂ × Molar mass of CO₂
Mass of carbon dioxide = Moles of MgCO₃ × Molar mass of CO₂
By following these steps, you can determine the mass of carbon dioxide evolved during the decomposition of magnesium carbonate in the ore sample.