Bornite (Cu3FeS3) is a copper ore used in the production of copper. When heated, the following reaction occurs.
2 Cu3FeS3(s) + 7 O2(g) 6 Cu(s) + 2 FeO(s) + 6 SO2(g)
If 3.88 metric tons of bornite is reacted with excess O2 and the process has an 75.6% yield of copper, what mass of copper,in metric tons, is produced?
help me with the answer ?
figure out how many moles of bornite one has in 3.88 metric tons. Then you get 3 times as much Cu (theoritical yield), so multiply that by .756
That is the standard way.
An easier way is to figure how much copper is in the bornite, and multiply that by the yield (.756)
fraction copper= 3atomicmassCu/molmassBornite.
To find the mass of copper produced, we need to use the stoichiometry of the reaction and the information given. Here's how to do it step-by-step:
Step 1: Determine the molar mass of Cu.
The molar mass of Cu is 63.55 g/mol.
Step 2: Calculate the moles of Cu3FeS3.
To calculate the moles of Cu3FeS3, divide the given mass of bornite by its molar mass.
Given mass of bornite = 3.88 metric tons = 3.88 x 10^6 g
Molar mass of Cu3FeS3 = (3 x atomic mass of Cu) + atomic mass of Fe + (3 x atomic mass of S)
= (3 x 63.55 g/mol) + 55.85 g/mol + (3 x 32.06 g/mol)
= 342.48 g/mol
Moles of Cu3FeS3 = mass of bornite / molar mass of Cu3FeS3
= 3.88 x 10^6 g / 342.48 g/mol
≈ 11320.99 mol
Step 3: Determine the molar ratio between Cu3FeS3 and Cu.
From the balanced equation, the molar ratio between Cu3FeS3 and Cu is 6:2 or 3:1.
This means that for every three moles of Cu3FeS3, we get one mole of Cu.
Step 4: Calculate the moles of Cu produced.
To find the moles of Cu produced, multiply the moles of Cu3FeS3 by the molar ratio.
Moles of Cu = moles of Cu3FeS3 x (1 mol Cu / 3 mol Cu3FeS3)
= 11320.99 mol x (1 mol Cu / 3 mol Cu3FeS3)
= 3773.66 mol
Step 5: Convert moles of Cu to mass in metric tons.
To convert moles of Cu to mass in metric tons, multiply the moles of Cu by the molar mass of Cu and divide by 1000000 (to convert from grams to metric tons).
Mass of Cu = (moles of Cu x molar mass of Cu) / 1000000
= (3773.66 mol x 63.55 g/mol) / 1000000
≈ 0.2399 metric tons
Therefore, approximately 0.2399 metric tons (or 239.9 kg) of copper is produced.
To find the mass of copper produced, we need to use the stoichiometry of the reaction and the given data.
Step 1: Write the balanced equation:
2 Cu3FeS3(s) + 7 O2(g) -> 6 Cu(s) + 2 FeO(s) + 6 SO2(g)
Step 2: Determine the molar mass of Cu:
The molar mass of Cu is 63.55 g/mol.
Step 3: Convert the mass of bornite to moles:
Given that 1 metric ton is equal to 1000 kg, and the molar mass of Cu3FeS3 is:
Cu: 63.55 g/mol
Fe: 55.84 g/mol
S: 32.06 g/mol
Adding them up, the molar mass of Cu3FeS3 = 63.55*3 + 55.84 + 32.06*3 = 342.51 g/mol
To convert the mass of bornite to moles, use the formula:
moles = mass / molar mass
moles of Cu3FeS3 = 3.88 metric tons * (1000 kg/ton) * (1 g/kg) * (1 mol/342.51 g) = X mol
Step 4: Use the stoichiometry of the reaction to find the moles of Cu:
From the balanced equation, we know that for every 2 moles of Cu3FeS3, we get 6 moles of Cu.
moles of Cu = X mol Cu3FeS3 * (6 mol Cu / 2 mol Cu3FeS3) = X mol
Step 5: Convert the moles of Cu to mass in metric tons:
mass = moles * molar mass
mass of Cu = X mol * 63.55 g/mol * (1 kg / 1000 g) * (1 ton / 1000 kg) = Y metric tons
However, we also need to account for the 75.6% yield of copper. This means that only 75.6% of the theoretical amount obtained in step 5 is actually produced.
mass of copper produced = 75.6% * Y metric tons
Therefore, to find the mass of copper produced in metric tons, you would substitute the value of X in step 4 into the equation in step 5, then multiply it by 75.6%.