An iron ore sample contains Fe2O3 together with other substances. Reaction of the ore with CO produces iron metal:
αFe2O3(s)+βCO(g)→γFe(s)+δCO2(g)
A)Balance this equation.
B)Calculate the number of grams of CO that can react with 0.320 kg of Fe2O3.
C)Calculate the number of grams of Fe formed when 0.320 kg of Fe2O3 reacts.
D)Calculate the number of grams of CO2 formed when 0.320 kg of Fe2O3 reacts.
A) Oh, it's time to balance some equations! Let's give it a go:
αFe2O3(s) + βCO(g) → γFe(s) + δCO2(g)
First, let's count the number of atoms on each side:
On the left side: 2 Fe, 3 O, 1 C
On the right side: 1 Fe, 2 O, 1 C
To balance the number of Fe atoms, we can put a 2 in front of Fe on the right side:
αFe2O3(s) + βCO(g) → 2Fe(s) + δCO2(g)
Now, let's balance the number of O atoms. Since there are 3 O on the left side and only 2 O on the right side, we can put a 3/2 in front of Fe2O3 on the left side:
3/2Fe2O3(s) + βCO(g) → 2Fe(s) + δCO2(g)
Finally, let's balance the number of C atoms. Since there is 1 C on each side, we don't need to make any changes there.
The balanced equation is:
3/2Fe2O3(s) + βCO(g) → 2Fe(s) + δCO2(g)
B) Alright, time to calculate! We have 0.320 kg of Fe2O3. Let's convert it to grams:
0.320 kg × 1000 g/kg = 320 g
From the balanced equation, we can see that 1 mole of Fe2O3 reacts with β moles of CO. So, we need to find the moles of Fe2O3 first:
Molar mass of Fe2O3 = 2(55.85 g/mol) + 3(16.00 g/mol) = 159.69 g/mol
Moles of Fe2O3 = 320 g / 159.69 g/mol ≈ 2.001 moles
Since 1 mole of Fe2O3 reacts with β moles of CO, the number of moles of CO is also β moles.
C) Now, let's calculate the number of grams of Fe formed. From the balanced equation, we know that 1 mole of Fe2O3 reacts to produce 2 moles of Fe. So, let's find the moles of Fe:
Moles of Fe = 2 moles × 2.001 moles = 4.002 moles
Molar mass of Fe = 55.85 g/mol
Grams of Fe = 4.002 moles × 55.85 g/mol ≈ 223.46 g
D) Lastly, let's calculate the number of grams of CO2 formed. From the balanced equation, we know that 1 mole of Fe2O3 reacts to produce δ moles of CO2. So, let's find the moles of CO2:
Moles of CO2 = δ moles × 2.001 moles
Since 1 mole of CO2 has a molar mass of 44.01 g/mol:
Grams of CO2 = (δ moles × 2.001 moles) × 44.01 g/mol
Apologies if my explanation got a bit iron(y)! I hope the calculations helped!
A) To balance the equation, you need to ensure that the number of each type of atom is the same on both sides of the equation.
First, let's count up the number of atoms for each element on both sides of the equation:
Left side (Reactants):
Fe: 2*α
O: 3*α
C: β
O: β
Right side (Products):
Fe: γ
C: δ
O: 2*δ
Now, we can set up the equation:
2*αFe2O3 + βCO -> γFe + δCO2
To balance the equation, we need to find values for α, β, γ, and δ that make the number of each type of atom the same on both sides.
Since the reaction produces 1 mole of Fe for every 2 moles of Fe2O3, γ = 1 and α = 2.
Since the reaction produces 1 mole of CO2 for every 1 mole of CO, δ = 1 and β = 1.
Therefore, the balanced equation is:
2Fe2O3 + CO -> 2Fe + CO2
B) To calculate the number of grams of CO that can react with 0.320 kg of Fe2O3, we need to use the balanced equation and convert the mass of Fe2O3 to moles.
First, we need to calculate the molar mass of Fe2O3:
Fe: 55.845 g/mol (from periodic table)
O: 16.00 g/mol (from periodic table)
Fe2O3: 2*Fe + 3*O = 2*55.845 + 3*16.00 = 159.69 g/mol
Now, we can convert the mass of Fe2O3 to moles:
moles of Fe2O3 = mass of Fe2O3 / molar mass of Fe2O3
moles of Fe2O3 = 0.320 kg * (1000 g / 1 kg) / 159.69 g/mol
moles of Fe2O3 = 2.002 moles
Since the balanced equation tells us that the ratio of moles of Fe2O3 to moles of CO is 2:1, the number of moles of CO is half the number of moles of Fe2O3:
moles of CO = 1/2 * moles of Fe2O3
moles of CO = 1/2 * 2.002 moles
moles of CO = 1.001 moles
Now, we can convert the moles of CO to grams using the molar mass of CO:
molar mass of CO: 12.01 g/mol (from periodic table)
mass of CO = moles of CO * molar mass of CO
mass of CO = 1.001 moles * 12.01 g/mol
mass of CO = 12.03 g
Therefore, the number of grams of CO that can react with 0.320 kg of Fe2O3 is approximately 12.03 grams.
C) To calculate the number of grams of Fe formed when 0.320 kg of Fe2O3 reacts, we need to use the balanced equation and convert the mass of Fe2O3 to moles.
From part B, we know that 0.320 kg of Fe2O3 is equal to 2.002 moles.
Since the balanced equation tells us that the ratio of moles of Fe2O3 to moles of Fe is 2:2, the number of moles of Fe formed is the same as the number of moles of Fe2O3.
Now, we can convert the moles of Fe to grams using the molar mass of Fe:
molar mass of Fe: 55.845 g/mol (from periodic table)
mass of Fe = moles of Fe * molar mass of Fe
mass of Fe = 2.002 moles * 55.845 g/mol
mass of Fe = 111.797 g
Therefore, the number of grams of Fe formed when 0.320 kg of Fe2O3 reacts is approximately 111.797 grams.
D) Similarly to part C, we can use the balanced equation to calculate the number of grams of CO2 formed when 0.320 kg of Fe2O3 reacts.
From part B, we know that 0.320 kg of Fe2O3 is equal to 2.002 moles.
Since the balanced equation tells us that the ratio of moles of Fe2O3 to moles of CO2 is 2:1, the number of moles of CO2 is half the number of moles of Fe2O3.
Now, we can convert the moles of CO2 to grams using the molar mass of CO2:
molar mass of CO2: 44.01 g/mol (from periodic table)
mass of CO2 = moles of CO2 * molar mass of CO2
mass of CO2 = 1/2 * moles of Fe2O3 * 44.01 g/mol
mass of CO2 = 1/2 * 2.002 moles * 44.01 g/mol
mass of CO2 = 44.09 g
Therefore, the number of grams of CO2 formed when 0.320 kg of Fe2O3 reacts is approximately 44.09 grams.
αFe2O3(s)+βCO(g)→γFe(s)+δCO2(g)
A)Balance this equation.
Fe2O3(s) + 3CO(g)→ 2Fe(s) + 3CO2(g)
B)Calculate the number of grams of CO that can react with 0.320 kg of Fe2O3.
mols Fe2O3 = g/molar mass = 320 g/approx 160 = approx 2
How many mols CO exactly reacts?
That's 2 mol Fe2O3 x (3 mols CO/1 mol Fe2O3) = 6 mols CO
Then convert to grams; ie. g = mols x molar mass = ? g and convert to kg. (NOTE) Note that ANY number of grams you want of CO will react with Fe2O3. I'm sure the author of the problem meant it to be "exactly" react.
C)Calculate the number of grams of Fe formed when 0.320 kg of Fe2O3 reacts.
This is just another stoichiometry problem. Work it the same way I did for grams CO.
D)Calculate the number of grams of CO2 formed when 0.320 kg of Fe2O3 reacts.
Another stoichiometry problem Works the same was as above.