Many important metals occur as sulfide, arsenide, and antimonide minerals, especially in the Sudbury
mineral complex. The first step in processing these ores involves “roasting” the ore in air to produce the metal
or metal oxide, along with nonmetal oxides that can be serious pollutants if not trapped.
Suppose that you roast 2.00 kg of the mineral marcasite, FeS2. The balanced equation for the reaction is:
4 FeS2 + 11 O2 → 2 Fe2O3 + 8 SO2
(a) How many kg of Fe2O3 can be produced?
(b) How many kg of the pollutant SO2 can be produced?
(c) How many liters of air at 25°C are required for roasting? Assume that air contains 23% O2 by mass,
and that the density of air at 25°C is 1.2 g/L.
Molar masses: FeS2 120.0 g/mol Fe2O3 159.69 g/mol SO2 64.06 g/mol
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To solve this problem, we will use stoichiometry to calculate the quantities of Fe2O3 and SO2 produced, as well as the volume of air needed.
(a) To determine the mass of Fe2O3 produced, we need to calculate the moles of FeS2 and use the stoichiometric ratio between FeS2 and Fe2O3.
Given:
Mass of FeS2 = 2.00 kg
Molar mass of FeS2 = 120.0 g/mol
First, convert the mass of FeS2 to moles:
2.00 kg = 2000 g
Moles of FeS2 = mass / molar mass = 2000 g / 120.0 g/mol = 16.67 mol
From the balanced equation, the stoichiometric ratio is 4:2, meaning that for every 4 moles of FeS2, 2 moles of Fe2O3 are produced.
Moles of Fe2O3 = (16.67 mol FeS2) * (2 mol Fe2O3 / 4 mol FeS2) = 8.33 mol Fe2O3
Now, calculate the mass of Fe2O3 produced:
Mass of Fe2O3 = moles of Fe2O3 * molar mass of Fe2O3 = 8.33 mol * 159.69 g/mol = 1330 g
Therefore, 1.33 kg of Fe2O3 can be produced.
(b) To determine the mass of SO2 produced, we will use the same approach as in part (a).
From the balanced equation, the stoichiometric ratio is 4:8, meaning that for every 4 moles of FeS2, 8 moles of SO2 are produced.
Moles of SO2 = (16.67 mol FeS2) * (8 mol SO2 / 4 mol FeS2) = 33.34 mol SO2
Now, calculate the mass of SO2 produced:
Mass of SO2 = moles of SO2 * molar mass of SO2 = 33.34 mol * 64.06 g/mol = 2136 g
Therefore, 2.14 kg of SO2 can be produced.
(c) To determine the volume of air required, we need to calculate the moles of O2 and use the stoichiometric ratio between O2 and FeS2.
Given:
Mass percent of O2 in air = 23%
Density of air at 25°C = 1.2 g/L
First, let's calculate the mass of O2 required using the mass of FeS2.
Moles of O2 = moles of FeS2 * (11 mol O2 / 4 mol FeS2) = 16.67 mol * (11 mol O2 / 4 mol FeS2) = 45.85 mol O2
Now, calculate the mass of O2 required:
Mass of O2 = moles of O2 * molar mass of O2 = 45.85 mol * 32.00 g/mol = 1467 g
Next, determine the volume of air required using the mass of O2:
Volume of air = (mass of O2 / mass percent of O2) * (1 L / density of air)
Volume of air = (1467 g / 0.23) * (1 L / 1.2 g) = 5274 L
Therefore, approximately 5274 liters of air at 25°C are required for roasting.
To answer these questions, we need to calculate the amount of Fe2O3 and SO2 produced from the given amount of FeS2. We also need to determine the amount of O2 required, considering the mass percent of O2 in air and the density of air at 25°C.
(a) To find the mass of Fe2O3 produced, we can use the stoichiometric ratio between FeS2 and Fe2O3 in the balanced equation. The ratio is 4:2, meaning for every 4 moles of FeS2, we get 2 moles of Fe2O3. Let's follow these steps:
Step 1: Convert mass of FeS2 to moles:
Given mass of FeS2 = 2.00 kg = 2000 g
Molar mass of FeS2 = 120.0 g/mol
Number of moles of FeS2 = (mass of FeS2)/(molar mass of FeS2)
= 2000 g / 120.0 g/mol
Step 2: Convert moles of FeS2 to moles of Fe2O3:
Since the stoichiometric ratio is 4:2, the moles of Fe2O3 will be half the moles of FeS2.
Number of moles of Fe2O3 = 0.5 * moles of FeS2
Step 3: Convert moles of Fe2O3 to mass of Fe2O3:
Molar mass of Fe2O3 = 159.69 g/mol
Mass of Fe2O3 = (number of moles of Fe2O3) * (molar mass of Fe2O3)
Finally, we can calculate the mass of Fe2O3 produced.
(b) To find the mass of SO2 produced, we follow a similar process. The stoichiometric ratio between FeS2 and SO2 is 4:8 in the balanced equation. Thus, for every 4 moles of FeS2, we get 8 moles of SO2.
Step 1: Convert moles of FeS2 to moles of SO2:
Since the stoichiometric ratio is 4:8, the moles of SO2 will be the same as the moles of FeS2.
Step 2: Convert moles of SO2 to mass of SO2:
Molar mass of SO2 = 64.06 g/mol
Mass of SO2 = (number of moles of SO2) * (molar mass of SO2)
Finally, we can calculate the mass of SO2 produced.
(c) To find the volume of air required, we need to consider the mass percent of O2 in air and the density of air at 25°C.
Step 1: Calculate the mass of O2 required:
Mass of O2 = (mass of FeS2) * (mass percent of O2 in air)
= (mass of FeS2) * (23%)
Step 2: Convert mass of O2 to moles of O2:
Molar mass of O2 = 32.00 g/mol
Number of moles of O2 = (mass of O2) / (molar mass of O2)
Step 3: Convert moles of O2 to volume of air at 25°C:
Density of air at 25°C = 1.2 g/L
Volume of air = (number of moles of O2) * (molar volume of gas at 25°C)
= (number of moles of O2) * (22.4 L/mol)
Now, we can calculate the volume of air required.
Let's plug in the given values and calculate the answers.