The rock in a lead ore deposit contains 84% PbS by mass. How many kilograms of the rock must be processed to obtain 1.0 kg of Pb?
I have no idea how to start or how I'm converting. Please help...
The following equation is not a possible reaction; I wrote it only to show there is 1 mol Pb in 1 mol PbS.
PbS ==> Pb + S
We want 1000 g Pb. Convert to mols Pb.
mols Pb = grams/atomic mass = approx 4.8
Since the ratio of Pb to PbS is 1:1, then 4.8 = mols PbS we must start with. How many grams is that? mols = g/molar mass; therefore, g = mols x molar mass = approx 4.8 x about 239 = approx 1150 g PbS but since the ore contains only 84% PbS we must start with approx 1150/0.84 = ?g ore.
You must go through each step and calculate more accurately than I've estimated.
To solve this problem, we can start by determining the mass of lead (Pb) in the rock containing 1.0 kg of PbS.
Step 1: Determine the percentage of lead in the rock
The rock contains 84% PbS by mass. This means that in 100 grams of rock, 84 grams would be PbS, and the remaining 16 grams would be other compounds. Since we want to find the mass of lead (Pb) in the rock, we need to calculate the mass of lead in 100 grams of rock.
Mass of Pb in 100 g of rock = 84% of 100 g = 84 g
Step 2: Determine the mass of lead (Pb) in 1.0 kg of rock
To determine the mass of lead (Pb) in 1.0 kg of rock, we can use a proportion:
Mass of Pb in 100 g of rock / Mass of rock = Mass of Pb in 1.0 kg of rock / 1.0 kg
Using the information from Step 1:
84 g / 100 g = Mass of Pb in 1.0 kg of rock / 1.0 kg
Simplifying the equation:
0.84 = Mass of Pb in 1.0 kg of rock / 1.0 kg
Rearranging the equation to solve for Mass of Pb in 1.0 kg of rock:
Mass of Pb in 1.0 kg of rock = 0.84 kg
So, to obtain 1.0 kg of Pb, we would need to process 0.84 kg of the rock.
To solve this problem, we need to calculate the mass of lead (Pb) in the rock using the given percentage of PbS (lead sulfide) and then determine how much rock (in kilograms) needs to be processed to obtain 1.0 kg of lead.
First, let's assume we have x kilograms of the rock. The mass of lead (Pb) in the rock can be calculated by multiplying the mass of the rock (x kg) by the percentage of lead sulfide (PbS) in the rock (84%):
Mass of Pb = x kg × 84%
We can convert the percentage to a decimal by dividing it by 100:
Mass of Pb = x kg × (84/100)
Simplifying the expression:
Mass of Pb = 0.84x kg
Now, we know that the mass of the rock containing Pb is equal to the mass of Pb. Therefore, 0.84x kg of rock must be processed to obtain 1.0 kg of Pb.
Setting up the equation:
0.84x kg = 1.0 kg
To solve for x (the mass of the rock), divide both sides of the equation by 0.84:
x kg = (1.0 kg) / (0.84)
Evaluating the expression:
x kg ≈ 1.1905 kg
Therefore, approximately 1.1905 kg of the rock must be processed to obtain 1.0 kg of Pb.