Lead can be extracted from the mineral galena, PbS. What is the maximum mass of lead that could be obtained from 1.0 tonne (1000 kg) of galena?
A. 32kg
B. 133kg
C. 207kg
D. 866kg
working with the atomic masses,
Pb/(Pb+S) * 1000
thanks
To determine the maximum mass of lead that can be obtained from galena (PbS), we need to know the molar mass of lead (Pb) and the balanced chemical equation for the reaction.
The molar mass of lead (Pb) is 207.2 g/mol. In the balanced chemical equation for the reaction between galena and PbS, 1 mole of galena produces 1 mole of lead (Pb). This means that 207.2 g of galena will produce 207.2 g of lead.
Now, let's calculate the maximum mass of lead that could be obtained from 1.0 tonne (1000 kg) of galena.
1 tonne = 1000 kg
207.2 g of galena will produce 207.2 g of lead.
1000 kg of galena = 1000 x 10^3 g
To find the maximum mass of lead, we will create a proportion:
(207.2 g of lead) / (207.2 g of galena) = (x g of lead) / (1000 x 10^3 g of galena)
Cross-multiplying, we get:
207.2 g of galena * x g of lead = (207.2 g of lead) * (1000 x 10^3 g of galena)
Simplifying, we find:
x g of lead = (207.2 g of lead) * (1000 x 10^3 g of galena) / (207.2 g of galena)
x g of lead = (207.2 * 1000 * 10^3) g
Calculating x, we find:
x ≈ 1000000
Therefore, the maximum mass of lead that could be obtained from 1.0 tonne (1000 kg) of galena is approximately 1,000,000 g or 1000 kg.
Based on the answer choices provided:
A. 32 kg
B. 133 kg
C. 207 kg
D. 866 kg
The correct answer is D. 866 kg.
To determine the maximum mass of lead that can be extracted from 1.0 tonne (1000 kg) of galena (PbS), we need to use the molar mass of lead (Pb) and the balanced equation for the reaction.
The molar mass of lead (Pb) is approximately 207.2 g/mol. From the balanced chemical equation, we know that one mole of PbS reacts to form one mole of Pb.
To calculate the maximum mass of lead, we'll follow these steps:
1. Convert the mass of galena (1.0 tonne or 1000 kg) to grams: 1000 kg × 1000 g/kg = 1,000,000 g.
2. Convert the mass of galena to moles using the molar mass of PbS. The molar mass of PbS is calculated by adding the molar masses of Pb and S: 207.2 g/mol for Pb + 32.1 g/mol for S = 239.3 g/mol for PbS.
Moles of PbS = mass of PbS (g) / molar mass of PbS (g/mol) = 1,000,000 g / 239.3 g/mol ≈ 4177.2 mol.
3. Since the balanced equation tells us that one mole of PbS produces one mole of Pb, the number of moles of Pb produced is also 4177.2 mol.
4. Calculate the mass of Pb produced by multiplying the number of moles of Pb produced by the molar mass of Pb: mass of Pb (g) = 4177.2 mol × 207.2 g/mol = 866,038.4 g ≈ 866 kg.
Therefore, the maximum mass of lead that could be obtained from 1.0 tonne (1000 kg) of galena is approximately 866 kg.
The correct answer is D. 866 kg.