To determine the grams of chromite (FeCr2O4) needed, we will follow these steps:
- Calculate the mass of lead(II) chromate (PbCrO4) required for 1 kilogram of paint.
- Convert the mass of PbCrO4 to moles using its molar mass.
- Use the mole ratio between PbCrO4 and K2CrO4 (from the replacement reaction) to find moles of K2CrO4.
- Use the mole ratio from the balanced chemical equation to find moles of FeCr2O4.
- Convert moles of FeCr2O4 to grams using its molar mass.
First, calculate the molar masses:
Molar mass of PbCrO4:
Pb: 207.2 g/mol
Cr: 52.00 g/mol
O: 16.00 g/mol
MolarmassofPbCrO4=207.2+52.00+(4×16.00)=323.2g/mol
Molar mass of FeCr2O4:
Fe: 55.845 g/mol
Cr: 52.00 g/mol
O: 16.00 g/mol
MolarmassofFeCr2O4=55.845+(2×52.00)+(4×16.00)=223.845g/mol
Step 1: Calculate the mass of PbCrO4 in 1 kg of paint.
A kilogram of paint is 1000 g. The paint is 0.511% PbCrO4 by mass.
MassofPbCrO4=1000gpaint×100gpaint0.511gPbCrO4=5.11gPbCrO4
Step 2: Convert the mass of PbCrO4 to moles.
MolesofPbCrO4=5.11gPbCrO4×323.2gPbCrO41molPbCrO4=0.0158106molPbCrO4
Step 3: Determine moles of K2CrO4.
The problem states that "Lead(II) ion then replaces the K+ ion" to form PbCrO4. This implies a 1:1 mole ratio between K2CrO4 and PbCrO4.
MolesofK2CrO4=MolesofPbCrO4=0.0158106molK2CrO4
Step 4: Determine moles of FeCr2O4 from the balanced equation.
The balanced equation is:
4FeCr2O4(s)+8K2CO3(aq)+7O2(g)⟶2Fe2O3(s)+8K2CrO4(aq)+8CO2(g)
From the equation, 4 moles of FeCr2O4 produce 8 moles of K2CrO4. The mole ratio is 4:8, or 1:2.
MolesofFeCr2O4=0.0158106molK2CrO4×8molK2CrO44molFeCr2O4=0.0079053molFeCr2O4
Step 5: Convert moles of FeCr2O4 to grams.
MassofFeCr2O4=0.0079053molFeCr2O4×1molFeCr2O4223.845gFeCr2O4=1.7695gFeCr2O4
Rounding to three significant figures, the mass of chromite needed is 1.77 g.
The final answer is 1.77g.
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