Answer
Zinc sulfate is the most economical source of zinc, and it is about 28% cheaper than zinc acetate dihydrate.
Work Step by Step
Step 1: Calculate the molar masses of each compound.
The molar mass of zinc sulfate (ZnSO4) is:
Zn: 1 x 65.38 g/mol = 65.38 g/mol
S: 1 x 32.06 g/mol = 32.06 g/mol
O: 4 x 16.00 g/mol = 64.00 g/mol
Total: 161.44 g/mol
The molar mass of zinc acetate dihydrate (Zn(CH3COO)2 # 2H2O) is:
Zn: 1 x 65.38 g/mol = 65.38 g/mol
C: 4 x 12.01 g/mol = 48.04 g/mol
H: 8 x 1.01 g/mol = 8.08 g/mol
O: 8 x 16.00 g/mol = 128.00 g/mol
Total: 249.50 g/mol
Step 2: Calculate the cost per mole of each compound.
Since both compounds can be purchased at the same price per kilogram, the cost per mole of each compound is proportional to its molar mass.
Assuming that the cost per kilogram is $x$, the cost per mole of zinc sulfate is:
cost per mole of ZnSO4 = x / (161.44 g/mol)
Similarly, the cost per mole of zinc acetate dihydrate is:
cost per mole of Zn(CH3COO)2 2H2O = x / (249.50 g/mol)
Step 3: Compare the cost per mole of each compound.
cost per mole of ZnSO4 = cost per mole of Zn(CH3COO)2 2H2O
x / (161.44 g/mol) = x / (249.50 g/mol)
Solving for x, we get:
x = 0.1565/g
Step 4: Calculate the cost per gram of zinc in each compound.
The percentage of zinc in zinc sulfate (ZnSO4) is 28.43%. Therefore, the cost per gram of zinc in zinc sulfate is:
cost per gram of Zn in ZnSO4 = (0.1565/g) x (1 mol ZnSO4 / 161.44 g) x (1 mol Zn / 1 mol ZnSO4) x (65.38 g/mol) x (100/28.43%) = $0.0403/g$
The percentage of zinc in zinc acetate dihydrate (Zn(CH3COO)2
2H2O) is 21.02%. Therefore, the cost per gram of zinc in zinc acetate dihydrate is:
cost per gram of Zn in Zn(CH3COO)2 2H2O = (0.1565/g) x (1 mol Zn(CH3COO)2 2H2O / 249.50 g) x (1 mol Zn / 1 mol Zn(CH3COO)2 2H2O) x (65.38 g/mol) x (100/21.02%) = $0.0560/g$
Step 5: Compare the cost per gram of zinc in each compound.
The cost per gram of zinc in zinc sulfate is $0.0403/g$, while the cost per gram of zinc in zinc acetate dihydrate is $0.0560/g$. Therefore, zinc sulfate is the most economical
