To calculate the final concentration of mercury in the solution, we need to first determine the total mass of mercury contributed by both mercury chloride (HgCl₂) and mercury sulfate (HgSO₄).
Step 1: Calculate the mass of mercury from each compound
1. Mercury chloride (HgCl₂)
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Molar mass of HgCl₂:
- Hg: 200.59 g/mol
- Cl: 35.45 g/mol × 2 = 70.90 g/mol
- Total: 200.59 + 70.90 = 271.49 g/mol
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Moles of HgCl₂:
- Moles = mass / molar mass
- Moles of HgCl₂ = 2.45 g / 271.49 g/mol ≈ 0.00903 mol
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Each mole of HgCl₂ contains 1 mole of mercury (Hg).
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Therefore, moles of mercury from HgCl₂ = 0.00903 mol.
2. Mercury sulfate (HgSO₄)
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Molar mass of HgSO₄:
- Hg: 200.59 g/mol
- S: 32.07 g/mol
- O: 16.00 g/mol × 4 = 64.00 g/mol
- Total: 200.59 + 32.07 + 64.00 = 296.66 g/mol
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Moles of HgSO₄:
- Moles = mass / molar mass
- Moles of HgSO₄ = 4.68 g / 296.66 g/mol ≈ 0.01577 mol
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Each mole of HgSO₄ contains 1 mole of mercury (Hg).
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Therefore, moles of mercury from HgSO₄ = 0.01577 mol.
Step 2: Total moles of mercury in the solution
Total moles of mercury = Moles from HgCl₂ + Moles from HgSO₄
- Total moles of mercury = 0.00903 mol + 0.01577 mol = 0.02480 mol.
Step 3: Calculate the molarity of mercury in the final solution
The final volume of the solution is 500 mL, which is 0.500 L.
Molarity (M) = Moles of solute / Volume of solution in liters
- Molarity of mercury = 0.02480 mol / 0.500 L = 0.0496 M.
Step 4: Calculate the percentage concentration (w/v)
To find the % (w/v), we first calculate the total mass of mercury from the compounds:
Path 1: Find the total mass of mercury directly.
- From HgCl₂: 0.00903 mol × 200.59 g/mol = 1.81 g of Hg.
- From HgSO₄: 0.01577 mol × 200.59 g/mol = 3.17 g of Hg.
- Total mass of mercury = 1.81 g + 3.17 g = 5.00 g.
Path 2: % (w/v) = (mass of solute in grams / volume of solution in mL) × 100
- % (w/v) = (5.00 g / 500 mL) × 100 = 1.00 % (w/v).
Final Results
- Molarity of mercury in the final solution = 0.0496 M (to 4 significant figures).
- Concentration of mercury in % (w/v) = 1.00 % (to 3 significant figures).