Calculate the mass of sodium phosphate dodecahydrate you will need to prepare 250 mL of 0.20 M aqueous sodium phosphate solution.
The Correct Answer and Explanation is:
To calculate the mass of sodium phosphate dodecahydrate (Na₃PO₄·12H₂O) needed to prepare a 250 mL (0.250 L) solution with a concentration of 0.20 M, we can follow these steps:
Step 1: Write down the given information
- Desired concentration of sodium phosphate solution: 0.20 M
- Volume of solution to prepare: 250 mL = 0.250 L
- Molar mass of sodium phosphate dodecahydrate (Na₃PO₄·12H₂O)
Step 2: Find the moles of sodium phosphate needed
The formula for calculating moles from concentration and volume is: Moles of Na₃PO₄\cdotp12H₂O=Molarity×Volume in Liters\text{Moles of Na₃PO₄·12H₂O} = \text{Molarity} \times \text{Volume in Liters}Moles of Na₃PO₄\cdotp12H₂O=Molarity×Volume in Liters Moles of Na₃PO₄\cdotp12H₂O=0.20 mol/L×0.250 L\text{Moles of Na₃PO₄·12H₂O} = 0.20 \, \text{mol/L} \times 0.250 \, \text{L}Moles of Na₃PO₄\cdotp12H₂O=0.20mol/L×0.250L Moles of Na₃PO₄\cdotp12H₂O=0.050 mol\text{Moles of Na₃PO₄·12H₂O} = 0.050 \, \text{mol}Moles of Na₃PO₄\cdotp12H₂O=0.050mol
Step 3: Calculate the molar mass of sodium phosphate dodecahydrate
Sodium phosphate dodecahydrate (Na₃PO₄·12H₂O) consists of:
- 3 sodium (Na) atoms = 3 × 22.99 = 68.97 g/mol
- 1 phosphate (PO₄) group = 1 × (30.97 + 4 × 16.00) = 94.97 g/mol
- 12 water (H₂O) molecules = 12 × (2 × 1.008 + 16.00) = 216.24 g/mol
Adding these up: Molar mass of Na₃PO₄\cdotp12H₂O=68.97+94.97+216.24=380.18 g/mol\text{Molar mass of Na₃PO₄·12H₂O} = 68.97 + 94.97 + 216.24 = 380.18 \, \text{g/mol}Molar mass of Na₃PO₄\cdotp12H₂O=68.97+94.97+216.24=380.18g/mol
Step 4: Calculate the mass of sodium phosphate dodecahydrate
To find the mass of sodium phosphate dodecahydrate needed, use the formula: Mass=Moles×Molar mass\text{Mass} = \text{Moles} \times \text{Molar mass}Mass=Moles×Molar mass Mass=0.050 mol×380.18 g/mol\text{Mass} = 0.050 \, \text{mol} \times 380.18 \, \text{g/mol}Mass=0.050mol×380.18g/mol Mass=19.01 g\text{Mass} = 19.01 \, \text{g}Mass=19.01g
Conclusion:
You will need 19.01 grams of sodium phosphate dodecahydrate to prepare 250 mL of a 0.20 M aqueous sodium phosphate solution.
