what is the molarity of 10.5 kg of Na2SO4·10H2O in 18.60 L of solution
The correct answer and explanation is :
To calculate the molarity of a solution, we need to know the amount of solute in moles and the volume of the solution in liters. In this case, the solute is sodium sulfate decahydrate (Na₂SO₄·10H₂O), and we are given its mass (10.5 kg) and the volume of the solution (18.60 L).
Step 1: Find the molar mass of Na₂SO₄·10H₂O
The formula Na₂SO₄·10H₂O represents sodium sulfate (Na₂SO₄) combined with 10 water molecules. To find its molar mass, we sum the atomic masses of all elements in the formula:
- Sodium (Na): 22.99 g/mol (there are 2 Na atoms)
- Sulfur (S): 32.07 g/mol (1 S atom)
- Oxygen (O): 16.00 g/mol (4 O atoms in Na₂SO₄ and 10 O atoms in H₂O)
- Hydrogen (H): 1.008 g/mol (20 H atoms in 10H₂O)
Now calculate the molar mass:
[
\text{Molar mass of Na₂SO₄·10H₂O} = (2 \times 22.99) + 32.07 + (4 \times 16.00) + (20 \times 1.008)
]
[
= 45.98 + 32.07 + 64.00 + 20.16 = 162.21 \, \text{g/mol}
]
Step 2: Convert the mass of Na₂SO₄·10H₂O to moles
We are given 10.5 kg of Na₂SO₄·10H₂O. First, convert the mass to grams:
[
10.5 \, \text{kg} = 10,500 \, \text{g}
]
Now, use the molar mass to find the number of moles:
[
\text{Moles of Na₂SO₄·10H₂O} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{10,500 \, \text{g}}{162.21 \, \text{g/mol}} = 64.74 \, \text{mol}
]
Step 3: Calculate the molarity
Molarity (M) is calculated as the number of moles of solute per liter of solution:
[
\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} = \frac{64.74 \, \text{mol}}{18.60 \, \text{L}} = 3.48 \, \text{M}
]
Conclusion:
The molarity of the Na₂SO₄·10H₂O solution is 3.48 M.