Calculate the formula (molar) mass of Na2S2O3·5H2O. Part B: With the mass of KAl(SO4)2·12H2O crystal, calculate the number of moles
The Correct Answer and Explanation is:
Let’s calculate the molar mass of Na₂S₂O₃·5H₂O and then solve for the number of moles in part B with the given mass of KAl(SO₄)₂·12H₂O.
Part A: Molar Mass of Na₂S₂O₃·5H₂O
The molar mass of a compound is the sum of the atomic masses of all the atoms in the formula. Here’s how to calculate it:
- Na₂S₂O₃·5H₂O consists of:
- Sodium (Na): The atomic mass of Na is 22.99 g/mol. Since there are 2 Na atoms, the total mass is 2×22.99=45.982 \times 22.99 = 45.982×22.99=45.98 g/mol.
- Sulfur (S): The atomic mass of sulfur is 32.07 g/mol. Since there are 2 sulfur atoms, the total mass is 2×32.07=64.142 \times 32.07 = 64.142×32.07=64.14 g/mol.
- Oxygen (O): The atomic mass of oxygen is 16.00 g/mol. There are 3 oxygen atoms in the thiosulfate group (Na₂S₂O₃) and 5 oxygen atoms in the 5 water molecules. Thus, the total mass from oxygen is (3×16.00)+(5×16.00)=48.00+80.00=128.00(3 \times 16.00) + (5 \times 16.00) = 48.00 + 80.00 = 128.00(3×16.00)+(5×16.00)=48.00+80.00=128.00 g/mol.
- Hydrogen (H): The atomic mass of hydrogen is 1.008 g/mol. There are 10 hydrogen atoms from the 5 water molecules (since each H₂O molecule has 2 hydrogens). Thus, the total mass from hydrogen is 10×1.008=10.0810 \times 1.008 = 10.0810×1.008=10.08 g/mol.
Now, add all the masses together:Molar mass of Na₂S₂O₃\cdotp5H₂O=45.98+64.14+128.00+10.08=248.20 g/mol\text{Molar mass of Na₂S₂O₃·5H₂O} = 45.98 + 64.14 + 128.00 + 10.08 = 248.20 \, \text{g/mol}Molar mass of Na₂S₂O₃\cdotp5H₂O=45.98+64.14+128.00+10.08=248.20g/mol
So, the molar mass of Na₂S₂O₃·5H₂O is 248.20 g/mol.
Part B: Number of Moles of KAl(SO₄)₂·12H₂O
To calculate the number of moles of KAl(SO₄)₂·12H₂O, you need the mass of the crystal and the molar mass of KAl(SO₄)₂·12H₂O.
- Find the molar mass of KAl(SO₄)₂·12H₂O:
- Potassium (K): Atomic mass = 39.10 g/mol. There’s 1 K atom, so total = 39.10 g/mol.
- Aluminum (Al): Atomic mass = 26.98 g/mol. There’s 1 Al atom, so total = 26.98 g/mol.
- Sulfur (S): Atomic mass = 32.07 g/mol. There are 2 sulfate groups (SO₄), so total = 2×32.07=64.142 \times 32.07 = 64.142×32.07=64.14 g/mol.
- Oxygen (O): Atomic mass = 16.00 g/mol. For sulfate (SO₄), there are 8 oxygen atoms, and for 12 water molecules, there are 24 oxygen atoms. Total oxygen = 8×16.00+24×16.00=128.00+384.00=512.008 \times 16.00 + 24 \times 16.00 = 128.00 + 384.00 = 512.008×16.00+24×16.00=128.00+384.00=512.00 g/mol.
- Hydrogen (H): Atomic mass = 1.008 g/mol. For 12 water molecules, there are 24 hydrogens. Total = 24×1.008=24.1924 \times 1.008 = 24.1924×1.008=24.19 g/mol.
Now, adding these together:Molar mass of KAl(SO₄)₂\cdotp12H₂O=39.10+26.98+64.14+512.00+24.19=666.41 g/mol\text{Molar mass of KAl(SO₄)₂·12H₂O} = 39.10 + 26.98 + 64.14 + 512.00 + 24.19 = 666.41 \, \text{g/mol}Molar mass of KAl(SO₄)₂\cdotp12H₂O=39.10+26.98+64.14+512.00+24.19=666.41g/mol
- Number of Moles:
To calculate the number of moles, use the formula:
Number of moles=Mass of sampleMolar mass\text{Number of moles} = \frac{\text{Mass of sample}}{\text{Molar mass}}Number of moles=Molar massMass of sample
So if you have a mass of KAl(SO₄)₂·12H₂O, just plug it into the formula above. For example, if the sample weighs 50 grams, the number of moles would be:Number of moles=50.00 g666.41 g/mol=0.075 mol\text{Number of moles} = \frac{50.00 \, \text{g}}{666.41 \, \text{g/mol}} = 0.075 \, \text{mol}Number of moles=666.41g/mol50.00g=0.075mol
Thus, the number of moles depends on the mass of the crystal you are working with.
