Answer :
The mass of sulfur in the sample is approximately 1453.86 g.
The correct answer is not provided in the options.
To determine the mass of sulfur in the sample, we need to consider the molecular formula and the molar mass of each element involved. The compound is potassium aluminum sulfate dodecahydrate, K₂SO₄⋅Al₂(SO₄)₃⋅24H₂O.
First, find the molar mass of each component:
- Molar mass of K₂SO₄ = 2(39.10) + 32.07 + 4(16.00) = 174.27 g/mol
- Molar mass of Al₂(SO₄)₃ = 2(26.98) + 3(32.07) + 12(16.00) = 342.16 g/mol
- Molar mass of 24H₂O = 24(2.02) = 48.48 g/mol
Now, find the molar mass of the entire compound:
[tex]\[174.27 + 342.16 + 48.48 = 564.91 \, \text{g/mol}\][/tex]
Given that the sample contains 6.4 kg of oxygen, convert this to grams:
[tex]\[6.4 \, \text{kg} \times 1000 \, \text{g/kg} = 6400 \, \text{g}\][/tex]
Calculate the moles of the compound using the molar mass:
[tex]\[6400 \, \text{g} / 564.91 \, \text{g/mol} \approx 11.32 \, \text{mol}\][/tex]
Now, determine the moles of sulfur in the compound. In K₂SO₄, there are 1 mole of sulfur, and in Al₂(SO₄)₃, there are 3 moles of sulfur:
[tex]\[11.32 \, \text{mol} \times (1 + 3) = 45.28 \, \text{mol}\][/tex]
Finally, calculate the mass of sulfur:
[tex]\[45.28 \, \text{mol} \times 32.07 \, \text{g/mol} \approx 1453.86 \, \text{g} \][/tex]
