Calculate the molar mass of Fe2(SO4)3.

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Calculate the molar mass of Fe2(SO4)3. Then Calculate the mass of iron(III) sulfate of 4.05×10^23 formula units. Work must be shown.​

The Correct Answer and Explanation is:

Step 1: Calculate the Molar Mass of Fe₂(SO₄)₃

To calculate the molar mass of iron(III) sulfate (Fe₂(SO₄)₃), we need to sum the atomic masses of each element in the compound, based on the number of atoms in one formula unit.

Atomic masses:

  • Iron (Fe) = 55.85 g/mol
  • Sulfur (S) = 32.07 g/mol
  • Oxygen (O) = 16.00 g/mol

Formula:
Fe₂(SO₄)₃ consists of:

  • 2 atoms of iron (Fe)
  • 3 sulfate ions (SO₄), each of which contains 1 sulfur (S) and 4 oxygens (O)

Now calculate the molar mass:

  • Mass of 2 Fe atoms:
    ( 2 \times 55.85 \, \text{g/mol} = 111.70 \, \text{g/mol} )
  • Mass of 3 sulfate ions (SO₄):
    ( 3 \times (32.07 \, \text{g/mol} \, (\text{S}) + 4 \times 16.00 \, \text{g/mol} \, (\text{O})) )
    ( = 3 \times (32.07 + 64.00) \, \text{g/mol} )
    ( = 3 \times 96.07 \, \text{g/mol} = 288.21 \, \text{g/mol} )

Total Molar Mass of Fe₂(SO₄)₃:
( 111.70 \, \text{g/mol} + 288.21 \, \text{g/mol} = 399.91 \, \text{g/mol} )

Step 2: Calculate the Mass of 4.05 × 10²³ Formula Units

To calculate the mass of 4.05 × 10²³ formula units of Fe₂(SO₄)₃, we first need to use Avogadro’s number, which is ( 6.022 \times 10^{23} ) formula units per mole.

Step 2a: Convert formula units to moles:

[
\text{Moles of Fe₂(SO₄)₃} = \frac{\text{Formula Units}}{\text{Avogadro’s Number}} = \frac{4.05 \times 10^{23}}{6.022 \times 10^{23}} = 0.673 \, \text{moles}
]

Step 2b: Calculate the mass:

Now use the molar mass to convert moles to grams:

[
\text{Mass of Fe₂(SO₄)₃} = \text{Moles} \times \text{Molar Mass} = 0.673 \, \text{moles} \times 399.91 \, \text{g/mol} = 268.65 \, \text{g}
]

Final Answer:

The mass of 4.05 × 10²³ formula units of iron(III) sulfate (Fe₂(SO₄)₃) is 268.65 grams.

Explanation:

  1. Molar Mass Calculation: First, we determine the molar mass of iron(III) sulfate by summing the atomic masses of all the elements in its formula (Fe, S, and O) based on their proportions in Fe₂(SO₄)₃. This gives us the total molar mass, which tells us how much one mole of the substance weighs.
  2. Mass Calculation: To find the mass of a given number of formula units, we first convert the number of units into moles using Avogadro’s number. Once we know how many moles we have, we can use the molar mass to determine the mass corresponding to that number of moles.

This process applies stoichiometric principles to relate atomic and molecular quantities to macroscopic amounts, helping us understand how much of a substance corresponds to a given number of formula units.

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